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My research is in the field of logic, a broad scientific discipline located in a fascinating intersection of several distinct areas, which has a lot to do with one of the defining human traits: our ability to reason correctly. In particular, I am interested in reasoning with graded properties, which are ubiquitious in rational action and discourse. This research mostly pertains to mathematics, with the study of several levels of logical formalism (propositional, modal, first- and higher-order predicate logics) and their syntactical and semantical aspects. Moreover, the topic has clear connections to philosophy, linguistics, and cognitive science, and a potential for applications in computer science and artificial intelligence. For more information, you can consult the Stanford Encyclopedia entry on fuzzy logic (cowritten with Petr Cintula and Chris Fermüller) or the three volumes of the Handbook of Mathematical Fuzzy Logic (coedited with Petr Hájek, Petr Cintula, and Chris Fermüller).
More generally, I am interested in the study of non-classical logics: reasoning systems that, in a variety of ways, go beyond the traditional paradigm of binary analysis in terms of true and false. Together with Petr Cintula, we have proposed a general approach to logics with implication, in the style of abstract algebraic logic. We have collected the results of a series of joint articles in a book, Logic and Implication. As we wrote on the back cover, "This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions."
Similarly, with Guillermo Badia, we are pursuing a systematic study of model-theoretic aspects and applications of non-classical predicate logics. You may check the forthcoming Dagstuhl Seminar on Semirings in Databases, Automata, and Logic!
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