- Tytuł:
- Functional Completeness in CPL via Correspondence Analysis
- Autorzy:
-
Leszczyńska-Jasion, Dorota
Petrukhin, Yaroslav
Shangin, Vasilyi
Jukiewicz, Marcin - Powiązania:
- https://bibliotekanauki.pl/articles/749866.pdf
- Data publikacji:
- 2019
- Wydawca:
- Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
- Tematy:
-
correspondence analysis
invertible rules
classical propositional logic
functional completeness
sequent calculus
automated deduction
automated rules generation - Opis:
- 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.
- Źródło:
-
Bulletin of the Section of Logic; 2019, 48, 1
0138-0680
2449-836X - Pojawia się w:
- Bulletin of the Section of Logic
- Dostawca treści:
- Biblioteka Nauki
Artykuł