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All I know: A study in autoepistemic logic. (English) Zbl 0724.03019
The author’s aim is to approach nonmonotonicity via epistemic logic. The word “autoepistemic” hereby refers to the fact that the epistemic operators are allowed to appear within their own ranges. The epistemic part of the language contains the unary belief-operator B together with an additional (unary propositional) operator \bO, with \bOH meaning “H is all that is believed”; of course the background idea is to apply \bO essentially to finite sets of sentences (via their conjunction).
In a natural way there is a possible worlds semantics such that the B- fragment corresponds to the modal logic weak S5 (i.e. K4.5). This extended epistemic logic the author introduces here is studied first in its own right, is then related to the autoepistemic logic of R. Moore [Proc. IJCAI-83, Karlsruhe, 272-279 (1983; Zbl 0536.68074)] and the stable expansions, given a sound and, for the propositional part, complete axiomatization (which, yet, for the first-order case is not recursive), and is applied to some problems of nonmonotonicity.

MSC:
03B60 Other nonclassical logic
03B45 Modal logic (including the logic of norms)
68T27 Logic in artificial intelligence
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