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A Tractable Knowledge Representation Service with Full Introspection

A Knowledge Representation service for a knowledge-based system (or agent) can be viewed as providing, at the very least, two operations that (a) give precise information about what is and is not believed (ASK) and (b) add new facts to the knowledge base when they become available (TELL). An appropriate model of belief for such operations should support the notion that only certain facts are believed, in particular those that have been added to a knowledge base via TELL. For logically omniscient and fully introspective agents, models of this kind lead to intractable ASK and TELL operations. In this paper, we show that tractability can be retained by giving up logical omniscience, but without sacrificing full introspection. This is done within the framework of a propositional logic of belief. In particular, the logic allows us to express that only a sentence (or finite set of them) is believed. We show that the validity of certain classes of sentences involving belief can be decided efficiently. These results are then applied to the specification of efficient TELL and ASK operations.