Correspondence Analysis for Some Fragments of Classical Propositional Logic

Abstract

In the paper, we apply Kooi and Tamminga’s correspondence analysis (that has been previously applied to some notable three- and four-valued logics) 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.

Non-transitive Correspondence Analysis

“…Table2in the latter's paper(Ripley, 2018) systematizes a dozen definitions of transitivity including the Weirian one which is explicitly highlighted in footnote 4 there.5 Note that the term itself is due toKooi and Tamminga (2012), though it isn't to be confused with the homonymous statistical data analysis method(Hirschfeld, 1935).6 Functional completeness in classical logic is studied via applying CA to its negation fragment(Leszczyńska-Jasion et al, 2019a). CA is applied to other functionally incomplete fragments of it inPetrukhin and Shangin (2021).…”