The Method of Socratic Proofs Meets Correspondence Analysis

Leszczyńska-Jasion, Dorota; Petrukhin, Yaroslav; Shangin, Vasilyi

doi:10.18778/0138-0680.48.2.02

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…Correspondence analysis was developed by Kooi and Tamminga [18] in order to formalize some three-valued logics. One may find in [19,20] a survey of the current stage of the development of correspondence analysis. We just mention that for LRA it was applied in [27].…”

Section: Natural Deduction For Liramentioning

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: Natural Deduction For Liramentioning

confidence: 99%

The Logic of Internal Rational Agent

Petrukhin

2021

AJL

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Non-transitive Correspondence Analysis

Petrukhin

Shangin

2022

J of Log Lang and Inf

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The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic $${\mathbf{NC}}_{\mathbf{3}}$$ NC 3 . As a result, for each binary extension of $${\mathbf{NC}}_{\mathbf{3}}$$ NC 3 , we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining n-sequent proof systems for any n-valent logic with deterministic or non-deterministic matrices is not applicable to $${\mathbf{NC}}_{\mathbf{3}}$$ NC 3 and its binary extensions.

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Correspondence Analysis for Some Fragments of Classical Propositional Logic

Petrukhin

Shangin

2021

Log. Univers.

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The Method of Socratic Proofs Meets Correspondence Analysis

Cited by 3 publications

References 23 publications

The Logic of Internal Rational Agent

The Logic of Internal Rational Agent

Non-transitive Correspondence Analysis

Correspondence Analysis for Some Fragments of Classical Propositional Logic

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