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A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4

100%

Robles G., López S. M., Blanco J. M., Recio M. M., Paradela J. R.

Bulletin of the Section of Logic

2016

tom 45

nr 2

The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.

The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework)

88%

Szmuc D. E.

Bulletin of the Section of Logic

2021

tom 50

nr 4

421-453

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.

Ograniczanie wyników

2 Bulletin of the Section of Logic

1 Blanco J. M.

1 López S. M.

1 Paradela J. R.

1 Recio M. M.

1 Robles G.

1 Szmuc D. E.

1 2021

1 2016

Wyniki wyszukiwania

A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4

The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework)