(A) unified proof mechanism for knowledge and belief based on box model

Abstract

In the last years, epistemology, the study of knowledge and belief, began to attract growing interest in many domains such as economics, linguistics, artificial intelligence, and computer science. As a result, it had become necessary to develop a well-formalized tool to describe each agent``s knowledge and belief, and epistemic logics, either modal logical forms or first-order logical forms, have been used for this purpose. For the semantics of epistemic logics, two different models have been used: one is the classical possible-worlds model, and the other is the more recent deduction model. In the possible-worlds model, a set of pre-assumed possible worlds exists, and each agent``s knowledge and belief are represented by accessibility relations between possible worlds. The characteristics of knowledge and belief can be given by restricting these accessibility relations. Possible-worlds model is in itself very simple, and natural in the point of man, but as it overidealizes the situation, it suffers from the famous problem, logical omniscience, that every agent knows or believes all logically valid formulas and all logical consequences. In the real world, this logically omniscient agent cannot exist, even though his inferential power is complete, as the resources he can use are very limited. On the other hand, deduction model assumes that each agent has a belief system, each of which is composed of base beliefs and deduction rules. Each agent``s knowledge and belief are represented by set-element relations for the belief system. As deduction model does not prescribe the inference power, it does not suffer from the logical omniscience, but it has weakness to formalize some important characteristics of knowledge and belief, such as introspectiveness. In this paper, we propose a new semantics for epistemic logics, called box model. It is designed to model real agents like deduction model, but it can handle various characteristics of knowledge and belief like possib...