Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Functional Completeness in CPL via Correspondence Analysis

100%

Leszczyńska-Jasion D., Petrukhin Y., Shangin V., Jukiewicz M.

Bulletin of the Section of Logic

2019

tom 48

nr 1

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.

The Method of Socratic Proofs Meets Correspondence Analysis

100%

Leszczyńska-Jasion D., Petrukhin Y., Shangin V.

Bulletin of the Section of Logic

2019

tom 48

nr 2

99-116

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.

Ograniczanie wyników

2 Bulletin of the Section of Logic

2 Leszczyńska-Jasion D.

2 Petrukhin Y.

2 Shangin V.

1 Jukiewicz M.

2 2019

Wyniki wyszukiwania

Functional Completeness in CPL via Correspondence Analysis

The Method of Socratic Proofs Meets Correspondence Analysis