Research focus

Our aim is to develop and apply non-classical logics for reasoning, in both natural and artificial scenarios, with real-life information, which is often uncertain, graded, or even contradictory and changing in time.

More specifically, we focus on the study of (abstract) algebraic logic, mathematical fuzzy logic, substructural, relevant, modal and paraconsistent logics, developing dynamic and non-monotonic frameworks, and studying complexity problems of these logics.

Current research projects

• Non-classical Logical Models of Information Dynamics. Czech Science Foundation, 2018-2020.
• The project aims at developing and studying dynamic logics based on non-classical logic.
• Predicate graded logics and their applications to computer science. Czech Science Foundation, 2017-2019.
• Joint project with Institute of Information Theory and Automation of the Czech Academy of Sciences with the goal to develop predicate graded logics by giving them solid mathematical foundations and applying the achieved results to three particular computer science problems involving graded notions: management of uncertainty, valued constraint satisfaction problems, and modelling of coalition games.
• Reasoning with Graded Properties. Czech Science Foundation, 2018-2020.
• Joint project with Institute of Information Theory and Automation of the Czech Academy of Sciences with the goal to develop a logic-based theory of reasoning with graded properties: to provide a conceptual study of the different kinds of such properties, new solutions to sorites paradoxes, comparison with linguistic graded theories, and a framework for counterfactual and defeasible reasoning.

Past research projects are listed here.

Monographs and edited volumes

• P. Cintula, P. Hájek, C. Fermüller, C. Noguera. Handbook of Mathematical Fuzzy Logic (in three volumes). Volume 37, 38, and 58 of Studies in Logic, Mathematical Logic and Foundations. College Publications, London, 2011, 2015.
• P. Hájek. Metamathematics of Fuzzy Logic. Kluwer, 1998.

Notable recent publications

• P. Cintula, J. Gil Férez, T. Moraschini, F. Paoli. An abstract approach to consequence relations. Forthcoming in The Review of Symbolic Logic,
• I. Sedlár, V. Punčochář. From positive PDL to its non-classical extensions. Forthcoming in the Logic Journal of the IGPL.
• T. Moraschini. On the complexity of the Leibniz hierarchy. Forthcoming in the Annals of Pure and Applied Logic, 2019.
• T. Moraschini, J.G. Raftery and J.J. Wannenburg. Varieties of De Morgan monoids: Covers of atoms. Forthcoming in the Review of Symbolic Logic, 2019.
• T. Moraschini, J.G. Raftery and J.J. Wannenburg. Epimorphisms, definability and cardinalities. Forthcoming in Studia Logica, 2019.
• T. Moraschini, J.G. Raftery and J.J. Wannenburg. Varieties of De Morgan monoids: Minimality and irreducible algebras. Journal of Pure and Applied Algebra, Volume 223, Issue 7, pages 2780-2803, 2019.
• T. Moraschini. A logical and algebraic characterization of adjunctions between generalized quasi-varieties. Journal of Symbolic Logic, Volume 83, Issue 3, pages 899-919, 2018.
• M. Bílková, G. Greco, A. Palmigiano, A. Tsimoulis and N. Wijnberg The logic of resources and capabilities. Review of Symbolic Logic, Volume 11, Issue 2, Pages 371-410, 2018.
• T. Moraschini. A study of truth predicates in matrix semantics. Review of Symbolic Logic, Volume 11, Issue 4, Pages 780-804, 2018.
• G. Bezhanishvili, T. Moraschini, J. Raftery. Epimorphisms in varieties of residuated structures. Journal of Algebra, Volume 492, pages 185-211, 2017.
• T. Moraschini. A computational glimpse at the Leibniz and Frege hierarchies. Annals of Pure and Applied Logic, Volume 169, Issue 1, Pages 1-20, 2017.
• Z. Haniková, P. Savický. Term satisfiability in FLew-algebras. Theoretical Computer Science, Volume 631, Pages 1-15, 2016.
• M. Bílková, O. Majer, M. Peliš. Epistemic logics for sceptical agents. Journal of Logic and Computation, Volume 26, Issue 6, Pages 1815-1841.
• I. Sedlár. Epistemic extensions of modal distributive substructural logics. Journal of Logic and Computation, Volume 26, Issue 6, Pages 1787-1813.
• T. Moraschini. The semantic isomorphism theorem in Abstract Algebraic Logic. Annals of Pure and Applied Logic, Volume 167, Issue 12, Pages 1298-1331, 2016.
• P. Cintula, C. Noguera. A Henkin-style proof of completeness for first-order algebraizable logics. Journal of Symbolic Logic, Volume 80, Issue 1, Pages 341-358, 2015.
• K Chvalovský. Undecidability of consequence relation in Full Non-associative Lambek Calculus. Journal of Symbolic Logic, Volume 80, Issue 2, Pages 567-586, 2015.
• R. Horčík. Word problem for knotted residuated lattices. Journal of Pure and Applied Algebra, Volume 219, Issue 5, Pages 1548-1563, 2015