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.

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

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.

Ramon Jansana

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

Algebraic logic. Modal Logic. Duality theory.

Postdocs

Stefano Bonzio

Beatriu de Pinos Fellow at the Artificial Inteligence Research Institute of the CSIC.

Three-valued logics. Universal Algebra. Algebraic Logic. Logic and Probability.

Tommaso Moraschini

Beatriz Galindo Fellow (tenure track) at the Department of Philosophy of the University of Barcelona.

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

Sara Ugolini

Marie Curie Fellow 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 at the Department of Philosophy of the University of Barcelona.

Algebraic Logic. Modal and Intuitionistic Logic. Duality Theory.

Publications

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.

Opportunities

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 and consolidated postdocs, 2-3 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.

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