PRUF—a meaning representation language for natural languages

PRUF—an acronym for Possibilistic Relational Universal Fuzzy—is a meaning representation language for natural languages which departs from the conventional approaches to the theory of meaning in several important respects. First, a basic assumption underlying PRUF is that the imprecision that is intrinsic in natural languages is, for the most part, possibilistic rather than probabilistic in nature. Thus, a proposition such as “Richard is tall” translates in PRUF into a possibility distribution of the variable Height (Richard), which associates with each value of the variable a number in the interval [0,11 representing the possibility that Height (Richard) could assume the value in question. More generally, a proposition, p , translates into a procedure, P, which returns a possibility distribution, Π p , with P and Π p representing, respectively, the meaning of p and the information conveyed by p . In this sense, the concept of a possibility distribution replaces that of truth as a foundation for the representation of meaning in natural languages. Second, the logic underlying PRUF is not a two-valued or multivalued logic, but a fuzzy logic, FL, in which the truth-values are linguistic, that is, are of the form true, not true, very true, more or less true, not very true , etc., with each such truth-value representing a fuzzy subset of the unit interval. The truth-value of a proposition is defined as its compatibility with a reference proposition, so that given two propositions p and r, one can compute the truth of p relative to r . Third, the quantifiers in PRUF—like the truth-values—are allowed to be linguistic, i.e. may be expressed as most, many, few, some, not very many, almost all, etc. Based on the concept of the cardinality of a fuzzy set, such quantifiers are given a concrete interpretation which makes it possible to translate into PRUF propositions exemplified by “Many tall men are much taller than most men,” “All tall women are blonde is not very true,” etc. The translation rules in PRUF are of four basic types: Type I—pertaining to modification; Type II—pertaining to composition; Type III—pertaining to quantification; and Type IV—pertaining to qualification and, in particular, to truth qualification, probability qualification and possibility qualification. The concepts of semantic equivalence and semantic entailment in PRUF provide a basis for question-answering and inference from fuzzy premises. In addition to serving as a foundation for approximate reasoning, PRUF may be employed as a language for the representation of imprecise knowledge and as a means of precisiation of fuzzy propositions expressed in a natural language.