Reasoning about actions: a model-theoretic approach

A knowledge-based agent reasons with its knowledge and answers queries while performing various tasks. We consider the case where we describe the agent's knowledge in a propositional fragment of the situation calculus and queries in a fragment of ID-logic, the extension of first-order logic with inductive definitions. This fragment of ID-logic is equivalently as expressive as the alternation-free p-calculus. We formulate the agent's reasoning process as the following question: does the representation T of the agent's knowledge logically entail the query 4 (i.e., T k +)? We provide an efficient algorithm for this task, using a modeltheoretic approach: we construct from T a canonical model gT of the agent's knowledge and ask whether zT satisfies 4. Using this approach, the agent can answer the query in time linear with respect to both the size of T and the size of 4.

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