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  Multi-valued autoepistemic logic (1996) [1 citations — 0 self]

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by Robert F. Stärk
Annals of Mathematics and Artificial Intelligence
http://www.inf.ethz.ch/~staerk/pdf/mAE.pdf
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Abstract:

We generalize Moore’s autoepistemic logic to multi-valued autoepistemic logic, where the set of truth-values can be any complete lattice. Multi-valued autoepistemic extensions can be characterized by admissible belief interpretations which are the concrete approximations of extensions and are appropriate to be computed and manipulated. We prove that multi-valued autoepistemic extensions are exactly the theories of maximal multi-valued Kripke models. The class of stratified theories is investigated and it is shown that stratified theories have exactly one multi-valued autoepistemic extension. Finally we present a sequent calculus for multi-valued logic which serves as a tool for a decision procedure for multi-valued autoepistemic logic. 1

Citations

557 Towards a theory of Declarative Knowledge – Apt, Blair, et al. - 1988
398 Semantical considerations on non-monotonic logic – Moore - 1985
170 Complexity results for nonmonotonic logics – Gottlob - 1992
167 All I know: a study in autoepistemic logic – Levesque - 1990
126 On the relation between default and autoepistemic logic – Konolige - 1988
104 On Stratified Autoepistemic Theories – Gelfond - 1987
65 Possible-world semantics for autoepistemic logic – Moore - 1984
47 Systematization of finite many-valued logics through the method of tableaux – Carnielli - 1987
44 Modal nonmonotonic logics: ranges, characterization, computation – Marek, Shvarts, et al. - 1993
34 Three-Valued Non-Monotonic Formalisms and Semantics of Logic Programs – Przymusinski - 1991
19 Bilattices and modal operators – Ginsberg - 1990
15 Towards an Efficient Tableau Proof Procedure for Multiple-Valued Logics – Hähnle - 1991
13 Decision Procedure for Autoepistemic Logic – Niemelä
11 The defining power of stratified and hierarchical logic programs – Jäger, Stärk - 1993
10 Stable theories in autoepistemic logic – Marek - 1989
8 An algorithm for axiomatizing every finite logic – Surma - 1984
5 Many-valued non-monotonic modal logics – Fitting - 1992
3 On the existence of fixpoints in Moore's autoepistemic logic and the non-monotonic logic of McDermott and Doyle – Stark - 1990
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