The processing of natural language (NL) queries and the search for semantic matches between such queries and the contents of multimedia documents necessitate powerful quantifiers that adequately model quantifying expressions in NL. In this report, we develop an axiomatic theory of fuzzy NL quantifiers and present a model of this theory which makes its systematical interpretation possible. The n...

Existing standards for crisp description logics facilitate information exchange between systems that reason with crisp ontologies. Applications with probabilistic or possibilistic extensions of ontologies and reasoners promise to capture more information, because they can deal with more uncertainties or vagueness of information. However, since there are no standards for either extension, inform...

Axiomatization of Gödel-Dummett predicate logics S2G, S3G, and PG, where PG is the weakest logic in which all prenex operations are sound, and the relationships of these logics to logics known from the literature are discussed. Examples of non-prenexable formulas are given for those logics where some prenex operation is not available. Inter-expressibility of quantifiers is explored for each of ...

During the past decade, knowledge representation research in AI has generated a class of languages called term subsumption languages (TSL), which is a knowledge representation formalism with a well-defined logic-based semanticsDue to its formal semantics, a term subsumption system can automatically infer the subsumption relationships between concepts defined in the system. However, these system...

Computing with Words is an emerging paradigm in knowledge representation and information processing. It provides a mathematical model to represent the meaning of imprecise words and phrases in natural language and introduces advanced techniques to perform reasoning on inexact knowledge. Since its introduction, there have been many studies on computing with words but mostly from the theoretical ...

PRUF--an acronym for Possibilistie 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 n...

The main idea motivating the development of fuzzy logic (FL) can be formulated as follows: Fuzzy logic is a special many-valued logic addressing the vagueness phenomenon and developing tools for its modeling via truth degrees taken from an ordered scale. It is expected to preserve as many properties of classical logic as possible. During the past 15 years, the mathematical FL has been developed...