Generating cooperative question-responses by means of erotetic search scenarios

The concept of cooperative question-responses as an extension of cooperative behaviours used by interfaces for databases and information systems is proposed. A procedure to generate question-responses based on question dependency and erotetic search scenarios is presented. The procedure is implemented in Prolog

An Investigation into Intuitionistic Logic with Identity

We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s propositional identity connective

The Method of Socratic Proofs Meets Correspondence Analysis

The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. In this paper it is used to consider sequent calculi with non-branching (the only exception being the rule of cut), invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions.Polish National Science Centre, grant no. 2017/26/E/HS1/00127Polish National Science Centre, grant no. 2017/25/B/HS1/0126

Functional Completeness in CPL via Correspondence Analysis

Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set (sets) of rules characterizing a two-argument Boolean function(s) to the negation fragment of classical propositional logic. The properties of soundness and completeness of the calculi are demonstrated. The proof of completeness is conducted by Kalmár's method. Most of the presented sequent-calculus rules have been obtained automatically, by a rule-generating algorithm implemented in Python. Correctness of the algorithm is demonstrated. This automated approach allowed us to analyse thousands of possible rules' schemes, hundreds of rules corresponding to Boolean functions, and to nd dozens of those invertible. Interestingly, the analysis revealed that the presented proof-theoretic framework provides a syntactic characteristics of such an important semantic property as functional completeness.Polish National Science Centre, grant no. 2017/26/E/HS1/00127Polish National Science Centre, grant no. 2017/25/B/HS1/0126

From Questions to Proofs. Between the Logic of Questions and Proof Theory

This work tackles issues lying at the intersection of question theory and reason-ing theory, leading from the issue of questions to proof-theoretical matters in broadly understood erotetic logic. Dorota Leszczyńska-Jasion consciously posi-tions her deliberations within the IEL (Inferential Erotetic Logic) paradigm, placing particular emphasis on so-called Socratic proofs. The book […] is consistent with the tradition of the logic community from which it derives, meaning the tradition of research into erotetic logic pioneered and developed in Poznań by Professor Andrzej Wiśniewski. […] At the same time, the book enriches the said tradition with ideas and solutions that have emerged over many years in the author’s own, independent investigations. This work can be expected to worthily represent the Polish logic community internationally, as an important and original contribution to the logic theory of questions and proofs

Synthetic Tableaux with Unrestricted Cut for First-Order Theories

The method of synthetic tableaux is a cut-based tableau system with synthesizing rules introducing complex formulas. In this paper, we present the method of synthetic tableaux for Classical First-Order Logic, and we propose a strategy of extending the system to first-order theories axiomatized by universal axioms. The strategy was inspired by the works of Negri and von Plato. We illustrate the strategy with two examples: synthetic tableaux systems for identity and for partial order