## In journals

1. X. Caicedo, M. Campercholi, K. A. Kearnes, P. Sánchez Terraf, Á. Szendrei, and D. Vaggione, “Every minimal dual discriminator variety is minimal as a quasivariety,” Algebra universalis 82 (2) p. 36 (2021). Let $\dagger$ denote the following property of a variety $\mathcal{V}$: \emph{Every subquasivariety of $\mathcal{V}$ is a variety}. In this paper, we prove that every idempotent dual discriminator variety has property $\dagger$ . Property $\dagger$ need not hold for nonidempotent dual discriminator varieties, but $\dagger$ does hold for \emph{minimal} nonidempotent dual discriminator varieties. Combining the results for the idempotent and nonidempotent cases, we obtain that every minimal dual discriminator variety is minimal as a quasivariety

@ARTICLE{minimal-dual-quasi,
author = {Caicedo, Xavier and Campercholi, Miguel and Kearnes, Keith A. and S{\'a}nchez Terraf, Pedro and Szendrei, {\'A}gnes and Vaggione, Diego},
year = 2021,
title = "Every minimal dual discriminator variety is minimal as a quasivariety",
journal = "Algebra universalis",
month="Apr",
day=29,
volume=82,
number=2,
pages=36,
abstract={Let $\dagger$ denote the following property of a variety $\mathcal{V}$: \emph{Every subquasivariety of $\mathcal{V}$ is a variety}. In this paper, we prove that every idempotent dual discriminator variety has property $\dagger$ . Property $\dagger$ need not hold for nonidempotent dual discriminator varieties, but $\dagger$ does hold for \emph{minimal} nonidempotent dual discriminator varieties. Combining the results for the idempotent and nonidempotent cases, we obtain that every minimal dual discriminator variety is minimal as a quasivariety},
issn={1420-8911},
doi={10.1007/s00012-021-00715-8},
url={https://doi.org/10.1007/s00012-021-00715-8}
}

2. J. Pachl and P. Sánchez Terraf, “Semipullbacks of labelled Markov processes,” Logical Methods in Computer Science 17 (2) (2021).
[ Abstract | BibTeX ]

A \emph{labelled Markov process (LMP)} consists of a measurable space $S$ together with an indexed family of Markov kernels from $S$ to itself. This structure has been used to model probabilistic computations in Computer Science, and one of the main problems in the area is to define and decide whether two LMP $S$ and $S’$ “behave the same”. There are two natural categorical definitions of sameness of behavior: $S$ and $S’$ are \emph{bisimilar} if there exist an LMP $T$ and measure preserving maps forming a diagram of the shape $S\leftarrow T \rightarrow{S’}$; and they are \emph{behaviorally equivalent} if there exist some $U$ and maps forming a dual diagram $S\rightarrow U \leftarrow{S’}$. These two notions differ for general measurable spaces but Edalat proved that they coincide for analytic Borel spaces, showing that from every diagram $S\rightarrow U \leftarrow{S’}$ one can obtain a bisimilarity diagram as above. Moreover, the resulting square of measure preserving maps is commutative (a \emph{semipullback}). In this paper, we extend Edalat’s result to measurable spaces $S$ isomorphic to a universally measurable subset of a Polish space with the trace of the Borel $\sigma$-algebra, using a version of Strassen’s theorem on common extensions of finitely additive measures.

@ARTICLE{2017arXiv170602801P,
author = {Pachl, Jan and S{\'a}nchez Terraf, Pedro},
title = "Semipullbacks of labelled {M}arkov processes",
JOURNAL = {Logical Methods in Computer Science},
VOLUME = 17,
number = 2,
YEAR = 2021,
MONTH = Apr,
archivePrefix = "arXiv",
eprint = {1706.02801},
primaryClass = "math.PR",
keywords = {Mathematics - Probability, Computer Science - Logic in Computer Science, 28A35, 28A60, 68Q85, F.4.1, F.1.2},
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
abstract = {A \emph{labelled Markov process (LMP)} consists of a measurable
space $S$ together with an indexed family of Markov kernels from $S$
to itself. This structure has been used to model probabilistic
computations in Computer Science, and one of the main problems in
the area is to define and decide whether two LMP $S$ and $S'$ behave
the same''. There are two natural categorical definitions of
sameness of behavior: $S$ and $S'$ are \emph{bisimilar}
if there exist an LMP $T$ and measure preserving maps
forming a diagram of the shape
$S\leftarrow T \rightarrow{S'}$; and they
are \emph{behaviorally equivalent}
if there exist some $U$ and maps forming a dual diagram
$S\rightarrow U \leftarrow{S'}$.
These two notions differ for general measurable spaces but Edalat
proved that they coincide for analytic Borel spaces, showing that
from every
diagram $S\rightarrow U \leftarrow{S'}$ one can obtain a
bisimilarity diagram as above. Moreover, the resulting square of
measure preserving maps is commutative (a \emph{semipullback}).
In this paper, we extend Edalat's result to measurable spaces $S$
isomorphic to a universally measurable subset of
a Polish space with the trace of the Borel $\sigma$-algebra, using a
version of Strassen's theorem on
common extensions of finitely additive measures.}
}

3. M. S. Moroni and P. Sánchez Terraf, “The Zhou Ordinal of Labelled Markov Processes over Separable Spaces,” arXiv e-prints 2005.03630 (2020). Accepted for publication at the Review of Symbolic Logic.
[ Abstract | BibTeX ]

There exist two notions of equivalence of behavior between states of a Labelled Markov Process (LMP): state bisimilarity and event bisimilarity. The first one can be considered as an appropriate generalization to continuous spaces of Larsen and Skou’s probabilistic bisimilarity, while the second one is characterized by a natural logic. C. Zhou expressed state bisimilarity as the greatest fixed point of an operator $\mathcal{O}$, and thus introduced an ordinal measure of the discrepancy between it and event bisimilarity. We call this ordinal the “Zhou ordinal” of $\mathbb{S}$, $\mathfrak{Z}(\mathbb{S})$. When $\mathfrak{Z}(\mathbb{S})=0$, $\mathbb{S}$ satisfies the Hennessy-Milner property. The second author proved the existence of an LMP $\mathbb{S}$ with $\mathfrak{Z}(\mathbb{S}) \geq 1$ and Zhou showed that there are LMPs having an infinite Zhou ordinal. In this paper we show that there are LMPs $\mathbb{S}$ over separable metrizable spaces having arbitrary large countable $\mathfrak{Z}(\mathbb{S})$ and that it is consistent with the axioms of $\mathit{ZFC}$ that there is such a process with an uncountable Zhou ordinal.

@article{moroni2020zhou,
title = "The {Z}hou Ordinal of Labelled {M}arkov Processes over Separable Spaces",
author = {Moroni, Martín Santiago and S\'anchez Terraf, Pedro},
journal = {arXiv e-prints},
month = May,
year = 2020,
eprint = {2005.03630},
volume = {2005.03630},
archivePrefix = {arXiv},
primaryClass = {cs.LO},
note = "Accepted for publication at the Review of Symbolic Logic",
abstract = {There exist two notions of equivalence of behavior between states of a
Labelled Markov Process (LMP): state bisimilarity and event bisimilarity. The
first one can be considered as an appropriate generalization to continuous
spaces of Larsen and Skou's probabilistic bisimilarity, while the second one is
characterized by a natural logic. C. Zhou expressed state bisimilarity as the
greatest fixed point of an operator $\mathcal{O}$, and thus introduced an
ordinal measure of the discrepancy between it and event bisimilarity. We call
this ordinal the "Zhou ordinal" of $\mathbb{S}$, $\mathfrak{Z}(\mathbb{S})$.
When $\mathfrak{Z}(\mathbb{S})=0$, $\mathbb{S}$ satisfies the Hennessy-Milner
property. The second author proved the existence of an LMP $\mathbb{S}$ with
$\mathfrak{Z}(\mathbb{S}) \geq 1$ and Zhou showed that there are LMPs having an
infinite Zhou ordinal. In this paper we show that there are LMPs $\mathbb{S}$
over separable metrizable spaces having arbitrary large countable
$\mathfrak{Z}(\mathbb{S})$ and that it is consistent with the axioms of
$\mathit{ZFC}$ that there is such a process with an uncountable Zhou ordinal.}
}

4. M. Campercholi, M. Tellechea, and P. Ventura, “Deciding Quantifier-free Definability in Finite Algebraic Structures,” Electronic Notes in Theoretical Computer Science 348: 23-41 (2020). 14th International Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2019). This work deals with the definability problem by quantifier-free first-order formulas over a finite algebraic structure. We show the problem to be coNP-complete and present a decision algorithm based on a semantical characterization of definable relations as those preserved by isomorphisms of substructures. Our approach also includes the design of an algorithm that computes the isomorphism type of a tuple in a finite algebraic structure. Proofs of soundness and completeness of the algorithms are presented, as well as empirical tests assessing their performances.

@article{CAMPERCHOLI202023,
title = {Deciding Quantifier-free Definability in Finite Algebraic Structures},
journal = {Electronic Notes in Theoretical Computer Science},
volume = {348},
pages = {23 - 41},
year = {2020},
note = {14th International Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2019)},
issn = {1571-0661},
doi = {https://doi.org/10.1016/j.entcs.2020.02.003},
url = {http://www.sciencedirect.com/science/article/pii/S1571066120300037},
author = {Miguel Campercholi and Mauricio Tellechea and Pablo Ventura},
keywords = {Definability, logic, decision algorithm, complexity},
abstract = {This work deals with the definability problem by quantifier-free first-order formulas over a finite algebraic structure. We show the problem to be coNP-complete and present a decision algorithm based on a semantical characterization of definable relations as those preserved by isomorphisms of substructures. Our approach also includes the design of an algorithm that computes the isomorphism type of a tuple in a finite algebraic structure. Proofs of soundness and completeness of the algorithms are presented, as well as empirical tests assessing their performances.}
}

5. D. Vaggione, “Baker-Pixley theorem for algebras in relatively congruence distributive quasivarieties.,” Int. J. Algebra Comput. 29 (3) p. 459–480 (2019). Zbl 1428.08002
[ BibTeX ]
@Article{zbMATH07062402,
Author = {D. {Vaggione}},
Title = {{Baker-Pixley theorem for algebras in relatively congruence distributive quasivarieties.}},
FJournal = {{International Journal of Algebra and Computation}},
Journal = {{Int. J. Algebra Comput.}},
ISSN = {0218-1967; 1793-6500/e},
Volume = {29},
Number = {3},
Pages = {459--480},
Year = {2019},
Publisher = {World Scientific, Singapore},
Language = {English},
MSC2010 = {08A40 03C40 08B10 08C15},
Zbl = {1428.08002}
}

6. C. Areces, M. Campercholi, D. Penazzi, and V. Pablo, “The Complexity of Definability by Open First-Order Formulas,” Logic Journal of the IGPL (2019). en prensa.
[ BibTeX ]
@article{Complejidad_parametrica,
author = {Areces, Carlos and Campercholi, Miguel and Penazzi, Daniel and Ventura Pablo},
title = {The Complexity of Definability by Open First-Order Formulas},
journal = {Logic Journal of the IGPL},
year = {2019},
note = {en prensa}
}

7. D. J. Vaggione, “Infinitary Baker-Pixley theorem.,” Algebra Univers. 79 (3) p. 14 (2018). Id/No 67.
[ BibTeX ]
@Article{zbMATH06968526,
Author = {Diego J. {Vaggione}},
Title = {{Infinitary Baker-Pixley theorem.}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {79},
Number = {3},
Pages = {14},
Note = {Id/No 67},
Year = {2018},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
MSC2010 = {08A40 03C40 03C05 08B10}
}

8. M. Campercholi, “Dominions and primitive positive function,” Journal of Symbolic Logic 83 (01) p. 40–54 (2018).
@article{Dominions,
author = {Campercholi, M.},
title = {Dominions and primitive positive function},
journal = {Journal of Symbolic Logic},
year = {2018},
volume = {83},
number = {01},
pages = {40–54},
url = {https://doi.org/10.1017/jsl.2017.18}
}

9. C. Areces, M. Campercholi, and P. Ventura, “Deciding Open Definability via Subisomorphisms,” in Logic, Language, Information, and Computation, Berlin, Heidelberg, 2018, p. 91–105.
[ Abstract | BibTeX ]

Given a logic {\$}{\$}{\backslash}varvec{\{}{\backslash}mathcal {\{}L{\}}{\}}{\$}{\$}L, the {\$}{\$}{\backslash}varvec{\{}{\backslash}mathcal {\{}L{\}}{\}}{\$}{\$}L-Definability Problem for finite structures takes as input a finite structure {\$}{\$}{\backslash}varvec{\{}A{\}}{\$}{\$}Aand a target relation T over the domain of {\$}{\$}{\backslash}varvec{\{}A{\}}{\$}{\$}A, and determines whether there is a formula of {\$}{\$}{\backslash}varvec{\{}{\backslash}mathcal {\{}L{\}}{\}}{\$}{\$}Lwhose interpretation in {\$}{\$}{\backslash}varvec{\{}A{\}}{\$}{\$}Acoincides with T. In this note we present an algorithm that solves the definability problem for quantifier-free first order formulas. Our algorithm takes advantage of a semantic characterization of open definability via subisomorphisms, which is sound and complete. We also provide an empirical evaluation of its performance.

@inproceedings{10.1007/978-3-662-57669-4_5,
author = {Areces, Carlos
and Campercholi, Miguel
and Ventura, Pablo},
editor = {Moss, Lawrence S.
and de Queiroz, Ruy
and Martinez, Maricarmen},
title = {Deciding Open Definability via Subisomorphisms},
booktitle = {Logic, Language, Information, and Computation},
year = {2018},
publisher = {Springer Berlin Heidelberg},
pages = {91--105},
abstract = {Given a logic {\$}{\$}{\backslash}varvec{\{}{\backslash}mathcal {\{}L{\}}{\}}{\$}{\$}L, the {\$}{\$}{\backslash}varvec{\{}{\backslash}mathcal {\{}L{\}}{\}}{\$}{\$}L-Definability Problem for finite structures takes as input a finite structure {\$}{\$}{\backslash}varvec{\{}A{\}}{\$}{\$}Aand a target relation T over the domain of {\$}{\$}{\backslash}varvec{\{}A{\}}{\$}{\$}A, and determines whether there is a formula of {\$}{\$}{\backslash}varvec{\{}{\backslash}mathcal {\{}L{\}}{\}}{\$}{\$}Lwhose interpretation in {\$}{\$}{\backslash}varvec{\{}A{\}}{\$}{\$}Acoincides with T. In this note we present an algorithm that solves the definability problem for quantifier-free first order formulas. Our algorithm takes advantage of a semantic characterization of open definability via subisomorphisms, which is sound and complete. We also provide an empirical evaluation of its performance.},
isbn = {978-3-662-57669-4}
}

10. P. Sánchez Terraf, “Bisimilarity is not Borel,” Mathematical Structures in Computer Science 27 (7) p. 1265–1284 (2017). Zbl 1377.68150
[ $e$-edition | Download PDF | Abstract | BibTeX ]

We prove that the relation of bisimilarity between countable labelled transition systems is $\Sigma_1^1$-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it. This has an impact on the theory of probabilistic and nondeterministic processes over uncountable spaces, since logical characterizations of bisimilarity (as, for instance, those based on the unique structure theorem for analytic spaces) require a countable logic whose formulas have measurable semantics. Our reduction shows that such a logic does not exist in the case of image-infinite processes.

@article{2012arXiv1211.0967S,
author = {S{\'a}nchez Terraf, Pedro},
title = {Bisimilarity is not {B}orel},
abstract = {We prove that the relation of bisimilarity between countable labelled transition systems is $\Sigma_1^1$-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it.
This has an impact on the theory of probabilistic and nondeterministic processes over uncountable spaces, since logical characterizations of bisimilarity (as, for instance, those based on the unique structure theorem for analytic spaces) require a countable logic whose formulas have measurable semantics. Our reduction shows that such a logic does not exist in the case of image-infinite processes.},
ee = {http://arxiv.org/abs/1211.0967},
keywords = {Mathematics - Logic, Computer Science - Logic in Computer Science, 03B70, 03E15, 28A05, F.4.1, F.1.2},
journal = {Mathematical Structures in Computer Science},
issn = {1469-8072},
doi = {10.1017/S0960129515000535},
zbl = {1377.68150},
url = {http://journals.cambridge.org/article_S0960129515000535},
pages = {1265--1284},
number = {7},
month = {10},
year = {2017},
volume = {27}
}

11. M. A. Campercholi and J. G. Raftery, “Relative congruence formulas and decompositions in quasivarieties,” Algebra universalis (2017). Quasivarietal analogues of uniform congruence schemes are discussed, and their relationship with the equational definability of principal relative congruences (EDPRC) is established, along with their significance for relative congruences on subalgebras of products. Generalizing the situation in varieties, we prove that a quasivariety is relatively ideal iff it has EDPRC; it is relatively filtral iff it is relatively semisimple with EDPRC. As an application, it is shown that a finitary sentential logic, algebraized by a quasivariety K, has a classical inconsistency lemma if and only if K is relatively filtral and the subalgebras of its nontrivial members are nontrivial. A concrete instance of this result is exhibited, in which K is not a variety. Finally, for quasivarieties {\$}{\$}{\{}{\backslash}sf{\{}M{\}} {\backslash}subseteq {\backslash}sf{\{}K{\}}{\}}{\$}{\$} M ⊆ K , we supply some conditions under which M is the restriction to K of a variety, assuming that K has EDPRC.

@article{Campercholi2017,
author = {Campercholi, Miguel A. and Raftery, James G.},
title = {Relative congruence formulas and decompositions in quasivarieties},
journal = {Algebra universalis},
year = {2017},
month = {Sep},
abstract = {Quasivarietal analogues of uniform congruence schemes are discussed, and their relationship with the equational definability of principal relative congruences (EDPRC) is established, along with their significance for relative congruences on subalgebras of products. Generalizing the situation in varieties, we prove that a quasivariety is relatively ideal iff it has EDPRC; it is relatively filtral iff it is relatively semisimple with EDPRC. As an application, it is shown that a finitary sentential logic, algebraized by a quasivariety K, has a classical inconsistency lemma if and only if K is relatively filtral and the subalgebras of its nontrivial members are nontrivial. A concrete instance of this result is exhibited, in which K is not a variety. Finally, for quasivarieties {\$}{\$}{\{}{\backslash}sf{\{}M{\}} {\backslash}subseteq {\backslash}sf{\{}K{\}}{\}}{\$}{\$} M ⊆ K , we supply some conditions under which M is the restriction to K of a variety, assuming that K has EDPRC.},
day = {27},
doi = {10.1007/s00012-017-0455-y},
issn = {1420-8911},
url = {https://doi.org/10.1007/s00012-017-0455-y}
}

12. M. Badano and D. Vaggione, “Characterization of context-free languages,” Theor. Comput. Sci. 676 p. 92–96 (2017). [ BibTeX ]
@Article{zbMATH06714282,
Author = {M. {Badano} and D. {Vaggione}},
Title = {{Characterization of context-free languages}},
FJournal = {{Theoretical Computer Science}},
Journal = {{Theor. Comput. Sci.}},
ISSN = {0304-3975},
Volume = {676},
Pages = {92--96},
Year = {2017},
Publisher = {Elsevier, Amsterdam},
Language = {English},
DOI = {10.1016/j.tcs.2017.03.002},
MSC2010 = {68Q}
}

13. C. Areces, M. Campercholi, D. Penazzi, and P. Sánchez Terraf, “The Lattice of Congruences of a Finite Linear Frame,” Journal of Logic and Computation 27 p. 2653–2688 (2017). Zbl 06981765
[ Abstract | BibTeX ]

Let $\mathbf{F}=\left\langle F,R\right\rangle$ be a finite Kripke frame. A congruence of $\mathbf{F}$ is a bisimulation of $\mathbf{F}$ that is also an equivalence relation on F. The set of all congruences of $\mathbf{F}$ is a lattice under the inclusion ordering. In this article we investigate this lattice in the case that $\mathbf{F}$ is a finite linear frame. We give concrete descriptions of the join and meet of two congruences with a nontrivial upper bound. Through these descriptions we show that for every nontrivial congruence $\rho$, the interval $[\mathrm{Id_{F},\rho]}$ embeds into the lattice of divisors of a suitable positive integer. We also prove that any two congruences with a nontrivial upper bound permute.

@ARTICLE{2015arXiv150401789A,
author = {Areces, Carlos and Campercholi, Miguel and Penazzi, Daniel and S{\'a}nchez Terraf, Pedro},
title = "{The Lattice of Congruences of a Finite Linear Frame}",
journal = {Journal of Logic and Computation},
archivePrefix = "arXiv",
eprint = {1504.01789},
primaryClass = "math.LO",
keywords = {Mathematics - Logic, Computer Science - Logic in Computer Science, 03B45 (Primary), 06B10, 06E25, 03B70 (Secondary), F.4.1, F.1.2},
doi = {10.1093/logcom/exx026},
zbl = {06981765},
pages = {2653--2688},
volume =27,
issue = 8,
abstract = "Let $\mathbf{F}=\left\langle F,R\right\rangle$ be a finite Kripke frame. A
congruence of $\mathbf{F}$ is a bisimulation of $\mathbf{F}$ that is also an
equivalence relation on F. The set of all congruences of $\mathbf{F}$ is a
lattice in the case that $\mathbf{F}$ is a finite linear frame. We give
concrete descriptions of the join and meet of two congruences with a nontrivial
upper bound. Through these descriptions we show that for every nontrivial
congruence $\rho$, the interval $[\mathrm{Id_{F},\rho]}$ embeds into the
lattice of divisors of a suitable positive integer. We also prove that any two
congruences with a nontrivial upper bound permute.",
year = 2017,
month = apr,
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

14. M. V. Badano and D. J. Vaggione, “Varieties with equationally definable factor congruences II,” Algebra Univers. (2017). In press.
[ BibTeX ]
@Article{edfc2,
Author = {Mariana V. {Badano} and Diego J. {Vaggione}},
Title = {{Varieties with equationally definable factor congruences II}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Year = {2017},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
note = "In press",
MSC2010 = {03C05 08B05 08B10}
}

15. M. Badano and D. Vaggione, “$\mathcal{V}_{SI}$ first order implies $\mathcal{V}_{DI}$ first order,” Acta Math. Hung. 151 (1) p. 47–49 (2017). [ BibTeX ]
@Article{zbMATH06707836,
Author = {M. {Badano} and D. {Vaggione}},
Title = {{$\mathcal{V}_{SI}$ first order implies $\mathcal{V}_{DI}$ first order}},
FJournal = {{Acta Mathematica Hungarica}},
Journal = {{Acta Math. Hung.}},
ISSN = {0236-5294; 1588-2632/e},
Volume = {151},
Number = {1},
Pages = {47--49},
Year = {2017},
Language = {English},
DOI = {10.1007/s10474-016-0676-0},
MSC2010 = {08B10}
}

16. M. Campercholi, D. Castaño, and J. P. Díaz Varela, “Algebraic functions in Łukasiewicz implication algebras,” International Journal of Algebra and Computation 26 (02): 223-247 (2016). @article{doi:10.1142/S0218196716500119,
author = {Campercholi, Miguel and Castaño, Diego and Díaz Varela, José Patricio},
title = {Algebraic functions in Łukasiewicz implication algebras},
journal = {International Journal of Algebra and Computation},
year = {2016},
volume = {26},
number = {02},
pages = {223-247},
doi = {10.1142/S0218196716500119},
eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0218196716500119},
url = {http://www.worldscientific.com/doi/abs/10.1142/S0218196716500119}
}

17. M. V. Badano and D. J. Vaggione, “Equational definability of (complementary) central elements,” Int. J. Algebra Comput. 26 (3) p. 509–532 (2016). [ BibTeX ]
@Article{zbMATH06596761,
Author = {Mariana V. {Badano} and Diego J. {Vaggione}},
Title = {{Equational definability of (complementary) central elements}},
FJournal = {{International Journal of Algebra and Computation}},
Journal = {{Int. J. Algebra Comput.}},
ISSN = {0218-1967; 1793-6500/e},
Volume = {26},
Number = {3},
Pages = {509--532},
Year = {2016},
Publisher = {World Scientific, Singapore},
Language = {English},
DOI = {10.1142/S0218196716500211},
MSC2010 = {03C05 08B05}
}

18. M. Campercholi and D. Vaggione, “Semantical conditions for the definability of functions and relations,” Algebra Univers. 76 (1) p. 71–98 (2016). [ BibTeX ]
@Article{zbMATH06627402,
Author = {Miguel {Campercholi} and Diego {Vaggione}},
Title = {{Semantical conditions for the definability of functions and relations}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {76},
Number = {1},
Pages = {71--98},
Year = {2016},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/s00012-016-0384-1},
MSC2010 = {03C40 08A35 08A30}
}

19. E. Doberkat and P. Sánchez Terraf, “Stochastic Nondeterminism and Effectivity Functions,” Journal of Logic and Computation (2015). [ Abstract | BibTeX ]

This paper investigates stochastic nondeterminism on continuous state spaces by relating nondeterministic kernels and stochastic effectivity functions to each other. Nondeterministic kernels are functions assigning each state a set o subprobability measures, and effectivity functions assign to each state an upper-closed set of subsets of measures. Both concepts are generalizations of Markov kernels used for defining two different models: Nondeterministic labelled Markov processes and stochastic game models, respectively. We show that an effectivity function that maps into principal filters is given by an image-countable nondeterministic kernel, and that image-finite kernels give rise to effectivity functions. We define state bisimilarity for the latter, considering its connection to morphisms. We provide a logical characterization of bisimilarity in the finitary case. A generalization of congruences (event bisimulations) to effectivity functions and its relation to the categorical presentation of bisimulation are also studied.

@ARTICLE{2014arXiv1405.7141D,
author = {Doberkat, Ernst-Erich and S{\'a}nchez Terraf, Pedro},
title = "Stochastic Nondeterminism and Effectivity Functions",
journal = {Journal of Logic and Computation},
archivePrefix = "arXiv",
eprint = {1405.7141},
primaryClass = "cs.LO",
keywords = {stochastic effectivity function, non-deterministic labelled Markov process, state bisimilarity, coalgebra},
year = 2015,
doi = {10.1093/logcom/exv049},
abstract = {This paper investigates stochastic nondeterminism on continuous state spaces by relating nondeterministic kernels and stochastic effectivity functions to each other. Nondeterministic kernels are functions assigning each state a set o subprobability measures, and effectivity functions assign to each state an upper-closed set of subsets of measures. Both concepts are generalizations of Markov kernels used for defining two different models: Nondeterministic labelled Markov processes and stochastic game models, respectively. We show that an effectivity function that maps into principal filters is given by an image-countable nondeterministic kernel, and that image-finite kernels give rise to effectivity functions. We define state bisimilarity for the latter, considering its connection to morphisms. We provide a logical characterization of bisimilarity in the finitary case. A generalization of congruences (event bisimulations) to effectivity functions and its relation to the categorical presentation of bisimulation are also studied.}
}

20. M. Campercholi, M. M. Stronkowski, and D. Vaggione, “On structural completeness versus almost structural completeness problem: A discriminator varieties case study,” Logic Journal of IGPL 23 (2): 235-246 (2015). We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that L has an adequate semantics given by a discriminator variety. Then L is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete.

@article{StrucVsAlmost,
author = {Campercholi, Miguel and Stronkowski, Michał M. and Vaggione, Diego},
title = {On structural completeness versus almost structural completeness problem: A discriminator varieties case study},
volume = {23},
number = {2},
pages = {235-246},
year = {2015},
doi = {10.1093/jigpal/jzu032},
abstract ={We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that L has an adequate semantics given by a discriminator variety. Then L is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete.},
URL = {http://jigpal.oxfordjournals.org/content/23/2/235.abstract},
eprint = {http://jigpal.oxfordjournals.org/content/23/2/235.full.pdf+html},
journal = {Logic Journal of IGPL}
}

21. M. Campercholi and D. Vaggione, “Algebraic functions in quasiprimal algebras,” Math. Log. Q. 60 (3) p. 154–160 (2014). [ BibTeX ]
@Article{zbMATH06301477,
Author = {Miguel {Campercholi} and Diego {Vaggione}},
Title = {{Algebraic functions in quasiprimal algebras}},
FJournal = {{Mathematical Logic Quarterly (MLQ)}},
Journal = {{Math. Log. Q.}},
ISSN = {0942-5616; 1521-3870/e},
Volume = {60},
Number = {3},
Pages = {154--160},
Year = {2014},
Publisher = {Wiley (Wiley-VCH), Berlin},
Language = {English},
DOI = {10.1002/malq.201200060},
MSC2010 = {03}
}

22. M. V. Badano and D. J. Vaggione, “Varieties with equationally definable factor congruences,” Algebra Univers. 70 (4) p. 327–345 (2013). Zbl 1316.03018
[ BibTeX ]
@Article{zbMATH06280979,
Author = {Mariana V. {Badano} and Diego J. {Vaggione}},
Title = {{Varieties with equationally definable factor congruences}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {70},
Number = {4},
Pages = {327--345},
Year = {2013},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/s00012-013-0252-1},
MSC2010 = {03C05 08B05 08B10},
Zbl = {1316.03018}
}

23. P. R. D’Argenio, P. Sánchez Terraf, and N. Wolovick, “Bisimulations for non-deterministic labelled Markov processes,” Mathematical Structures in Comp. Sci. 22 (1) p. 43–68 (2012). Zbl 1234.68316

We extend the theory of labeled Markov processes with \emph{internal} nondeterminism, a fundamental concept for the further development of a process theory with abstraction on nondeterministic continuous probabilistic systems. % We define \emph{nondeterministic labeled Markov processes (NLMP)} and provide three definition of bisimulations: a bisimulation following a traditional characterization, a \emph{state} based bisimulation tailored to our “measurable” non-determinism, and an \emph{event} based bisimulation. % We show the relation between them, including that the largest state bisimulation is also an event bisimulation. % We also introduce a variation of the Hennessy-Milner logic that characterizes event bisimulation and that is sound w.r.t.\ the other bisimulations for arbitrary NLMP. % This logic, however, is infinitary as it contains a denumerable $\bigvee$. % We then introduce a finitary sublogic that characterize all bisimulations for image finite NLMP whose underlying measure space is also analytic. Hence, in this setting, all notions of bisimulation we deal with turn out to be equal. % Finally, we show that all notions of bisimulations are different in the general case. The counterexamples that separate them turn to be \emph{non-probabilistic} NLMP.

@article{D'Argenio:2012:BNL:2139682.2139685,
author = {D'Argenio, Pedro R. and S\'{a}nchez Terraf, Pedro and Wolovick, Nicol\'{a}s},
title = {Bisimulations for non-deterministic labelled {M}arkov processes},
journal = {Mathematical Structures in Comp. Sci.},
issue_date = {February 2012},
volume = {22},
number = {1},
issue = 1,
month = feb,
year = {2012},
issn = {0960-1295},
pages = {43--68},
numpages = {26},
url = {http://dx.doi.org/10.1017/S0960129511000454},
doi = {10.1017/S0960129511000454},
acmid = {2139685},
publisher = {Cambridge University Press},
address = {New York, NY, USA},
abstract = { We extend the theory of labeled Markov processes with
\emph{internal} nondeterminism, a fundamental concept for the further
development of a process theory with abstraction on nondeterministic
continuous probabilistic systems.
%
We define \emph{nondeterministic labeled Markov processes (NLMP)}
and provide three definition of bisimulations: a bisimulation
following a traditional characterization, a \emph{state} based
bisimulation tailored to our measurable'' non-determinism, and an
\emph{event} based bisimulation.
%
We show the relation between them, including that the largest state
bisimulation is also an event bisimulation.
%
We also introduce a variation of the Hennessy-Milner logic that
characterizes event bisimulation and that is sound w.r.t.\ the other
bisimulations for arbitrary NLMP.
%
This logic, however, is infinitary as it contains a denumerable
$\bigvee$.
%
We then introduce a finitary sublogic that characterize all
bisimulations for image finite NLMP whose underlying measure space
is also analytic. Hence, in this setting, all notions of
bisimulation we deal with turn out to be equal.
%
Finally, we show that all notions of bisimulations are different in
the general case. The counterexamples that separate them turn to be
\emph{non-probabilistic} NLMP.},
Zbl = {1234.68316}
}

24. M. A. Campercholi and D. J. Vaggione, “Implicit definition of the quaternary discriminator,” Algebra Univers. 68 (1-2) p. 1–16 (2012). Zbl 1261.08003
[ BibTeX ]
@Article{zbMATH06110487,
Author = {Miguel A. {Campercholi} and Diego J. {Vaggione}},
Title = {{Implicit definition of the quaternary discriminator}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {68},
Number = {1-2},
Pages = {1--16},
Year = {2012},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/s00012-012-0189-9},
MSC2010 = {08C15 08A30},
Zbl = {1261.08003}
}

25. M. Campercholi, D. Castaño, and J. P. Díaz Varela, “Quasivarieties and Congruence Permutability of \Lukasiewicz Implication Algebras,” Studia Logica 98 (1) p. 267–283 (2011). In this paper we study some questions concerning {\L}ukasiewicz implication algebras. In particular, we show that every subquasivariety of {\L}ukasiewicz implication algebras is, in fact, a variety. We also derive some characterizations of congruence permutable algebras. The starting point for these results is a representation of finite {\L}ukasiewicz implication algebras as upwardly-closed subsets in direct products of MV-chains.

@article{CampercholiCastanoDiazVarela2011,
author = {Campercholi, M. and Casta{\~{n}}o, D. and D{\'i}az Varela, J. P.},
title = {Quasivarieties and Congruence Permutability of {\L}ukasiewicz Implication Algebras},
journal = {Studia Logica},
year = {2011},
volume = {98},
number = {1},
pages = {267--283},
month = {Jul},
abstract = {In this paper we study some questions concerning {\L}ukasiewicz implication algebras. In particular, we show that every subquasivariety of {\L}ukasiewicz implication algebras is, in fact, a variety. We also derive some characterizations of congruence permutable algebras. The starting point for these results is a representation of finite {\L}ukasiewicz implication algebras as upwardly-closed subsets in direct products of MV-chains.},
day = {01},
doi = {10.1007/s11225-011-9329-z},
issn = {1572-8730},
url = {https://doi.org/10.1007/s11225-011-9329-z}
}

26. M. Campercholi and D. Vaggione, “Axiomatizability by ${\forall \exists!}$-sentences,” Arch. Math. Logic 50 (7-8) p. 713–725 (2011). Zbl 1237.03018
[ BibTeX ]
@Article{zbMATH05977563,
Author = {Miguel {Campercholi} and Diego {Vaggione}},
Title = {{Axiomatizability by ${\forall \exists!}$-sentences}},
FJournal = {{Archive for Mathematical Logic}},
Journal = {{Arch. Math. Logic}},
ISSN = {0933-5846; 1432-0665/e},
Volume = {50},
Number = {7-8},
Pages = {713--725},
Year = {2011},
Publisher = {Springer, Berlin/Heidelberg},
Language = {English},
DOI = {10.1007/s00153-011-0244-9},
MSC2010 = {03C40 03C05 03C07 03C13 06D35},
Zbl = {1237.03018}
}

27. M. A. Campercholi and D. J. Vaggione, “An implicit function theorem for algebraically closed fields,” Algebra Univers. 65 (3) p. 299–304 (2011). Zbl 1254.12006
[ BibTeX ]
@Article{zbMATH05902947,
Author = {Miguel A. {Campercholi} and Diego J. {Vaggione}},
Title = {{An implicit function theorem for algebraically closed fields}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {65},
Number = {3},
Pages = {299--304},
Year = {2011},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/s00012-011-0130-7},
MSC2010 = {12E99 13P15},
Zbl = {1254.12006}
}

28. P. Sánchez Terraf, “Factor Congruences in Semilattices,” Revista de la Unión Matemática Argentina 52 (1) p. 1–10 (2011). Zbl 1242.06006
[ $e$-edition | Download PDF | Abstract | BibTeX ]

We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum (maximum) element, these generalized ideals turn into ordinary (dual) ideals.

@article{fact_slat,
author = {S{\'a}nchez Terraf, Pedro},
title = {Factor Congruences in Semilattices},
journal = {Revista de la {U}ni\'on {M}atem\'atica {A}rgentina},
volume = {52},
number = {1},
year = {2011},
ee = {http://arxiv.org/abs/0809.3822v2},
eprint = {0809.3822},
keywords = {semilattice, direct factor, factor congruence, generalized direct sum, generalized ideal},
pages = {1--10},
url = {http://inmabb.criba.edu.ar/revuma/pdf/v52n1/v52n1a03.pdf},
abstract = {We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum
(maximum) element, these generalized ideals turn into ordinary (dual) ideals.},
Zbl = {1242.06006}
}

29. P. Sánchez Terraf, “Boolean factor congruences and property $(*)$,” Int. J. Algebra Comput. 21 (6): 931-950 (2011). Zbl 1228.08003
[ Abstract | BibTeX ]

{Summary: A variety ${\cal V}$ has Boolean factor congruences (BFC) if the set of factor congruences of any algebra in ${\cal V}$ is a distributive sublattice of its congruence lattice; this property holds in rings with unit and in every variety which has a semilattice operation. BFC has a prominent role in the study of uniqueness of direct product representations of algebras, since it is a strengthening of the refinement property. We provide an explicit Mal’tsev condition for BFC. With the aid of this condition, it is shown that BFC is equivalent to a variant of the definability property $(*)$, an open problem in {\it R. Willard}’s work [J. Algebra 132, No.~1, 130–153 (1990; Zbl 0737.08006)].}

@article{1228.08003,
author="S{\'a}nchez Terraf, Pedro",
title="{{B}oolean factor congruences and property $(*)$}",
language="English",
journal="Int. J. Algebra Comput. ",
volume="21",
number="6",
pages="931-950",
year="2011",
doi={10.1142/S021819671100656X},
abstract="{Summary: A variety ${\cal V}$ has Boolean factor congruences (BFC) if
the set of factor congruences of any algebra in ${\cal V}$ is a distributive
sublattice of its congruence lattice; this property holds in rings with unit
and in every variety which has a semilattice operation. BFC has a prominent
role in the study of uniqueness of direct product representations of
algebras, since it is a strengthening of the refinement property.
We
provide an explicit Mal'tsev condition for BFC. With the aid of this
condition, it is shown that BFC is equivalent to a variant of the
definability property $(*)$, an open problem in {\it R. Willard}'s work [J.
Algebra 132, No.~1, 130--153 (1990; Zbl 0737.08006)].}",
keywords="{Boolean factor congruences; strict refinement property; definability;
preservation by direct factors}",
classmath="{*08B05 (Equational logic in varieties of algebras)
}",
Zbl = {1228.08003}
}

30. P. Sánchez Terraf, “Unprovability of the logical characterization of bisimulation,” Information and Computation 209 (7) p. 1048–1056 (2011). Zbl 1216.68196

We quickly review \emph{labelled Markov processes (LMP)} and provide a counterexample showing that in general measurable spaces, event bisimilarity and state bisimilarity differ in LMP. This shows that the logic in the work by Desharnais does not characterize state bisimulation in non-analytic measurable spaces. Furthermore we show that, under current foundations of Mathematics, such logical characterization is unprovable for spaces that are projections of a coanalytic set. Underlying this construction there is a proof that stationary Markov processes over general measurable spaces do not have semi-pullbacks.

@article{Pedro20111048,
title = "Unprovability of the logical characterization of bisimulation",
journal = "Information and Computation",
volume = 209,
number = 7,
issue = 7,
pages = "1048--1056",
year = 2011,
issn = "0890-5401",
doi = "10.1016/j.ic.2011.02.003",
url = "http://www.sciencedirect.com/science/article/pii/S0890540111000691",
author = "S{\'a}nchez Terraf, Pedro",
keywords = "Labelled Markov process",
keywords = "Probabilistic bisimulation",
keywords = "Modal logic",
keywords = "Nonmeasurable set",
abstract = {We quickly review \emph{labelled Markov processes
(LMP)} and provide a counterexample showing that in general
measurable spaces, event
bisimilarity and state bisimilarity differ in LMP. This shows that
the logic in the work by Desharnais does not
characterize state bisimulation in non-analytic measurable
spaces. Furthermore we show that, under current foundations of
Mathematics, such logical characterization is unprovable for spaces
that are projections of a coanalytic set. Underlying this construction
there is a proof that stationary Markov processes over general
measurable spaces do not have semi-pullbacks.},
Zbl = {1216.68196}
}

31. M. Campercholi and D. Vaggione, “Algebraic functions,” Stud. Log. 98 (1-2) p. 285–306 (2011). Zbl 1264.08001
[ BibTeX ]
@Article{zbMATH06013474,
Author = {M. {Campercholi} and D. {Vaggione}},
Title = {{Algebraic functions}},
FJournal = {{Studia Logica}},
Journal = {{Stud. Log.}},
ISSN = {0039-3215; 1572-8730/e},
Volume = {98},
Number = {1-2},
Pages = {285--306},
Year = {2011},
Publisher = {Springer Netherlands, Dordrecht; Polish Academy of Sciences, Institute of Philosophy and Sociology, Warsaw},
Language = {English},
DOI = {10.1007/s11225-011-9334-2},
MSC2010 = {08A40 06D05 06D15 08B05 15A03 20K01},
Zbl = {1264.08001}
}

32. M. Campercholi, “Algebraically expandable classes of implication algebras,” International Journal of Algebra and Computation 20 (05) p. 605–617 (2010). @article{CAMPERCHOLI2010,
author = {Miguel Campercholi},
title = {Algebraically expandable classes of implication algebras},
journal = {International Journal of Algebra and Computation},
year = {2010},
volume = {20},
number = {05},
pages = {605--617},
month = {aug},
doi = {10.1142/s0218196710005704},
publisher = {World Scientific Pub Co Pte Lt},
url = {https://doi.org/10.1142/s0218196710005704}
}

33. P. Sánchez Terraf, “Existentially definable factor congruences,” Acta Scientiarum Mathematicarum (Szeged) 76 (1–2) p. 49–53 (2010). Zbl 1274.08028

A variety $\mathcal{V}$ has \emph{definable factor congruences} if and only if factor congruences can be defined by a first-order formula $\Phi$ having \emph{central elements} as parameters. We prove that if $\Phi$ can be chosen to be existential, factor congruences in every algebra of $\mathcal{V}$ are compact.

@article{EDFC,
author = {S\'anchez Terraf, Pedro},
title = {Existentially definable factor congruences},
journal = {Acta Scientiarum Mathematicarum (Szeged)},
volume = {76},
number = {1--2},
year = {2010},
pages = {49--53},
url = {https://bit.ly/3cBZP9f},
eprint = {0906.4722},
abstract = {A variety $\mathcal{V}$ has \emph{definable factor congruences} if and only if
factor congruences can be defined by a first-order formula $\Phi$ having
\emph{central elements} as parameters. We prove that if $\Phi$
can be chosen to be existential, factor congruences in every
algebra of $\mathcal{V}$ are compact.},
Zbl = {1274.08028}
}

34. M. Campercholi and D. Vaggione, “Algebraically expandable classes,” Algebra Univers. 61 (2) p. 151–186 (2009). Zbl 1223.08003
[ BibTeX ]
@Article{zbMATH05646234,
Author = {Miguel {Campercholi} and Diego {Vaggione}},
Title = {{Algebraically expandable classes}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {61},
Number = {2},
Pages = {151--186},
Year = {2009},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/s00012-009-0008-0},
MSC2010 = {08C10 03C40 06D30 08B10},
Zbl = {1223.08003}
}

35. P. Sánchez Terraf and D. Vaggione, “Varieties with Definable Factor Congruences,” Trans. Amer. Math. Soc. 361 p. 5061–5088 (2009). Zbl 1223.08001
[ Abstract | BibTeX ]

We study direct product representations of algebras in varieties. We collect several conditions expressing that these representations are \emph{definable} in a first-order-logic sense, among them the concept of Definable Factor Congruences (DFC). The main results are that DFC is a Mal’cev property and that it is equivalent to all other conditions formulated; in particular we prove that $\mathcal{V}$ has DFC if and only if $\mathcal{V}$ has $\vec{0}$ & $\vec{1}$ and \emph{Boolean Factor Congruences}. We also obtain an explicit first order definition $\Phi$ of the kernel of the canonical projections via the terms associated to the Mal’cev condition for DFC, in such a manner it is preserved by taking direct products and direct factors. The main tool is the use of \emph{central elements,} which are a generalization of both central idempotent elements in rings with identity and neutral complemented elements in a bounded lattice.

@article{DFC,
author = {S\'anchez Terraf, Pedro and Vaggione, Diego},
title = {Varieties with Definable Factor Congruences},
journal = {Trans. Amer. Math. Soc.},
volume = {361},
year = {2009},
pages = {5061--5088},
doi = {10.1090/S0002-9947-09-04921-6},
abstract = {We study direct product representations of algebras in
varieties. We collect several
conditions expressing that these representations are \emph{definable}
in a first-order-logic sense, among them the concept of Definable
Factor Congruences (DFC). The main results are that DFC is a Mal'cev
property and that it is equivalent to all other conditions
formulated; in particular we prove that $\mathcal{V}$ has DFC if and only if
$\mathcal{V}$ has $\vec{0}$ \& $\vec{1}$ and \emph{Boolean Factor Congruences}. We also obtain an explicit
first order definition $\Phi$ of the kernel of the canonical projections via the terms
associated to the Mal'cev condition for DFC, in such a manner it is preserved
by taking direct products and direct factors. The main tool is the use
of \emph{central elements,} which are a generalization of
both central idempotent elements in rings with identity and neutral
complemented elements in a bounded lattice.},
Zbl = {1223.08001},
MRNUMBER = {2515803}
}

36. P. Sánchez Terraf, “Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids,” Order 25 (4) p. 377–386 (2008). Zbl 1168.08005
[ Abstract | BibTeX ]

We study varieties with a term-definable poset structure, \emph{po-groupoids}. It is known that connected posets have the \emph{strict refinement property} (SRP). In a previous work by Vaggione and the author it is proved that semidegenerate varieties with the SRP have definable factor congruences and if the similarity type is finite, directly indecomposables are axiomatizable by a set of first-order sentences. We obtain such a set for semidegenerate varieties of connected po-groupoids and show its quantifier complexity is bounded in general.

@article{pogroupoids,
author = {S\'anchez Terraf, Pedro},
title = {Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids},
journal = {Order},
volume = {25},
number = {4},
year = {2008},
pages = {377--386},
doi = {10.1007/s11083-008-9101-9},
abstract = {We study varieties with a term-definable poset structure, \emph{po-groupoids}. It is known
that connected posets have the \emph{strict refinement property}
(SRP). In a previous work by Vaggione and the author it is proved that
semidegenerate varieties with the SRP have definable factor congruences
and if the similarity type is finite, directly indecomposables are
axiomatizable by a set of first-order sentences. We obtain such a set
for semidegenerate varieties of connected po-groupoids
and show its quantifier complexity is bounded in general.},
Zbl = {1168.08005}
}

37. D. Vaggione, “Infinitary simultaneous recursion theorem.,” Mathware Soft Comput. 15 (3) p. 273–283 (2008). Zbl 1167.68016
[ Abstract | BibTeX ]

We prove an infinitary version of the Double Recursion Theorem of Smullyan. We give some applications which show how this form of the Recursion Theorem can be naturally applied to obtain interesting infinite sequences of programs

@Article{zbMATH05532075,
Author = {D. {Vaggione}},
Title = {{Infinitary simultaneous recursion theorem.}},
FJournal = {{Mathware \& Soft Computing}},
Journal = {{Mathware Soft Comput.}},
ISSN = {1134-5632},
Volume = {15},
Number = {3},
Pages = {273--283},
Year = {2008},
Publisher = {Universitat Polit\ecnica de Catalunya, Escola T\ecnica Superior d'Arquitectura, Secci\'o de Matem\atiques i Inform\atica, Barcelona},
Language = {English},
MSC2010 = {68N30 03D20 68N15},
abstract = {We prove an infinitary version of the Double Recursion Theorem of Smullyan. We give some applications which show how this form of the Recursion Theorem can be naturally applied to obtain interesting infinite sequences of programs},
Zbl = {1167.68016}
}

38. M. Campercholi and D. Vaggione, “An implicit function theorem for regular fuzzy logic functions,” Fuzzy Sets Syst. 159 (22) p. 2983–2987 (2008). Zbl 1175.03014
[ BibTeX ]
@Article{zbMATH05599500,
Author = {Miguel {Campercholi} and Diego {Vaggione}},
Title = {{An implicit function theorem for regular fuzzy logic functions}},
FJournal = {{Fuzzy Sets and Systems}},
Journal = {{Fuzzy Sets Syst.}},
ISSN = {0165-0114},
Volume = {159},
Number = {22},
Pages = {2983--2987},
Year = {2008},
Publisher = {Elsevier (North-Holland), Amsterdam},
Language = {English},
DOI = {10.1016/j.fss.2008.03.007},
MSC2010 = {03B52},
Zbl = {1175.03014}
}

39. M. Campercholi and D. Vaggione, “A note on congruence systems of MS-algebras,” Math. Bohem. 132 (4) p. 337–343 (2007). Zbl 1174.06312
[ BibTeX ]
@Article{zbMATH05538207,
Author = {M. {Campercholi} and D. {Vaggione}},
Title = {{A note on congruence systems of MS-algebras}},
FJournal = {{Mathematica Bohemica}},
Journal = {{Math. Bohem.}},
ISSN = {0862-7959},
Volume = {132},
Number = {4},
Pages = {337--343},
Year = {2007},
Publisher = {Academy of Sciences of the Czech Republic, Mathematical Institute, Prague},
Language = {English},
MSC2010 = {06D30},
Zbl = {1174.06312}
}

40. M. Campercholi and D. Vaggione, “Congruence permutable MS-algebras,” Algebra Univers. 56 (2) p. 119–131 (2007). Zbl 1116.06011
[ BibTeX ]
@Article{zbMATH05139579,
Author = {M. {Campercholi} and D. {Vaggione}},
Title = {{Congruence permutable MS-algebras}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {56},
Number = {2},
Pages = {119--131},
Year = {2007},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/s00012-007-1976-6},
MSC2010 = {06D30 08B05},
Zbl = {1116.06011}
}

41. D. Vaggione and P. Sánchez Terraf, “Compact factor congruences imply Boolean factor congruences,” Algebra univers. 51 p. 207–213 (2004). Zbl 1087.08001
[ Preprint | Abstract | BibTeX ]

We prove that any variety $\mathcal{V}$ in which every factor congruence is compact has Boolean factor congruences, i.e., for all $A$ in $\mathcal{V}$ the set of factor congruences of A is a distributive sublattice of the congruence lattice of A.

@article{CFC,
author = {Vaggione, Diego and S\'anchez Terraf, Pedro},
title = {Compact factor congruences imply {B}oolean factor congruences},
journal = {Algebra univers. },
abstract = {We prove that any variety $\mathcal{V}$ in which every factor congruence is compact has Boolean factor congruences, i.e., for all $A$ in $\mathcal{V}$ the set of factor congruences of A is a distributive sublattice of the congruence lattice of A.},
volume = {51},
year = {2004},
pages = {207--213},
doi = {10.1007/s00012-004-1857-1},
Zbl = {1087.08001}
}

42. D. Vaggione, “Characterization of discriminator varieties.,” Proc. Am. Math. Soc. 129 (3) p. 663–666 (2001). Zbl 0962.08005
[ BibTeX ]
@Article{zbMATH01549537,
Author = {Diego {Vaggione}},
Title = {{Characterization of discriminator varieties.}},
FJournal = {{Proceedings of the American Mathematical Society}},
Journal = {{Proc. Am. Math. Soc.}},
ISSN = {0002-9939; 1088-6826/e},
Volume = {129},
Number = {3},
Pages = {663--666},
Year = {2001},
Publisher = {American Mathematical Society (AMS), Providence, RI},
Language = {English},
DOI = {10.1090/S0002-9939-00-05627-6},
MSC2010 = {08B25 08A05 08A30 08B10},
Zbl = {0962.08005}
}

43. J. Blanco, M. Campercholi, and D. Vaggione, “The subquasivariety lattice of a discriminator variety,” Adv. Math. 159 (1) p. 18–50 (2001). Zbl 0984.08007
[ BibTeX ]
@Article{zbMATH01598986,
Author = {Javier {Blanco} and Miguel {Campercholi} and Diego {Vaggione}},
Title = {{The subquasivariety lattice of a discriminator variety}},
ISSN = {0001-8708},
Volume = {159},
Number = {1},
Pages = {18--50},
Year = {2001},
Publisher = {Elsevier (Academic Press), San Diego, CA},
Language = {English},
DOI = {10.1006/aima.2000.1962},
MSC2010 = {08B15 08C15},
Zbl = {0984.08007}
}

44. D. Vaggione, “Equational characterization of the quaternary discriminator,” Algebra Univers. 43 (1) p. 99–100 (2000). Zbl 1011.08001
[ BibTeX ]
@Article{zbMATH01899927,
Author = {Diego {Vaggione}},
Title = {{Equational characterization of the quaternary discriminator}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {43},
Number = {1},
Pages = {99--100},
Year = {2000},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/s000120050147},
MSC2010 = {08A30 08A40 08B05},
Zbl = {1011.08001}
}

45. D. Vaggione, “Central elements in varieties with the Fraser-Horn property,” Adv. Math. 148 (2) p. 193–202, art. no. aima.1999.1855 (1999). Zbl 0946.08002
[ BibTeX ]
@Article{zbMATH01415892,
Author = {Diego {Vaggione}},
Title = {{Central elements in varieties with the Fraser-Horn property}},
ISSN = {0001-8708},
Volume = {148},
Number = {2},
Pages = {193--202, art. no. aima.1999.1855},
Year = {1999},
Publisher = {Elsevier (Academic Press), San Diego, CA},
Language = {English},
DOI = {10.1006/aima.1999.1855},
MSC2010 = {08B05 08A30},
Zbl = {0946.08002}
}

46. D. Vaggione, “Modular varieties with the Fraser-Horn property,” Proc. Am. Math. Soc. 127 (3) p. 701–708 (1999). Zbl 0910.08003
[ BibTeX ]
@Article{zbMATH01245383,
Author = {Diego {Vaggione}},
Title = {{Modular varieties with the Fraser-Horn property}},
FJournal = {{Proceedings of the American Mathematical Society}},
Journal = {{Proc. Am. Math. Soc.}},
ISSN = {0002-9939; 1088-6826/e},
Volume = {127},
Number = {3},
Pages = {701--708},
Year = {1999},
Publisher = {American Mathematical Society (AMS), Providence, RI},
Language = {English},
DOI = {10.1090/S0002-9939-99-04647-X},
MSC2010 = {08B10 08A05},
Zbl = {0910.08003}
}

47. H. Gramaglia and D. Vaggione, “A note on distributive double $p$-algebras,” Czech. Math. J. 48 (2) p. 321–327 (1998). Zbl 0952.06012
[ BibTeX ]
@Article{zbMATH01528743,
Author = {Hector {Gramaglia} and Diego {Vaggione}},
Title = {{A note on distributive double $p$-algebras}},
FJournal = {{Czechoslovak Mathematical Journal}},
Journal = {{Czech. Math. J.}},
ISSN = {0011-4642; 1572-9141/e},
Volume = {48},
Number = {2},
Pages = {321--327},
Year = {1998},
Publisher = {Springer, Berlin/Heidelberg},
Language = {English},
DOI = {10.1023/A:1022893605321},
MSC2010 = {06D15 06B10},
Zbl = {0952.06012}
}

48. D. Vaggione, “On the fundamental theorem of algebra,” Colloq. Math. 73 (2) p. 193–194 (1997). Zbl 0876.12001
[ BibTeX ]
@Article{zbMATH01019480,
Author = {Diego {Vaggione}},
Title = {{On the fundamental theorem of algebra}},
FJournal = {{Colloquium Mathematicum}},
Journal = {{Colloq. Math.}},
ISSN = {0010-1354; 1730-6302/e},
Volume = {73},
Number = {2},
Pages = {193--194},
Year = {1997},
Publisher = {Polish Academy of Sciences (Polska Akademia Nauk - PAN), Institute of Mathematics (Instytut Matematyczny), Warsaw},
Language = {English},
MSC2010 = {12D10},
Zbl = {0876.12001}
}

49. D. Vaggione, “A note on sheaf representation in arithmetical varieties,” Acta Math. Hung. 75 (1-2) p. 23–25 (1997). Zbl 0922.08005
[ BibTeX ]
@Article{zbMATH01336394,
Author = {D. {Vaggione}},
Title = {{A note on sheaf representation in arithmetical varieties}},
FJournal = {{Acta Mathematica Hungarica}},
Journal = {{Acta Math. Hung.}},
ISSN = {0236-5294; 1588-2632/e},
Volume = {75},
Number = {1-2},
Pages = {23--25},
Year = {1997},
Language = {English},
DOI = {10.1023/A:1006522532214},
MSC2010 = {08B26 14G40},
Zbl = {0922.08005}
}

50. H. Gramaglia and D. J. Vaggione, “(Finitely) subdirectly irreducible and Birkhoff-like sheaf representation for certain varieties of lattice ordered structures,” Algebra Univers. 38 (1) p. 56–91 (1997). Zbl 0903.08013
[ BibTeX ]
@Article{zbMATH01226226,
Author = {H. {Gramaglia} and D.J. {Vaggione}},
Title = {{(Finitely) subdirectly irreducible and Birkhoff-like sheaf representation for certain varieties of lattice ordered structures}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {38},
Number = {1},
Pages = {56--91},
Year = {1997},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/s000120050038},
MSC2010 = {08B26 06B20 06D30 06D15},
Zbl = {0903.08013}
}

51. D. J. Vaggione, “Varieties of shells,” Algebra Univers. 36 (4) p. 483–487 (1996). Zbl 0901.08010
[ BibTeX ]
@Article{zbMATH01226562,
Author = {D.J. {Vaggione}},
Title = {{Varieties of shells}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {36},
Number = {4},
Pages = {483--487},
Year = {1996},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/BF01233918},
MSC2010 = {08B05 08A30},
Zbl = {0901.08010}
}

52. H. Gramaglia and D. Vaggione, “Birkhoff-like sheaf representation for varieties of lattice expansions,” Stud. Log. 56 (1-2) p. 111–131 (1996). Zbl 0854.08006
[ BibTeX ]
@Article{zbMATH00883886,
Author = {Hector {Gramaglia} and Diego {Vaggione}},
Title = {{Birkhoff-like sheaf representation for varieties of lattice expansions}},
FJournal = {{Studia Logica}},
Journal = {{Stud. Log.}},
ISSN = {0039-3215; 1572-8730/e},
Volume = {56},
Number = {1-2},
Pages = {111--131},
Year = {1996},
Publisher = {Springer Netherlands, Dordrecht; Polish Academy of Sciences, Institute of Philosophy and Sociology, Warsaw},
Language = {English},
DOI = {10.1007/BF00370143},
MSC2010 = {08B26 06B20 06D99},
Zbl = {0854.08006}
}

53. D. Vaggione, “$\mathcal{V}$ with factorable congruences and $\mathcal{V}=\text{I}\Gamma^\alpha(\mathcal{V}_{DI})$ imply $\mathcal{V}$ is a discriminator variety,” Acta Sci. Math. 62 (3-4) p. 359–368 (1996). Zbl 0880.08007
[ BibTeX ]
@Article{zbMATH01101410,
Author = {D. {Vaggione}},
Title = {{$\mathcal{V}$ with factorable congruences and $\mathcal{V}=\text{I}\Gamma^\alpha(\mathcal{V}_{DI})$ imply $\mathcal{V}$ is a discriminator variety}},
FJournal = {{Acta Scientiarum Mathematicarum}},
Journal = {{Acta Sci. Math.}},
ISSN = {0001-6969},
Volume = {62},
Number = {3-4},
Pages = {359--368},
Year = {1996},
Publisher = {University of Szeged, Bolyai Institute, Szeged},
Language = {English},
MSC2010 = {08B26 08A30},
Zbl = {0880.08007}
}

54. D. Vaggione, “On Jónsson’s theorem,” Math. Bohem. 121 (1) p. 55–58 (1996). Zbl 0863.06008
[ BibTeX ]
@Article{zbMATH01001199,
Author = {Diego {Vaggione}},
Title = {{On J\'onsson's theorem}},
FJournal = {{Mathematica Bohemica}},
Journal = {{Math. Bohem.}},
ISSN = {0862-7959},
Volume = {121},
Number = {1},
Pages = {55--58},
Year = {1996},
Publisher = {Academy of Sciences of the Czech Republic, Mathematical Institute, Prague},
Language = {English},
MSC2010 = {06B15 08B15 06B30 08B10},
Zbl = {0863.06008}
}

55. D. Vaggione, “Definability of directly indecomposable congruence modular algebras,” Stud. Log. 57 (2-3) p. 239–241 (1996). Zbl 0857.03016
[ BibTeX ]
@Article{zbMATH00957478,
Author = {Diego {Vaggione}},
Title = {{Definability of directly indecomposable congruence modular algebras}},
FJournal = {{Studia Logica}},
Journal = {{Stud. Log.}},
ISSN = {0039-3215; 1572-8730/e},
Volume = {57},
Number = {2-3},
Pages = {239--241},
Year = {1996},
Publisher = {Springer Netherlands, Dordrecht; Polish Academy of Sciences, Institute of Philosophy and Sociology, Warsaw},
Language = {English},
DOI = {10.1007/BF00370834},
MSC2010 = {03C05 08B10},
Zbl = {0857.03016}
}

56. D. Vaggione, “Varieties in which the Pierce stalks are directly indecomposable,” J. Algebra 184 (2) p. 424–434, art. no. 0268 (1996). Zbl 0868.08003
[ BibTeX ]
@Article{zbMATH00930150,
Author = {Diego {Vaggione}},
Title = {{Varieties in which the Pierce stalks are directly indecomposable}},
FJournal = {{Journal of Algebra}},
Journal = {{J. Algebra}},
ISSN = {0021-8693},
Volume = {184},
Number = {2},
Pages = {424--434, art. no. 0268},
Year = {1996},
Publisher = {Elsevier (Academic Press), San Diego, CA},
Language = {English},
DOI = {10.1006/jabr.1996.0268},
MSC2010 = {08B05 08A30 08B26},
Zbl = {0868.08003}
}

57. D. J. Vaggione, “Locally Boolean spectra,” Algebra Univers. 33 (3) p. 319–354 (1995). Zbl 0821.08001
[ BibTeX ]
@Article{zbMATH00759385,
Author = {D.J. {Vaggione}},
Title = {{Locally Boolean spectra}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {33},
Number = {3},
Pages = {319--354},
Year = {1995},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/BF01190703},
MSC2010 = {08A30 03C20 08B26},
Zbl = {0821.08001}
}

58. D. J. Vaggione, “Free algebras in discriminator varieties,” Algebra Univers. 34 (3) p. 391–403 (1995). Zbl 0840.08008
[ BibTeX ]
@Article{zbMATH00836821,
Author = {D.J. {Vaggione}},
Title = {{Free algebras in discriminator varieties}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {34},
Number = {3},
Pages = {391--403},
Year = {1995},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/BF01182095},
MSC2010 = {08B20 08C15},
Zbl = {0840.08008}
}

59. D. J. Vaggione, “Sheaf representation and Chinese Remainder Theorems,” Algebra Univers. 29 (2) p. 232–272 (1992). Zbl 0772.08005
[ BibTeX ]
@Article{zbMATH00064762,
Author = {Diego J. {Vaggione}},
Title = {{Sheaf representation and Chinese Remainder Theorems}},
FJournal = {{Algebra Universalis}},
Journal = {{Algebra Univers.}},
ISSN = {0002-5240; 1420-8911/e},
Volume = {29},
Number = {2},
Pages = {232--272},
Year = {1992},
Publisher = {Springer (Birkh\"auser), Basel; University of Manitoba, Department of Mathematics, Winnipeg},
Language = {English},
DOI = {10.1007/BF01190609},
MSC2010 = {08B26 06E15 08A45 08A30 06D30},
Zbl = {0772.08005}
}

## In peer-reviewed conferences

1. E. Gunther, M. Pagano, and P. Sánchez Terraf, “Formalization of Forcing in Isabelle/ZF,” in Automated Reasoning. 10th International Joint Conference, IJCAR 2020, Paris, France, July 1–4, 2020, Proceedings, Part II, 2020, p. 221–235. [ Abstract | BibTeX ]

We formalize the theory of forcing in the set theory framework of Isabelle/ZF. Under the assumption of the existence of a countable transitive model of $\mathit{ZFC}$, we construct a proper generic extension and show that the latter also satisfies $\mathit{ZFC}$. In doing so, we remodularized Paulson’s ZF-Constructibility library.

@inproceedings{2020arXiv200109715G,
author = {Gunther, Emmanuel and Pagano, Miguel and S{\'a}nchez Terraf, Pedro},
title = "{Formalization of Forcing in Isabelle/ZF}",
isbn = {978-3-662-45488-6},
booktitle = {Automated Reasoning. 10th International Joint Conference, IJCAR 2020, Paris, France, July 1--4, 2020, Proceedings, Part II},
volume = 12167,
series = {Lecture Notes in Artificial Intelligence},
editor = {Peltier, Nicolas and Sofronie-Stokkermans, Viorica},
publisher = {Springer International Publishing},
doi = {10.1007/978-3-030-51054-1},
pages = {221--235},
journal = {arXiv e-prints},
keywords = {Computer Science - Logic in Computer Science, Mathematics - Logic, 03B35 (Primary) 03E40, 03B70, 68T15 (Secondary), F.4.1},
year = 2020,
eid = {arXiv:2001.09715},
archivePrefix = {arXiv},
eprint = {2001.09715},
primaryClass = {cs.LO},
abstract = {We formalize the theory of forcing in the set theory framework of
Isabelle/ZF. Under the assumption of the existence of a countable
transitive model of $\mathit{ZFC}$, we construct a proper generic extension and show
that the latter also satisfies $\mathit{ZFC}$. In doing so, we remodularized
Paulson's ZF-Constructibility library.},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

2. E. Gunther, M. Pagano, and P. Sánchez Terraf, “First steps towards a formalization of Forcing,” Electronic Notes in Theoretical Computer Science 344: 119-136 (2019). The proceedings of LSFA 2018, the 13th Workshop on Logical and Semantic Frameworks with Applications (LSFA’18). We lay the ground for an Isabelle/ZF formalization of Cohen’s technique of \emph{forcing}. We formalize the definition of forcing notions as preorders with top, dense subsets, and generic filters. We formalize a version of the principle of Dependent Choices and using it we prove the Rasiowa-Sikorski lemma on the existence of generic filters. Given a transitive set $M$, we define its generic extension $M[G]$, the canonical names for elements of $M$, and finally show that if $M$ satisfies the axiom of pairing, then $M[G]$ also does.

@ARTICLE{2018arXiv180705174G,
author = {Gunther, Emmanuel and Pagano, Miguel and S{\'a}nchez Terraf, Pedro},
title = "{First steps towards a formalization of Forcing}",
journal = {Electronic Notes in Theoretical Computer Science},
archivePrefix = "arXiv",
eprint = {1807.05174},
primaryClass = "cs.LO",
keywords = {Computer Science - Logic in Computer Science, 03B35 (Primary) 03E40, 03B70, 68T15 (Secondary), F.4.1},
month = jul,
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
abstract = {We lay the ground for an Isabelle/ZF formalization of Cohen's
technique of \emph{forcing}. We formalize the definition of forcing notions as
preorders with top, dense subsets, and generic filters. We formalize
a version of the principle of Dependent Choices and using it
we prove the Rasiowa-Sikorski lemma on the existence of generic filters.
Given a transitive set $M$, we define its generic extension $M[G]$,
the canonical names for elements of $M$, and finally show that if $M$
satisfies the axiom of pairing, then $M[G]$ also does.},
volume = "344",
pages = "119 - 136",
year = "2019",
issn = "1571-0661",
doi = "10.1016/j.entcs.2019.07.008",
url = "http://www.sciencedirect.com/science/article/pii/S157106611930026X",
note = "The proceedings of LSFA 2018, the 13th Workshop on Logical and Semantic Frameworks with Applications (LSFA’18)"
}

3. C. E. Budde, P. R. D’Argenio, P. Sánchez Terraf, and N. Wolovick, “A Theory for the Semantics of Stochastic and Non-deterministic Continuous Systems,” in Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems, A. Remke and M. Stoelinga, Eds., Springer Berlin Heidelberg (2014) 8453, pp. 67-86. The description of complex systems involving physical or biological components usually requires to model involved continuous behavior induced by variables such as time, distances, speed, temperature, alkalinity of a solution, etc. Often, such variables can be quantified probabilistically to better understand the behavior of the complex systems. For example, the arrival time of events may be considered a Poisson process or the weight of an individual may be assumed to be distributed according to a log-normal distribution. However, it is also common that the uncertainty on how these variables behave make us prefer to leave out the choice of a particular probability and rather model it as a purely non-deterministic decision, as it is the case when a system is intended to be deployed in a variety of very different computer or network architectures. Therefore, the semantics of these systems needs to be represented by a variant of probabilistic automata that involves continuous domains on the state space and the transition relation. In this paper, we provide a survey to the theory of such kind of models. We present the theory of the so called labeled Markov processes (LMP) and its extension with internal non-determinism (NLMP). We show that in these complex domains, the bisimulation relation can be understood in different manners. We show the relation among these different definitions and try to understand the boundaries among them through examples. We also study variants of Hennessy-Milner logic that provides logical characterizations of some of these bisimulations.

@incollection{ROCKS,
year = 2014,
isbn = {978-3-662-45488-6},
booktitle = {Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems},
volume = 8453,
series = {Lecture Notes in Computer Science},
editor = {Remke, Anne and Stoelinga, Mariëlle},
doi = {10.1007/978-3-662-45489-3\_3},
title = {A Theory for the Semantics of Stochastic and Non-deterministic Continuous Systems},
url = {http://dx.doi.org/10.1007/978-3-662-45489-3_3},
publisher = {Springer Berlin Heidelberg},
pages = {67-86},
language = {English},
author = { Budde, Carlos E. and D'Argenio, Pedro R. and S{\'a}nchez Terraf, Pedro and Wolovick, Nicol\'as},
abstract = {The description of complex systems involving physical or biological components usually requires to model involved continuous behavior induced by variables such as time, distances, speed, temperature, alkalinity of a solution, etc. Often, such variables can be quantified probabilistically to better understand the behavior of the complex systems. For example, the arrival time of events may be considered a Poisson process or the weight of an individual may be assumed to be distributed according to a log-normal distribution. However, it is also common that the uncertainty on how these variables behave make us prefer to leave out the choice of a particular probability and rather model it as a purely non-deterministic decision, as it is the case when a system is intended to be deployed in a variety of very different computer or network architectures. Therefore, the semantics of these systems needs to be represented by a variant of probabilistic automata that involves continuous domains on the state space and the transition relation.
In this paper, we provide a survey to the theory of such kind of models. We present the theory of the so called labeled Markov processes (LMP) and its extension with internal non-determinism (NLMP). We show that in these complex domains, the bisimulation relation can be understood in different manners. We show the relation among these different definitions and try to understand the boundaries among them through examples. We also study variants of Hennessy-Milner logic that provides logical characterizations of some of these bisimulations.}
}

4. P. R. D’Argenio, N. Wolovick, P. Sánchez Terraf, and P. Celayes, “Nondeterministic Labeled Markov Processes: Bisimulations and Logical Characterization,” in QEST, Sixth International Conference on the Quantitative Evaluation of Systems, 2009, p. 11–20. Zbl 1426.68188
[ $e$-edition | BibTeX ]
@inproceedings{DWTC09:qest,
author = {D'Argenio, Pedro R. and Wolovick, Nicol\'as and S{\'a}nchez Terraf, Pedro and Celayes, Pablo},
title = {Nondeterministic Labeled {M}arkov Processes: Bisimulations
and Logical Characterization},
publisher = {IEEE Computer Society},
booktitle = {QEST, Sixth International Conference on the Quantitative Evaluation of Systems},
year = 2009,
pages = {11--20},
zbl = {1426.68188},
doi = {10.1109/QEST.2009.17},
ee = {http://doi.ieeecomputersociety.org/10.1109/QEST.2009.17},
bibsource = {DBLP, http://dblp.uni-trier.de}
}

5. D. J. Vaggione, “Representation by sheaves of lattice structures.,” in Actas del primer congreso de matemática ”Dr. Antonio A.R. Monteiro”, Bahia Blanca: Dept. de Matemática, Universidad Nacional del Sur (1991), p. 185–196. Zbl 0798.06019
[ BibTeX ]
@InCollection{zbMATH00437509,
Author = {Diego J. {Vaggione}},
Title = {{Representation by sheaves of lattice structures.}},
BookTitle = {{Actas del primer congreso de matem\'atica ''Dr. Antonio A.R. Monteiro''}},
Pages = {185--196},
Year = {1991},
Publisher = {Bahia Blanca: Dept. de Matem\'atica, Universidad Nacional del Sur},
Language = {Spanish},
MSC2010 = {06D05 06D20 06D15 06D25 08A30 18F20 06B10 06B20},
Zbl = {0798.06019}
}