A Post-style proof of completeness theorem for symmetric relatedness Logic S

Klonowski, Mateusz

doi:10.18778/0138-0680.47.3.05

Cited by 4 publications

(5 citation statements)

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“…We define the relation of tableau consequence by referring to the concept of closure under tableau rules. 15 This is the equivalent of |= Λ for the individual logics Λ we are considering. Of course, any particular tableau consequence relation depends on the rules for a given logic used in the proof.…”

Section: Tableau Consequence Relationmentioning

confidence: 99%

“…It is important to notice that Paoli also presented results concerning not only the fragments of Epstein's logics. In[21], he presented the constructive completeness of S (for an alternative proof see[15]) and determined the limited principle of substitution of equivalent formulas for S. In cooperation with Antonio Ledda and Michele Pra Baldi, he examined in[18] various algebraic interpretations of a demodalized analytic implication understood as an implication of the logic D (cf [5]…”

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confidence: 99%

“…Examples of applications of (R R→ ), (R R¬→(1)) and (R R¬→(2)) are presented in Appendix, see Figs. 3, 10 and 11 15. The concept of closure under tableau rules was introduced in[11].…”

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confidence: 99%

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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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Section: Tableau Consequence Relationmentioning

confidence: 99%

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confidence: 99%

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Tableaux for Logics of Content Relationship and Set-Assignment Semantics

Jarmużek

Klonowski

2022

Log. Univers.

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“…1. classical mono-relating logic [see Jarmużek and Klonowski, 2021;Klonowski, 2018Klonowski, , 2019; Jarmużek and Klonowski, submitted,m] 2. fragments of classical mono-relating logic:…”

Section: The 1st Workhop On Relating Logicmentioning

confidence: 99%

“…• 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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Relating Semantics as Fine-Grained Semantics for Intensional Logics

Jarmużek

2020

Logic in High Definition

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A Post-style proof of completeness theorem for symmetric relatedness Logic S

Cited by 4 publications

References 2 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

Relating Semantics as Fine-Grained Semantics for Intensional Logics

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