A sequence formalization for SCI

Wasilewska, Anita

doi:10.1007/bf02282483

Cited by 5 publications

(6 citation statements)

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“…The logic SCI is decidable, while the systems in question are not decision procedures for SCI as, in particular, they may generate infinite trees. Although there is a decision procedure for SCI based on G SCI -system, as shown in [13], but a procedure described in [13] contains external machinery that is not a part of the system itself, so it provides rather another proof for decidability of SCI than a decision procedure itself. Hence, further research on deduction systems for SCI should focus on seeking its decision procedure.…”

Section: Discussionmentioning

confidence: 99%

“…The first sequent calculus for the logic SCI was built by Michaels (see [12]); then, it has been simplified by Wasilewska in [13]) and modified by Chlebowski in [14]. Below, we present the basics of a sequent calculus for SCI, which is a version of systems from [12] and [13] adjusted to the well known sequent axiomatization of classical propositional logic.…”

Section: Sequent-style Formalizations For Scimentioning

confidence: 99%

“…The deduction system for SCI was originally defined in a Hilbert-style. Since then, some other systems for SCI have been proposed: Gentzen sequent calculus ( [12][13][14]) and a dual tableau system ([15,16]). The aim of the paper is to present a new dual tableau system for SCI, which is suitable for automated reasoning in SCI.…”

Section: Introductionmentioning

confidence: 99%

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Deduction in Non-Fregean Propositional Logic SCI

Golińska-Pilarek

Welle

2019

Axioms

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We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI. The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side, SCI is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for SCI known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for SCI and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper.

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Section: Discussionmentioning

confidence: 99%

Section: Sequent-style Formalizations For Scimentioning

confidence: 99%

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Deduction in Non-Fregean Propositional Logic SCI

Golińska-Pilarek

Welle

2019

Axioms

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“…In the original works by Suszko and Bloom the deduction system for SCI was defined in the Hilbert style [1,2]. Sound and complete deduction systems which are better suited for automated theorem proving were constructed later: Gentzen sequent calculi [18,22,23,3] and dual tableau systems [5,19,10]. A detailed presentation of all of them can be found in [10].…”

Section: Introductionmentioning

confidence: 99%

Tableau-based Decision Procedure for Non-Fregean Logic of Sentential Identity

Golińska-Pilarek

Huuskonen

Zawidzki

2021

Automated Deduction – CADE 28

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Sentential Calculus with Identity ($$\mathsf {SCI}$$ SCI ) is an extension of classical propositional logic, featuring a new connective of identity between formulas. In $$\mathsf {SCI}$$ SCI two formulas are said to be identical if they share the same denotation. In the semantics of the logic, truth values are distinguished from denotations, hence the identity connective is strictly stronger than classical equivalence. In this paper we present a sound, complete, and terminating algorithm deciding the satisfiability of $$\mathsf {SCI}$$ SCI -formulas, based on labelled tableaux. To the best of our knowledge, it is the first implemented decision procedure for $$\mathsf {SCI}$$ SCI which runs in NP, i.e., is complexity-optimal. The obtained complexity bound is a result of dividing derivation rules in the algorithm into two sets: decomposition and equality rules, whose interplay yields derivation trees with branches of polynomial length with respect to the size of the investigated formula. We describe an implementation of the procedure and compare its performance with implementations of other calculi for $$\mathsf {SCI}$$ SCI (for which, however, the termination results were not established). We show possible refinements of our algorithm and discuss the possibility of extending it to other non-Fregean logics.

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“…These rules make use of substitution of identical subformulas and deriving classical equivalence from identity. A simplified account of this approach is given in [12]. In this instance the system is purely right-sided, with all sequents having empty antecedents.…”

Section: Introductionmentioning

confidence: 99%

Sequent Calculi for $${\mathsf {SCI}}$$ SCI

Chlebowski

2017

Stud Logica

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Abstract.In this paper we are applying certain strategy described by Negri and Von Plato (Bull Symb Log 4(04): [418][419][420][421][422][423][424][425][426][427][428][429][430][431][432][433][434][435] 1998), allowing construction of sequent calculi for axiomatic theories, to Suszko's Sentential calculus with identity. We describe two calculi obtained in this way, prove that the cut rule, as well as the other structural rules, are admissible in one of them, and we also present an example which suggests that the cut rule is not admissible in the other.

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A sequence formalization for SCI

Cited by 5 publications

References 1 publication

Deduction in Non-Fregean Propositional Logic SCI

Deduction in Non-Fregean Propositional Logic SCI

Tableau-based Decision Procedure for Non-Fregean Logic of Sentential Identity

Sequent Calculi for $${\mathsf {SCI}}$$ SCI

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