A Complete Calculus for Possibilistic Logic Programming with Fuzzy Propositional Variables
Teresa Alsinet, Lluis Godo
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.
Keywords: Possibilistic logic programming, fuzzy unification.
PS Link: http://fermat.eup.udl.es/~tracy/uai2000.ps
PDF Link: /papers/00/p1-alsinet.pdf
AUTHOR = "Teresa Alsinet
and Lluis Godo",
TITLE = "A Complete Calculus for Possibilistic Logic Programming with Fuzzy Propositional Variables",
BOOKTITLE = "Proceedings of the Sixteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-00)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2000",
PAGES = "1--10"