AN EPISTEMIC LOGIC WITH QUANTIFICATION OVER NAMES

Sentential theories of belief hold that propositions (the things that agents believe and know) are sentences of a representation language. To analyze quantification into the scope of attitudes, these theories require a naming map a function that maps objects to their names in the representation language. Epistemic logics based on sentential theories usually assume a single naming map, which is built into the logic. I argue that to describe everyday knowledge, the user of the logic must be able to define new naming maps for particular problems. Since the range of a naming map is usually an infinite set of names, defining a map requires quantification over names. This paper describes an epistemic logic with quantification over names, presents a theorem-proving algorithm based on translation to first-order logic, and proves soundness and completeness. The first version of the logic suffers from the problem of logical omniscience; a second version avoids this problem, and soundness and completeness are proved for this version also.