Logics for Nonomniscient Agents: An Axiomatic Approach
It has long been recognized that solving the logical omniscience problem requires using some kind of nonstandard possible worlds. While many such logics have been proposed, none has an obvious claim as the "right" logic to use to describe the reasoning of agents who are not logically omniscient. I show how to derive such nonstandard worlds as part of a representation of an agent's preferences. In this sense, the agent's logic is given the same basis as a utility function or subjective probability. As an illustration, I give conditions on preferences which imply that the agent's logic is a version of the logic of inconsistency proposed by Rescher and Brandom (1979).
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