The Method of Socratic Proofs for Modal Propositional Logics: K5, S4.2, S4.3, S4F, S4R, S4M and G

Abstract

The aim of this paper is to present the method of Socratic proofs for seven modal propositional logics: K5, S4.2, S4.3, S4M, S4F, S4R and G. This work is an extension of [10] where the method was presented for the most common modal propositional logics: K, D, T, KB, K4, S4 and S5.Keywords: modal propositional logics, extensions of logic S4, the method of Socratic proofs, logic of questions, Inferential Erotetic Logic.

Generating cooperative question-responses by means of erotetic search scenarios

“…11 It is worth to mention that also other techniques of cooperative answering might be used with e-scenarios (after their execution, see [13]). …”

“…A theorem-prover (an implementation of the method of Socratic proofs for Classical Propositional Logic described in [21]) written in Prolog by Albrecht Heefer is available at: http://logica.ugent.be/albrecht/ socratic.html. A theorem-prover (an implementation of the method of Socratic proofs for 15 basic propositional modal logics described in [10,11]) written in Prolog by Albrecht Heefer and Dorota Leszczynska-Jasion, is available at: http://logica. ugent.be/albrecht/socratic-modal.htm.…”

Rasiowa–Sikorski Deduction Systems with the Rule of Cut: A Case Study

“…An erotetic calculus is a set of rules transforming such questions; at the same time, it constitutes a deduction system for the underlying logic. The method has been described for classical [12,37,39] and various non-classical logics [14,27,28,40].…”

Dual Erotetic Calculi and the Minimal $${\mathsf{LFI}}$$ LFI

“…If the questions are constructed in such a way that they concern the consequence relation in L, then the method becomes in fact a proof-method for L. The method has been adjusted to CPL [26], to First-Order Logic [28], to the propositional parts of CLuN and CLuNs [30], to a large class of propositional modal logics [13][14][15], and to propositional intuitionistic logic [21]. Yet still, an erotetic calculus remains a calculus of questions.…”