## Research team

• Guillermo Incatasciato
• Martín Moroni
• Mauricio Tellechea (Assistant Professor)
• Pablo Ventura
• Gonzalo Zigarán

## Recent journal articles

1. J. Pachl and P. Sánchez Terraf, “Semipullbacks of labelled Markov processes,” arXiv:1706.02801 1706.02801 (2020). To be published in Logical Methods in Computer Science.
[ arXiv | 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 = {ArXiv e-prints},
archiveprefix = {arXiv},
eprint = {1706.02801},
volume = {1706.02801},
primaryclass = {math.PR},
keywords = {Mathematics - Probability, Computer Science - Logic in Computer Science, 28A35, 28A60, 68Q85, F.4.1, F.1.2},
year = 2020,
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
note = {To be published in Logical Methods in Computer Science},
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.}
}

2. 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.}
}

3. 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}
}

4. 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}
}

## Recent conference papers

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)}
}