Valuaciones de complejidad: un marco semántico general para lenguajes proposicionales

Jorge, Juan Pablo and Vázquez, Hernán Luis and Holik, Federico (2024) Valuaciones de complejidad: un marco semántico general para lenguajes proposicionales. [Preprint]

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Official URL: https://www.researchgate.net/publication/369830780...

Abstract

A general mathematical framework is presented, based on countable partitions of Natural Numbers,is presented [1], that allows to provide a Semantics to propositional languages. It has the particularity of allowing both the valuations and the interpretation Sets for the connectives to discriminate complexity of the formulas. This allows different adequacy criteria to be used to assess formulas associated with the same connective, but that differ in their complexity. The presented method can be adapted to an potentially infinite number of connec-tives and truth values, therefore, it can be considered a general framework to provide semantics to several of the known logic systems (eg, LC, L3 LP, FDE). The presented semantics allow to converge to different standard semantics if the separation complexity procedure is annulled. Therefore, it can be understood as a framework that allows greater precision (in complexity terms) with respect to formula satisfaction. Naturally, because of how it is built, it can be incorporated into non-deterministic semantics. The presented procedure also allows generating valuations that grant a different truth value to each formula of propositional language. As a positive side effect, our method allows a constructive proof of the equipotence between N and N^n for all Natural n.

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Creators:

Creators	Email	ORCID
Jorge, Juan Pablo	jorgejpablo@gmail.com	0000-0003-4517-8729
Vázquez, Hernán Luis	vazquez.hernan.luis@gmail.com	0000-0003-3962-901X
Holik, Federico	holik@fisica.unlp.edu.ar	0000-0002-6776-5281