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

Chlebowski, Szymon

doi:10.1007/s11225-017-9754-8

Cited by 7 publications

(4 citation statements)

References 12 publications

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“…Negri and Von Plato [25] provide the method of the transformation of the axioms into sequent rules. Being applied to a particular logic this method may produce the left rules only, as it was, for example, in the case of Suszko's [38] logic SCI which was considered by Chlebowski [10]. Interestingly, Chlebowski presented also a version of sequent calculus for SCI with the right rules only.…”

Section: Then a Truth Table Entrymentioning

confidence: 99%

The Logic of Internal Rational Agent

Petrukhin

2021

AJL

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In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent \textbf{LRA} \cite{LRA}. We call our logic $ \bf LIRA$ (Logic of Internal Rational Agency). In contrast to \textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic \cite{ZS}. This logic may be useful in a situation when according to an agent's point of view (i.e. internal point of view) her/his reasoning is rational, while from the external one it might be not the case. One may use \textbf{LIRA}, if one wants to reconstruct an agent's way of thinking, compare it with respect to the real state of affairs, and understand why an agent thought in this or that way. Moreover, we discuss Kubyshkina and Zaitsev's necessity and possibility operators for \textbf{LRA} definable by means of four-valued Kripke-style semantics and show that, due to two negations (as well as their combination) of \textbf{LRA}, two more possibility operators for \textbf{LRA} can be defined. Then we slightly modify all these modalities to be appropriate for $\bf LIRA$. Finally, we formalize all the truth-functional $ n $-ary extensions of the negation fragment of $\bf LIRA$ (including $\bf LIRA$ itself) as well as their basic modal extension via linear-type natural deduction systems.

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Section: Then a Truth Table Entrymentioning

confidence: 99%

The Logic of Internal Rational Agent

Petrukhin

2021

AJL

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“…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%

“…For details of Chlebowski's systems, we refer the reader to [14]. Figure 1 presents a closed G SCI -derivation of the formula (p 1 ≡ p 2 ) → (p 1 → p 2 ), which is an instance of the axiom schema (≡ 3 ), while, in Figure 2, we show how to prove in G SCI the formula…”

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

Cited by 7 publications

References 12 publications

The Logic of Internal Rational Agent

The Logic of Internal Rational Agent

Deduction in Non-Fregean Propositional Logic SCI

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

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