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		A Formal Treatment Of Ignorance

Abstract :


We augment well known decidable variants of (Propositional) Modal
Logics of Knowledge with a validity operator V, where Vp means that 
p is valid. The next step involves an attempt to define what we may
claim to know, based on a fixed knowledge base S. An interesting
case is that we can conclude ¬Kp whenever we fail to prove Kp. In
particular, we argue for assuming the axiom ¬Kp ⊃ K¬Kp whenever 
Kp ⊃ KKp is assumed. Should time allow, we shall remark on the 
Unexpected Examination (Hangman's) Paradox, presenting a new approach
to discribing how to avoid the real world's "refuting logic".
This talk will consist of a presentation of research in progress.