The Method of Socratic Proofs Meets Correspondence Analysis

Dorota Leszczyńska-Jasion; Yaroslav Petrukhin; Vasilyi Shangin

Bulletin of the Section of Logic (2019)

  • Volume: 48, Issue: 2, page 99-116
  • ISSN: 0138-0680

Abstract

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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.

How to cite

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Dorota Leszczyńska-Jasion, Yaroslav Petrukhin, and Vasilyi Shangin. "The Method of Socratic Proofs Meets Correspondence Analysis." Bulletin of the Section of Logic 48.2 (2019): 99-116. <http://eudml.org/doc/295561>.

@article{DorotaLeszczyńska2019,
abstract = {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.},
author = {Dorota Leszczyńska-Jasion, Yaroslav Petrukhin, Vasilyi Shangin},
journal = {Bulletin of the Section of Logic},
keywords = {Socratic proofs; correspondence analysis; invertible rule; inferential erotetic logic; classical propositional logic; sequent calculus},
language = {eng},
number = {2},
pages = {99-116},
title = {The Method of Socratic Proofs Meets Correspondence Analysis},
url = {http://eudml.org/doc/295561},
volume = {48},
year = {2019},
}

TY - JOUR
AU - Dorota Leszczyńska-Jasion
AU - Yaroslav Petrukhin
AU - Vasilyi Shangin
TI - The Method of Socratic Proofs Meets Correspondence Analysis
JO - Bulletin of the Section of Logic
PY - 2019
VL - 48
IS - 2
SP - 99
EP - 116
AB - 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.
LA - eng
KW - Socratic proofs; correspondence analysis; invertible rule; inferential erotetic logic; classical propositional logic; sequent calculus
UR - http://eudml.org/doc/295561
ER -

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