A multi-valued epistemic logi

In the last decade there has been a resurgence of work on epistemic logic in artificial intelligence to alleviate the problem of logical omniscience. Among them were the logic of implicit and explicit belief and the logic of awareness. Although these logics have surface dissimilarities, a closer examination shows that they have strong resemblance. In this research, I consider a multi-valued epistemic logic (MEL) which has a unifying semantics that subsumes the semantics of several existing epistemic logics. This formulation is based on the realization that epistemic notions such as implicit belief, explicit belief and awareness can be modeled by restricting the truth assignments of atomic sentences to subsets of truth values in a bilattice. A bilattice is a structure that can be viewed as a class of truth values that can accommodate incomplete and inconsistent information. In bilattice theory, formulas are ordered along two dimensions: truth/falsity and certainty/uncertainty. Subsequently, by adopting a bilattice interpretation, the issue of representing degree of belief can also be addressed. Most of the previously proposed logic for reasoning about knowledge characterize an agent's knowledge base with the two absolute notions of total belief and total disbelief. Unfortunately, restricting to such a dichotomy limits the expressiveness of these logics. In MEL, beliefs of agents are associated with a degree of truth and a degree of certainty. Additionally, this research investigates the issue of employing a model-theoretic approach for examining the validity and provability of sentences in the logic. In particular, it is shown that the validity and provability of a sentence in MEL can be checked in a finite number of steps. This rests on the fact that not only is MEL determined by (or sound and complete with respect to) a class of models, but it is also determined by a class of finite models and there is an algorithm to examine if a sentence is true in these models. A polynomial time model-checking algorithm for determining the satisfiability of a sentence at a particular state in a given model of MEL and for computing the associated degree of truth and degree of certainty of the sentence is also presented. In outline, this dissertation presents a multi-valued epistemic logic that not only has a sound and complete axiomatization and is decidable, but also (i) has a general semantics for representing belief, (ii) provides a means to represent degree of belief and (iii) adopts a model-theoretic approach for characterizing belief.