2013/01/16 by Teresa Alsinet, Alsinet, Teresa, Lluı́s Godo +1
Computer Science · Decision Sciences · #Advanced Algebra and Logic #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge #Multi-Criteria Decision Making
paper · pdf · doi:10.48550/arxiv.1301.3832
openalex publication_date 2013/01/16 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is value in the unit interval [0,1] which denotes a lower bound on the belief on A in terms of necessity measures. Belief states are modeled by possibility distributions on the set of all many-valued interpretations. In this framework, (i) we define a syntax and a semantics of the general underlying uncertainty logic; (ii) we provide a modus ponens-style calculus for a sublanguage of Horn-rules and we prove that it is complete for determining the maximum degree of possibilistic belief with which a fuzzy propositional variable can be entailed from a set of formulas; and finally, (iii) we show how the computation of a partial matching between fuzzy propositional variables, in terms of necessity measures for fuzzy sets, can be included in our logic programming system.