A Reasoning System for Fuzzy Distributed Knowledge Representation in Multi-Agent Systems

Knowledge does not necessarily exist only within a single agent; it may exist collectively within a number of agents combined together (cf. the wisdom of the crowd), and this sort of knowledge is called distributed knowledge. In light of bounded rationality and uncertainty, distributed knowledge can be incomplete, and there may be gradations in the certainty of distributed knowledge, that is, knowledge may be distributed within a system of agents up to some degree of certainty only. Fagin, Halpern, Moses, and Vardi gave an axiomatic system for reasoning about distributed knowledge, and developed a special technique to prove its fundamental properties such as completeness. Here we extend their classic results so as to incorporate fuzzy distributed knowledge; in addition we prove several other properties of fuzzy modal systems such as the finite model property and Gödel-style translation theorems.