Correspondence Analysis for Some Fragments of Classical Propositional Logic

Logica Universalis 15 (1):67-85 (2021)
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Abstract

In the paper, we apply Kooi and Tamminga’s correspondence analysis to some conventional and functionally incomplete fragments of classical propositional logic. In particular, the paper deals with the implication, disjunction, and negation fragments. Additionally, we consider an application of correspondence analysis to some connectiveless fragment with certain basic properties of the logical consequence relation only. As a result of the application, one obtains a sound and complete natural deduction system for any binary extension of each fragment in question. With the focus on exclusive disjunction we comparatively study the proposed systems. Finally, we discuss Segerberg’s systems for connectiveless and negation fragments and compare them with our systems.

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Yaroslav Petrukhin
Moscow State University

Citations of this work

Non-transitive Correspondence Analysis.Yaroslav Petrukhin & Vasily Shangin - 2023 - Journal of Logic, Language and Information 32 (2):247-273.
Two-sided Sequent Calculi for FDE-like Four-valued Logics.Barteld Kooi & Allard Tamminga - 2023 - Journal of Philosophical Logic 52 (2):495-518.

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References found in this work

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How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle (ed.), Contemporary aspects of philosophy. Boston: Oriel Press.
On notation for ordinal numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.

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