Relating Semantics for Connexive Logic

In the paper, we examine tableau systems for R. Epstein’s logics of content relationship: $$\mathbf {D}$$ D (Dependence Logic), $$\mathbf {DD}$$ DD (Dual Dependence Logic), $$\mathbf {Eq}$$ Eq (Logic of Equality of Content), $$\mathbf {S}$$ S (Symmetric Relatedness Logic) and $$\mathbf {R}$$ R (Nonsymmetric Relatedness Logic) (Epstein in The semantic foundations of Logic, Springer Science + Business Media, Dordrecht, (1990), cf. Epstein in Philos Stud 36:137–173, 1979, Epstein in Rep. Math. Logic 21:19–34, 1987, Klonowski in Logic Log Philos, accepted for publication, Krajewski in J Non Class Logic 8:7–33, 1991). The first tableau systems for those logics were defined by Carnielli (Rep Math Logic 21:35–46, 1987). However, his approach has some limitations, for example, it requires a proof of functional completeness and axiomatization. Notwithstanding the first two constraints, it does not include all Epstein logics, e.g., logic $$\mathbf {Eq}$$ Eq . Unlike Carnielli’s approach, here we use set-assignment semantics to determine those logics. Since syntax and semantics of a given logic usually determine a minimal syntax and structure of a tableau system for the logic along with other properties, we propose a uniform tableau framework for the logics determined by set-assignment semantics. What distinguishes our tableau systems is that they combine the features of tableaux for propositional logics and syllogistic logics when the problem of content of propositions is analysed in tableau proofs. To denote the content of propositions in the proofs, we use generalised labels (explored in the syllogistic context in Jarmużek and Goré (In: Fitting (ed.) Landscapes in Logic, College Publications, London, accepted)).

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“…[4,5,16,17]) and by means of relating semantics (see [7], cf. [10][11][12]16,19]). 3 We focus, however, on the first approach.…”

Section: Language and Semanticsmentioning

confidence: 99%

Tableaux for Logics of Content Relationship and Set-Assignment Semantics

Jarmużek

Klonowski

2022

Log. Univers.

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“…• Boolean connexive logic [see Jarmużek and Malinowski, 2019a,b;Malinowski and Palczewski, 2021;Klonowski, 2018Klonowski, , 2021],…”

Section: The 1st Workhop On Relating Logicmentioning

confidence: 99%

Relating Logic and Relating Semantics. History, Philosophical Applications and Some of Technical Problems

Jarmużek¹,

Paoli

2021

LLP

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Here, we discuss historical, philosophical and technical problems associated with relating logic and relating semantics. To do so, we proceed in three steps. First, Section 1 is devoted to providing an introduction to both relating logic and relating semantics. Second, we address the history of relating semantics and some of the main research directions and their philosophical applications. Third, we discuss some technical problems related to relating semantics, particularly whether the direct incorporation of the relation into the language of relating logic is needed. The starting point for our considerations presented here is the 1st Workshop On Relating Logic and the selected papers for this issue.

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“…Such a class is denoted by MQ. The class of all models for L is MR. 2 In some articles on relating semantics and its connexive applications the symbol → w was used to denote implication (see [8,12]). Such a symbol was introduced in order to distinguish between relating and material implication denoted sometimes as → (cf.…”

Section: Relating Semanticsmentioning

confidence: 99%

“…In[12] Boolean connexive logic was used in the analysis of Lewis Carroll's barbershop paradox (cf. [11, pp.…”

mentioning

confidence: 99%

Axiomatization of Some Basic and Modal Boolean Connexive Logics

Klonowski

2021

Log. Univers.

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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 (i) a sentence cannot imply its negation and the negation of a sentence cannot imply the sentence; and (ii) 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 first introduced by Jarmużek and Malinowski, by means of so-called relating semantics and tableau systems. Subsequently its modal extension was determined by means of the combination of possible-worlds semantics and relating semantics. In the following article we present axiomatic systems of some basic and modal Boolean connexive logics. Proofs of completeness will be carried out using canonical models defined with respect to maximal consistent sets.

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Relating Semantics for Connexive Logic

Cited by 11 publications

References 13 publications

Tableaux for Logics of Content Relationship and Set-Assignment Semantics

Tableaux for Logics of Content Relationship and Set-Assignment Semantics

Relating Logic and Relating Semantics. History, Philosophical Applications and Some of Technical Problems

Axiomatization of Some Basic and Modal Boolean Connexive Logics

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