I am developing non-classical logics using algebraic methods with primary focus on developement of a uniform theory which relates abstract notions of connectives in propositional logics (disjunction, implication, and negation) with the corresponding characteristic sets of formulas (prime, semilinear, and maximally consistent). An important part of this investigation resides in study of logics which allows for infinitely-long proofs (the so-called infinitary logics).

Currently, together with Adam Přenosil, we are preparing a series of papers on a new class of logics that generalize the one of protoalgebraic logics. We call this logics protonegational (particular examples are the negation fragments of protoalgebraic logics). We argue that these logics, which to some degree retain all the important properties of protoalgebraic logics, are the right framework to study notions like inconsistency, inconsistency lemmas (recently introduced by J. Raftery), negation, or semisimplicity. As an application of the general theory we present a syntactical explanation for Glivenko-like theorems. Most of the results can be already found in my thesis (see chapter 6).

We are also preparing a new project driven by applications in portfolio management in economics. We intend to combine the two layer logical syntax for probability modeling with logics for preferential modeling to capture, in logical terms, the structure of the recent contribution to the theory of stochastic orderings invented by M. Pištěk. Who proposed a particular solution to the Steinhaus-Trybula paradox.

Papers

• A New Hierarchy of Infinitary Logics in Abstract Algebraic Logic. Studia Logica 105(3), pp. 521–551, 2017. (with C. Noguera) (pdf) (link)

• Extension Properties and Subdirect Representation in Abstract Algebraic Logic. Studia Logica 106(6), pp. 1065–1095, 2018 . (with C. Noguera) (pdf) (link)

• Lindenbaum and Pair Extension Lemma in Infinitary Logics. WoLLIC 2018, pp. 130­–144 . (with M. Bílková and P. Cintula) (pdf) (link)

• Completely Separable MAD families and the Modal Logic of βω. Accepted t o Journal of Symbolic Logic 2020 (with J. Verner) (pdf)(DOI)

• The Algebraic Significance of Weak Excluded Middle Laws. Accepted to Mathematical Logic Quaterly 2022 (with J. Raftery and T. Moraschini)

Preprints

• Semisimplicity, the excluded middle, and Glivenko theorems. Submitted (with A.Přenosil) (preprint)

PhD Thesis

• Abstract Study of Completeness in Infinitary Logics. 2018 (pdf)