Title: Semantics for some non-classical possibilistic logics

Authors: Rubén Octavio Vélez-Salazar; José Ramón Enrique Arrazola-Ramírez; Iván Martínez-Ruiz

Addresses: Faculty of Physical-Mathematical Sciences, Autonomous University of Puebla, Puebla, Mexico ' Faculty of Physical-Mathematical Sciences, Autonomous University of Puebla, Puebla, Mexico ' Faculty of Physical-Mathematical Sciences, Autonomous University of Puebla, Puebla, Mexico

Abstract: Possibilistic logic was developed as an approach to automated reasoning. The standard possibilistic expressions are classical logic formulas associated with weights. Intuitionistic logic and paraconsistent logics have proved to be useful in knowledge representation, because of their constructive and inconsistent, but non-trivial nature, respectively. Possibilistic intuitionistic logic has already been defined and some of its syntactic properties have been proved. This paper continues in that direction, defining the possibilistic C_ω logic and presenting some syntactic results as well as suitable Kripke and topological semantics to both of these logics. It also provides a topological semantics for the C_ω logic via closed subsets and the closure operator.

Keywords: possibilistic logic; paraconsistent logic; intuitionistic logic; Kripke semantics; topological semantics; intermediate logic; automated reasoning; knowledge representation.

DOI: 10.1504/IJAIP.2014.065224

International Journal of Advanced Intelligence Paradigms, 2014 Vol.6 No.3, pp.191 - 213

Received: 31 May 2013
Accepted: 04 Feb 2014
Published online: 29 Oct 2014 *

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