Some Intensional Logics Defined by Relating Semantics and Tableau Systems

Jarmużek, Tomasz; Klonowski, Mateusz

doi:10.1007/978-3-030-53487-5_3

Cited by 16 publications

(38 citation statements)

References 6 publications

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“…That is, by means of material implication. If, in turn, we allow A to be tautological, then, in result, we get one of the SDL problems which can be easily eliminated within relating deontic logic, by replacing the material implication with the relating implication, in which truth depends on the logical value of the constituent sentences and the occurrence of the relations between them (see [10], [12]). 7.…”

Section: Discussionmentioning

confidence: 99%

“…61-84, 115-143] with some particular conditions imposed on the models. A more general approach -where the starting point are models containing all binary relations specified on the set of formulas -proposed by Jarmużek and Kaczkowski [10] and explored by Jarmużek and Klonowski [12] (cf. [9]).…”

Section: Relating Deontic Logicmentioning

confidence: 99%

“…In other words, sentences should be related to the same normative system. 12 The advantage of such an approach is that it allows us to avoid SDL problems.…”

Section: Normative Inferences Metaethical Naturalism and Deontic Relationshipmentioning

confidence: 99%

“…In the paper, we limit ourselves merely to deontic logic, to the normative concepts analysed herein, while omitting what is also the subject of Jan Woleński's analyses and also find formal representations (often very close to deontic ones), that is, imperative and bonitive sentences, or more broadly: axiological ones. At the same time, we omit many formal details related to the relating deontic logic, or more broadly to the relating logic as such, see [9], [10], [12].…”

Section: Introductionmentioning

confidence: 99%

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Deontic Relationship in the Context of Jan Woleński’s Metaethical Naturalism

2020

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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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Section: Discussionmentioning

confidence: 99%

Section: Relating Deontic Logicmentioning

confidence: 99%

“…In other words, sentences should be related to the same normative system. 12 The advantage of such an approach is that it allows us to avoid SDL problems.…”

Section: Normative Inferences Metaethical Naturalism and Deontic Relationshipmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deontic Relationship in the Context of Jan Woleński’s Metaethical Naturalism

2020

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“…1 Such a semantics enables one to consider in a straightforward way various relationships that may have an impact on the interpretation of complex propositions built by various connectives (cf. [4], [5, p. 54], [6,7]). Examples of such relationships might be temporal order, content dependence or causality.…”

Section: ¬(¬A → A) ( a 2 ) (A → B) → ¬(A → ¬B) ( B 1 ) (A → ¬B) → ¬(A → B) (B2)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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Tableaux for Logics of Content Relationship and Set-Assignment Semantics

Jarmużek

Klonowski

2022

Log. Univers.

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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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Some Intensional Logics Defined by Relating Semantics and Tableau Systems

Cited by 16 publications

References 6 publications

Deontic Relationship in the Context of Jan Woleński’s Metaethical Naturalism

Deontic Relationship in the Context of Jan Woleński’s Metaethical Naturalism

Axiomatization of Some Basic and Modal Boolean Connexive Logics

Tableaux for Logics of Content Relationship and Set-Assignment Semantics

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