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14Boolean Connexive Logic and Content RelationshipStudia Logica 112 (1): 207-248. 2023.We present here some Boolean connexive logics (BCLs) that are intended to be connexive counterparts of selected Epstein’s content relationship logics (CRLs). The main motivation for analyzing such logics is to explain the notion of connexivity by means of the notion of content relationship. The article consists of two parts. In the first one, we focus on the syntactic analysis by means of axiomatic systems. The starting point for our syntactic considerations will be the smallest BCL and the smal…Read more
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15Problem wszechwiedzy logicznej. Krytyka światów nienormalnych i propozycja nowego rozwiązaniaFilozofia Nauki 27 (1): 27-48. 2018.
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16$$\varvec{Brings~It~About~That}$$ Operators Decomposed with Relating SemanticsStudia Logica 112 (3): 541-559. 2024.In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic _bringing it about that_. These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can …Read more
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17Tableaux for some deontic logics with the explicit permission operatorBulletin of the Section of Logic 51 (2): 281-295. 2022.In this paper we present a tableau system for deontic logics with the operator of explicit permission. By means of this system the decidability of the considered logics can be proved. We will sketch how these logics are semantically defined by means of relating semantics and how they provide a simple solution to the free choice permission problem. In short, these logics employ relating implication and a certain propositional constant. These two are in turn used to define deontic operators simila…Read more
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25History of Relating Logic. The Origin and Research DirectionsLogic and Logical Philosophy 30 (4). 2021.In this paper, we present the history of and the research directions in relating logic. For this purpose we will describe Epstein's Programme, which postulates accounting for the content of sentences in logical research. We will focus on analysing the content relationship and Epstein's logics that are based on it, which are special cases of relating logic. Moreover, the set-assignment semantics will be discussed. Next, the Torunian Programme of Relating Semantics will be presented; this programm…Read more
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25Free choice permission, legitimization and relating semanticsLogic Journal of the IGPL. forthcoming.In this paper, we apply relating semantics to the widely discussed problem of free choice between permitted actions or situations in normative systems. Leaving aside contexts in which the free choice principle is obviously unacceptable or uncontroversially valid, we concentrate on free choice for explicit permissions. In order to construct a formal representation of explicit permissions, we introduce a special constant, $\texttt {permit}$, which is analogous to the constant $\texttt {violation}$…Read more
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8Axiomatization of BLRI Determined by Limited Positive Relational PropertiesLogic and Logical Philosophy 1-29. forthcoming.In the paper a generalised method for obtaining an adequate axiomatic system for any relating logic expressed in the language with Boolean connectives and relating implication, determined by the limited positive relational properties is studied. The method of defining axiomatic systems for logics of a given type is called an algorithm since the analysis allows for any logic determined by the limited positive relational properties to define the adequate axiomatic system automatically, step-by-ste…Read more
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20Deontic Relationship in the Context of Jan Woleński’s Metaethical NaturalismStudia Humana 9 (3-4): 120-130. 2020.In this paper, we indicate how Jan Woleński’s non-linguistic concept of the norm allows us to clarify the deontic relationship between sentences and the given normative system. A relationship of this kind constitutes a component of the metalogic of relating deontic logic, which subjects the logical value of the deontic sentence to the logical value of the constituent sentence and its relationship with a given normative system in the accessible possible worlds.
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39Simplified Kripke-Style Semantics for Some Normal Modal LogicsStudia Logica 108 (3): 451-476. 2020.Pietruszczak (Bull Sect Log 38(3/4):163–171, 2009) proved that the normal logics K45 , KB4 (=KB5), KD45 are determined by suitable classes of simplified Kripke frames of the form ⟨W,A⟩ , where A⊆W. In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of K45. Furthermore, a modal logic is a normal extension of K45 (resp. KD45; KB4; S5) if and only if it is determined by a set consi…Read more
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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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18Axiomatization of Some Basic and Modal Boolean Connexive LogicsLogica Universalis 15 (4): 517-536. 2021.Boolean connexive logic is an extension of Boolean logic that is closed under Modus Ponens and contains Aristotle’s and Boethius’ theses. According to these theses a sentence cannot imply its negation and the negation of a sentence cannot imply the sentence; and if the antecedent implies the consequent, then the antecedent cannot imply the negation of the consequent and if the antecedent implies the negation of the consequent, then the antecedent cannot imply the consequent. Such a logic was fir…Read more
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1Rozumowanie Mistrza a determinizm, rec. z: Tomasz Jarmużek, Jutrzejsza bitwa morska. Rozumowanie Diodora Kronosa, Wydawnictwo Naukowe UMK, Toruń 2013 (review)Analiza I Egzystencja 33 109-116. 2016.
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22Tableaux for Logics of Content Relationship and Set-Assignment SemanticsLogica Universalis 16 (1-3): 195-219. 2022.In the paper, we examine tableau systems for R. Epstein’s logics of content relationship: D (Dependence Logic), DD (Dual Dependence Logic), Eq (Logic of Equality of Content), S (Symmetric Relatedness Logic) and R (Nonsymmetric Relatedness Logic) (cf. Epstein in Philos Stud 36:137–173, 1979, Epstein in Rep. Math. Logic 21:19–34, 1987, Klonowski in Logic Log Philos 30(4):579–629, 2021, Krajewski in J Non Class Logic 8:7–33, 1991). The first tableau systems for those logics were defined by Carniel…Read more
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16A post-style proof of completeness theorem for symmetric relatedness Logic SBulletin of the Section of Logic 47 (3): 201. 2018.One of the logic defined by Richard Epstein in a context of an analysis of subject matter relationship is Symmetric Relatedness Logic S. In the monograph [2] we can find some open problems concerning relatedness logic, a Post-style completeness theorem for logic S is one of them. Our paper introduces a solution of this metalogical issue.
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34Incorporating the Relation into the Language?Logic and Logical Philosophy 30 (4). 2021.In this paper we discuss whether the relation between formulas in the relating model can be directly introduced into the language of relating logic, and present some stances on that problem. Other questions in the vicinity, such as what kind of functor would be the incorporated relation, or whether the direct incorporation of the relation into the language of relating logic is really needed, will also be addressed.
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13About a New Solution to the Problem of Future Contingents (review)Logic and Logical Philosophy 26 (2): 277-281. 2017.Book Reviews: Marcin Tkaczyk, "Futura contingentia", Wydawnictwo KUL, Lublin, 2015, 450 pages, ISBN 978-83-8061-111-5.
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19Metoda tablicowa a poprawność rozumowań (review)Roczniki Filozoficzne 64 (2): 155-158. 2016.Fantastyka naukowa (ang. science fiction, w skrócie - SF) jest często przedstawianajako gatunek literacki dobrze przystosowany do spekulacji filozoficznej. SF i filozofia dzielą zainteresowanie kwestią nieśmiertelności, a ich ujęcia tego tematu można zestawić i porównać. Proponujemy tutaj zarys taksonomii różnych modeli czy wizji nieśmiertelności oferowanych przez filozofów i autorów fantastyki naukowej. Po wskazaniu istotnych rozbieżności między tymi modelami przedstawiamy sugestię, że pewne pr…Read more
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33Bayesian Propositional LogicBulletin of the Section of Logic 46 (3/4). 2017.We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w, for all w, and give some formal properties of it.
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16Tomasz Jarmużek and Marcin Tkaczyk: "Normaine logiki pozycyjne", Wydawnictwo KUL, Lublin, 2015 (review)Logic and Logical Philosophy 25 (2): 235-241. 2016.Book Reviews: Tomasz Jarmużek and Marcin Tkaczyk, Normalne logiki pozycyjne, Wydawnictwo KUL, Lublin, 2015, 202 pages, ISBN 978-838061-114-6.
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1Overview of Results Presented in "Trends in Logic XIII" (review)Logic and Logical Philosophy 26 (1): 137-142. 2017.Book Reviews: Andrzej Indrzejczak, Janusz Kaczmarek, and Michał Zawidzki, “Trends in Logic XIII. Gentzen’s and Jaśkowski’s Heritage. 80 Years of Natural Deduction and Sequent Calculi”, Wydawnictwo UŁ, Łódź, 2014, 269 pages, ISBN 978-83-7969-161-6.
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46On Logic of Strictly-Deontic Modalities. A Semantic and Tableau ApproachLogic and Logical Philosophy 29 (3). 2020.Standard deontic logic (SDL) is defined on the basis of possible world semantics and is a logic of alethic-deontic modalities rather than deontic modalities alone. The interpretation of the concepts of obligation and permission comes down exclusively to the logical value that a sentence adopts for the accessible deontic alternatives. Here, we set forth a different approach, this being a logic which additionally takes into consideration whether sentences stand in relation to the normative system …Read more
Toruń, Poland
Areas of Specialization
Deontic Logic |
Nonclassical Logics |
Logical Semantics and Logical Truth |
History of Logic |
Logic in Philosophy |