A Weak Logic of Knowledge and Belief: Epistemic and Doxastic Logic for the Yuppie Generation
SRI INTERNATIONAL MENLO PARK CA ARTIFICIAL INTELLIGENCE CENTER
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Modern modal logic begins with the work of C.I. Lewis early on in the present century. We can think of Lewis thinking to himself as follows Well, I cant analyze the notions of metaphysical or logical possibility and necessity but I can sure formulate alternative axiomatizations of such notions. I can then compare and contrast such axiomatic systems and see what I learn. Thus were born the Lewis Systems, S1-S5, axiomatizing increasingly strong conceptions of necessity. Another 40 or so years went by before the purely axiomatic approach was properly systematized and rendered fit for human consumption. In current lore, a certain axiomatic system, K, is central. The standard presentation of K consists of infinitely many axioms plus one axiom scheme and two rules of inference... It may be, then, that to take epistemicdoxastic logics seriously, one must both be working from within that conceptualization of cognitive states according to which they are either essentially or importantly language involving and, further, conceive of the languages in question on the model of standard formal languages, as consisting, that is, of eternal sentences only. This could be taken as an argument to the effect that the proper home of epistemicdoxastic logic is theoretical computer science -- precisely the locus of its greatest current vitality.
- Theoretical Mathematics