- Tytuł:
- The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework)
- Autorzy:
- Szmuc, Damian E.
- Tematy:
-
Relevant logics
non-transitive logics
p-matrix
weak Kleene algebra
infectious logics - Pokaż więcej
- Wydawca:
- Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
- Powiązania:
- https://bibliotekanauki.pl/articles/2033853.pdf  Link otwiera się w nowym oknie
- Opis:
- We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is defined in terms of a \(p\)-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints.
- Dostawca treści:
- Biblioteka Nauki
Artykuł