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18Tableau Systems for Epistemic Positional LogicsBulletin of the Section of Logic 50 (2): 177-204. 2021.The goal of the article is twofold. The first one is to provide logics based on positional semantics which will be suitable for the analysis of epistemic modalities such as ‘agent... knows/beliefs that...’. The second one is to define tableau systemsfor such logics. Firstly, we present the minimal positional logic MR. Then, we change the notion of formulas and semantics in order to consider iterations of the operator of realization and “free” classical formulas. After that, we move on to weaker …Read more
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24Deduction Theorem in Congruential Modal LogicsNotre Dame Journal of Formal Logic 64 (2): 185-196. 2023.We present an algebraic proof of the theorem stating that there are continuum many axiomatic extensions of global consequence associated with modal system E that do not admit the local deduction detachment theorem. We also prove that all these logics lack the finite frame property and have exactly three proper axiomatic extensions, each of which admits the local deduction detachment theorem.
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16Ultravaluations and their Applications in $$\textsf{CPL}$$Logica Universalis 17 (3): 259-267. 2023.This paper introduces the construct of an ultravaluation inspired by the well-known ultraproduct. Basic properties and exemplary applications of this notion are shown: for compactness and definability theorems. We also use ultravaluations to check failure of compactness and undefinability.
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20Two Maximality Results for the Lattice of Extensions of $$\vdash _{\mathbf {RM}}$$Studia Logica 110 (5): 1243-1253. 2022.We use an algebraic argument to prove that there are exactly two premaximal extensions of \’s consequence. We also show that one of these extensions is the minimal structurally complete extension of the unique maximal paraconsistent extension of \. Precisely, we show that there are exactly two covers of the variety of Boolean algebras in the lattice of quasivarieties of Sugihara algebras and that there is a unique minimal paraconsistent quasivariety in that lattice. We also obtain a corollary st…Read more
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14Three Model-Theoretic Constructions for Generalized Epstein SemanticsReview of Symbolic Logic 15 (4): 1023-1032. 2022.This paper introduces three model-theoretic constructions for generalized Epstein semantics: reducts, ultramodels and $\textsf {S}$ -sets. We apply these notions to obtain metatheoretical results. We prove connective inexpressibility by means of a reduct, compactness by an ultramodel and definability theorem which states that a set of generalized Epstein models is definable iff it is closed under ultramodels and $\textsf {S}$ -sets. Furthermore, a corollary concerning definability of a set of mo…Read more
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41Tomasz Jarmużek, Marcin Tkaczyk, Normalne logiki pozycyjne, Wydawnictwo KUL, Lublin 2015, ss. 202Ruch Filozoficzny 72 (3): 173. 2017.
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15Problem wszechwiedzy logicznej. Krytyka światów nienormalnych i propozycja nowego rozwiązaniaFilozofia Nauki 27 (1): 27-48. 2018.
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19Knowability as De Re Modality: A Certain Solution to Fitch ParadoxRoczniki Filozoficzne 68 (4): 291-313. 2020.Poznawalność jako modalność de re: pewne rozwiązanie paradoksu Fitcha W artykule staramy się znaleźć nowe, intuicyjne rozwiązanie paradoksu Fitcha. Twierdzimy, że tradycyjne wyrażenie zasady poznawalności opiera się na błędnym rozumieniu poznawalności jako modalności de dicto. Zamiast tego proponujemy rozumieć poznawalność jako modalność de re. W artykule przedstawiamy minimalną logikę poznawalności, w której zasada poznawalności jest ważna, ale paradoks Fitcha już nie obowiązuje. Logikę charakt…Read more
Kraków, Lesser Poland Voivodeship, Poland
Areas of Specialization
Logical Consequence and Entailment |
Relevance Logic |
Substructural Logic |
Science, Logic, and Mathematics |
Areas of Interest
Nonclassical Logics |
Algebra |
Relevance Logic |
Substructural Logic |
Modal Logic |