Research

Algebraic Logic

Algebraic Logic is the discipline that studies "Bridge Theorems" that allow to cross the mirror between Logic and Algebra by associating a purely semantic interpretation (such as the amalgamation property) with a given metalogical property (such as the interpolation property). This allows to study metalogical phenomena through the lenses of their semantic counterparts, which are typically amenable to the powerful methods of Universal Algebra, Lattice Theory and Category Theory. This perspective proved to be very fruitful both in the study of concrete logical systems such as Fuzzy, Modal and Intuitionistic Logics as well as in its most general formulation known as Abstract Algebraic Logic.

Mathematical Fuzzy Logic

Mathematical Fuzzy Logic is the part of Mathematical Logic that studies logical systems which extend the two-valued semantics of classical logic by allowing formulas to take value in the real unit interval. These formalisms provide a more faithful representation of those properties and predicates which, for their own nature, are perceived as graded. Several points of contact with other areas of mathematics such as functional analysis, probability theory, universal algebra, real convex geometry, have been explored and are a fruitful ongoing line of research.

Modal and Intuitionistic Logic

Modal and Intuitionistic Logics are some of the main non-classical logics. Modal Logic is known for extending the expressive power of classical (and many-valued) logic, while preserving many of its desirable computational features. On the other hand, Intuitionistic Logic is the deductive system that governs the constructive aspects of mathematics. Both these logics have a natural semantics consisting of topological Kripke frames, which proved to be a versatile tool in the modellization of problems ranging from Theoretical Computer Science and Artificial Intelligence to Philosophy and Metaphysics. In view of Duality Theory, this topological semantics is dually equivalent to a purely algebraic one which, moreover, is amenable to the methods of Algebraic Logic.

Formal Logics for Artificial Inteligence

The development of formal logics capable to simulate human-like reasoning is one of the central objective around which the logical community of Artificial Intelligence moved its first steps. Besides being a fundamental tool for analysis and the unquestionable ground for knowledge representation and reasoning, tools arising from the study of formal logic are retained to play a key role in the future of AI and, in particular for the integration between symbolic and sub-symbolic AI. This line of research aims at investigating formal logical methods for non-monotonic, causal, uncertain, preferencial reasoning and to lift them to more general and abstract levels.

Seminar on Non-classical logics

The seminar is back!


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If you are interested in receiving the news on the seminar, please contact our memeber Joan Gispert.

Next Session:


February 21st at 10:30 at the IMUB room (second floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
Algebraic and coalgebraic analysis of some many-valued modal logics, , by Wolfgang Poiger, from the University of Luxembourg.
Abstract: In this talk, we identify a class of algebraically 'well-behaved' many-valued logics, and study their modal extensions from an algebraic and coalgebraic perspective. These 'well-behaved' logics are the ones whose algebras of truth-degrees are semi-primal, for example, finitely-valued Łukasiewicz logic.
In more detail, in this talk we show how to lift algebra/coalgebra dualities (e.g., Jónsson-Tarski duality), as well as coalgebraic logics (e.g., normal or non-normal classical modal logic) to the semi-primal level. This involves a canonical way to lift endofunctors on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal algebra. We show that completeness, expressivity and finite axiomatizability of the corresponding classical logics are preserved under this lifting, and show how some of the resulting varieties of many-valued modal algebras may be axiomatized.

Previous Sessions:

  • February 9th at 10:15 at room B6 (ground floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    Pointed lattice subreducts of varieties of residuated lattices, , by Adam Prenosil, UB.
    Abstract: We shall discuss the lattice and pointed lattice subreducts of varieties of residuated lattices (RLs). While it is easy to observe that every lattice is a subreduct of an integral commutative RL, the problem of describing the pointed lattice subreducts (that is, subreducts in the lattice signature expanded by the constant 1 for the multiplicative unit) is more subtle. We axiomatize the quasivarieties of pointed lattice subreducts of integral and of semiconic commutative RLs, and show that they coincide with the subreducts of integral and of semiconic RLs. We also show that every lattice is a subreduct of a commutative cancellative RL, thus settling a basic open problem about this variety of RLs. The talk will cover some new results as well as some older ones, and list some remaining open problems.
  • Tuesday 30th at 10:30h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    On subresiduated lattices and some generalizations, , by Hernán San Martín Universidad Nacional de La Plata.
    Abstract
  • Wednesday, May 24th at 10:30h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    Bounded distributive lattices with a weak strict implication , by Sergio Celani Universidad Nacional del Centro.
    Abstract
  • Wednesday, May 17th at 10:30h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    Elementary equivalence in positive logic via prime products, by Tommaso Moraschini from the University of Barcelona.
    Abstract
  • Wednesday, May 10st at 10:00h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    Subordination algebras and closed relations between compact Hausdorff spaces, by Luca Carai from the University of Barcelona.
    Abstract
  • Wednesday, March 8st at 10:30h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    A new look at the dual discriminator, by Paolo Aglianò from the Università de Siena (Italia).
    Abstract
  • Wednesday, March 1st at 11:00h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    The complexity of the Chinese Remainder Theorem , by Miguel Campercholi from the Universidad de Córdoba(Argentina).
    Abstract
  • Wednesday, March 1st at 11:00h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    The complexity of the Chinese Remainder Theorem , by Miguel Campercholi from the Universidad de Córdoba(Argentina).
    Abstract
  • Tuesday, February 21st at 12:30h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    Algebraic Semantics of n-valued Modal Logics , by Manuela Busaniche from the Universidad Nacional del Litoral (Argentina)
    Abstract
  • Wednesday November 23rd, 10:30h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    Unification and (passive) structural completeness , by Sara Ugolini from the Institiut d'investigació en Intel·ligència Artificial (CSIC).
    Abstract: Unification problems in algebraizable logics can be studied from a purely algebraic point of view, following Ghilardi’s approach which uses the study of finitely presented and projective algebras in the (quasi)variety associated to the logic. In the first part of this talk, we show some results about projective algebras in varieties of residuated structures, and we connect them to the theory of unification of the corresponding logics.
    The second part of the talk is about the study of passive structural completeness in quasivarieties. A rule is passive for a logic L if there is no substitution making its premises a theorem for L, and L is said to be passively structurally complete if all of its passive rules are derivable in the logic. Since a rule is passive exactly when its premises are not unifiable, the study of passive structural completeness (or PSC) is connected to the study of unification problems for the logic, or equivalently for its equivalent algebraic semantics. We show a characterization for the PSC of quasivarieties, which has an interesting interpretation in quasivarieties of bounded residuated lattices in general, and of MTL-algebras in particular.
    This is joint work with Paolo Aglianò.
  • Wednesday October 5th, 10:30h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    Intuitionistic Sahlqvist theory for deductive systems, by Tommaso Moraschini from the Universitat de Barcelona.
    Abstract: In the previous session of the seminar, Sahlqvist theory was extended to the fragments of the intuitionistic propositional calculus that include the conjunction connective. In this talk, we will see how this allows us to introduce a Sahlqvist theory of intuitionistic character amenable to arbitrary protoalgebraic deductive systems. As an application, we will obtain a Sahlqvist theorem for the fragments of the intuitionistic propositional calculus that include the implication connective and for the extensions of the intuitionistic linear logic (a.k.a. full Lambek calculus with exchange). The results of this talk have been collected in a manuscript available at https://arxiv.org/pdf/2208.00691.pdf.
  • Wednesday September 28th at 10:30h in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    Sahlquist theory for fragments of intuitionistic logic., by Damiano Fornasiere from the Universitat de Barcelona.
    Abstract
  • Wednesday, September 21st at 10:30 in the IMUB classroom (2nd floor) of the Facultat de Matemàtiques i Informàtica of Universitat de Barcelona.
    Bi-Intermediate Logics of Trees and Co-trees., by Miguel Martins from the Universitat de Barcelona.
    Abstract

People

Permanent Staff

Pilar Dellunde

Full Professor at the Department of Philosophy of the Autonomous University of Barcelona.

Logics for Artificial Intelligence. Probabilistic Argumentation Frameworks in AI. Explainable AI.

Francesc Esteva

Adjunct Professor Ad Honorem at the Artificial Inteligence Research Institute (IIIA) of the CSIC.

Mathematical Fuzzy Logic. Approximate and Uncertain Reasoning and Soft computing. Algebraic logic. Modal logic.

Tommaso Flaminio

Tenured Scientist at the Artificial Inteligence Research Institute (IIIA) of the CSIC.

Mathematical Fuzzy Logic. Probability logic. Uncertain Reasoning. Algebraic logic. Modal logic.

Joan Gispert

Associate Professor at the Department of Mathematics and Computer Science of the University of Barcelona.

Many Valued and Fuzzy Logic. Algebraic Logic. Universal Algebra.

Lluís Godo

Research Professor at the Artificial Intelligence Research Institute (IIIA) of the CSIC.

Possibilistic logic. Mathematical Fuzzy Logic. Similarity-based reasoning. Argumentation systems. Multi-Agent systems.

Tommaso Moraschini

Associate Professor at the Department of Philosophy of the University of Barcelona.

Algebraic Logic. Modal and Intuitionistic Logic. Duality Theory. Universal Algebra.

Postdocs

Adam Prenosil

Beatriu de Pinos fellow at the Department of Philosophy of the University of Barcelona.

Algebraic logic. Universal algebra. Residuated lattices. Paraconsistent Logic.

Sara Ugolini

Ramon y Cajal Fellow (tenure track) at the Artificial Inteligence Research Institute of the CSIC.

Algebraic Logic. Mathematical Fuzzy Logic. Universal Algebra. Uncertain Reasoning.

Amanda Vidal

Marie Curie Fellow at the Artificial Inteligence Research Institute of the CSIC.

Formal logic in AI. Mathematical Fuzzy Logic. Modal Logic. Complexity theory in non-classical logics.

Students

Damiano Fornasiere

PhD Fellow of J. Gispert and T. Moraschini at the UB.

Algebraic Logic. Modal and Intuitionistic Logic. Duality Theory.

Valeria Giustarini,

PhD fellow of T. Moraschini and S. Ugolini at the IIIA - CSIC and the UB.

Algebraic Logic, Non-classical Logic, Universal Algebra.

Miriam kurtzhals

PhD fellow of L. Carai (Milano U.) and T. Moraschini at the UB.

Algebraic Logic. Modal and Intuitionistic Logic. Duality Theory. Universal Algebra.

Francesco Manfucci

Master student of S. Ugolini at the University of Siena and JAE intro fellow at the IIIA- CSIC.

Algebraic Logic. Mathematical Fuzzy Logic. Universal Algebra.

Miguel Martins

PhD fellow of J. Gispert and T. Moraschini and the UB.

Algebraic logic. Modal and (bi-)intuitionistic logic. Duality theory.

Publications

2022

Journal Papers

Indexed Proceedings & Book Chapters

  • E. A. Corsi, T. Flaminio, H. Hosni. Towards a unified view on logics for un- certainty. In Proceedings of SUM’22. Lecture Notes in Artificial Intelligence. 2022.e Forthcoming
  • T. Flaminio, A. Gilio, L. Godo, G. Sanfilippo. Compound conditionals as random quantities and Boolean algebras. Proceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning – KR’22: 141–151, 2022.
  • T. Flaminio, A. Gilio, L. Godo, G. Sanfilippo. Canonical extensions of conditional probabilities and compound conditionals. Proceedings of IPMU’22. Communications in Computer and Information Science 1602: 584–597, 2022.
  • T. Flaminio, L. Godo, P. Menchón, R. O. Rodríguez (In Press). Algebras and relational frames for Gödel modal logic and some of its extensions. M. Coniglio, E. Koubychkina, D. Zaitsev (Eds.), Many-valued Semantics and Modal Logics: Essays in Honour of Yuriy Vasilievich Ivlev. Springer (Also as CoRR, abs/2110.02528). Forthcoming.
  • T. Flaminio, L. Godo, P. Menchón, R.O. Rodriguez. Rotations of Gö del algebras with modal operators. Proceedings of IPMU’22. Communications in Computer and Information Science 1601: 676–688, 2022.
  • T. Flaminio, L. Godo, S. Ugolini. An approach to inconsistency-tolerant reasoning about probability based on Łukasiewicz logic. In Proceedings of SUM’22. Lecture Notes in Artificial Intelligence. 2022. Forthcoming.

2021

Journal Papers

Indexed Proceedings & Book Chapters

2020

Journal Papers

Indexed Proceedings & Book Chapters

2019

Journal Papers

Indexed Proceedings & Book Chapters

2018

Journal Papers

Indexed Proceedings & Book Chapters

2017

Journal Papers

Indexed Proceedings & Book Chapters

Projects

Running projects

  • The Geometry of Non-Classical Logics

    I+D+i research project funded by the Ministry of Science and Innovation of Spain.
    2020 - 2023
    Principal Investigator: Tommaso Moraschini.

  • ISINC: Inference Systems for Inconsistent Information: logical foundations

    I+D+i research project funded by the Ministry of Science and Innovation of Spain.
    2020 - 2023
    Principal Investigator: Lluís Godo.

  • SuMoL. Substructural Modal Logics for Knowledge Representation

    I-Link project funded by the Spanish National Research Council (CSIC).
    2020 - 2022
    Principal Invertigator: Tommaso Flaminio.

  • Mosaic. Modalities in Substructural Logics: Theory, Methods and Applications

    Marie Skłodowska-Curie RISE project funded by the Horizon 2020 of the European Union.
    2021 - 2024
    Principal Invertigator: Tommaso Flaminio.

  • Non-Classical Logics Research Group

    Funded by the Agency for Management of University and Research Grants of the Government of Catalonia.
    2017 - 2021.
    Principal Invertigator: Joan Gispert.

Previous projects

  • Applied Philosophy for the Value-Based Design of Social Network Apps

    Project RECERCAIXA, funded by La Caixa Foundation.
    2019 - 2021
    Principal Investigator: Pilar Dellunde.

  • RASO: Razonamiento, Satisfacción y Optimización

    I+D+i research project funded by the Ministry of Science and Innovation of Spain.
    2016 - 2020
    Principal Investigator: Lluís Godo.

  • SYSMICS. Syntax Meets Semantics: Methods, Interactions, and Connections in Substructural logics

    Marie Skłodowska-Curie RISE project funded by the Horizon 2020 of the European Union.
    2016 - 2019.
    Coordinating researcher at the University of Barcelona: Ramon Jansana.
    Coordinating researcher at the Artificial Inteligence Research Institute (CSIC): Lluis Godo.
    Coordinating researcher at the Autonomous University of Barcelona: Pilar Dellunde.

  • Algebraic Logic and Non-Classical Logics

    I+D+i research project funded by the Ministry of Economy and Competitiveness of Spain.
    2017 - 2019.
    Principal Invertigator: Ramon Jansana.

Funding

There is a number of Master, PhD, postdoctoral and tenure track schemes available for researchers interested in coming to work with our group, including the following.

Master

CSIC JAE-ICU and Master grants at the UB. To apply, please contact in advance a member of our research group from the IIIA-CSIC or the UB.

PhD

You can find general information on PhDs the UB here . There are grants at national (FPU), regional (FI) and university (APIF) level, as well as grants associated to research projects (FPI) which will be publicized here when available.

Postdocs

Funding opportunities include the Juan de la Cierva national scheme (for young postdocs, 2 years), the Beatriu de Pinos Catalan scheme cofunded by the European Union (3 years), and Marie Skłodowska-Curie Actions funded by the European Union (2 years).

Tenure Traks

Funding opportunities include the Ramon y Cajal national scheme (4 years), the Beatriz Galindo national scheme (4 years), and the Serra Hunter Catalan scheme (4 years).

Teaching

The Barcino research group gravitates around Bachelor, Master and PhD programmes devoted to logic and its applications to computer science.

The Bachelor in Artificial Intelligence of the Autonomous University of Barcelona offers training in the rapidly evolving field of AI where logic finds a natural application as a tool for explaining algorithmic based decisions.

The Master in Pure and Applied Logic of the University of Barcelona centers on some of the most influential areas of mathematical logics including Set Theory, Model Theory, Non-Classical Logics, Algebraic Logic, Computability Theory and Proof Theory.

Lastly, the Univeristy of Barcelona offers a PhD programme in Mathematical Logic. For information, please check the PhD Program in Mathematics and Computer Science.

Recent & Upcoming Events

2024

"Topology, Algebra and Categories in Logic"

We are excited to announce the group is organizing the 2024 edition of the TACL conference, to be held in Barcelona in July 2024.

"Conditionals 2024"

Members of the group are organizing the first edition of the Conditionals meeting, to be held in Barcelona in October 2024.

2022

"Non-classical logic days"

During October 11th and 14th, 2022, Barcino is organizing a workshop in non-classical logics, where colleagues from the Institute of Computer Science from the Czech Academy of Sciences, and from the Universidad Nacional de La Plata (Argentina) will talk. The programme can be consulted here.

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