Abstract
A novel scheme for weakened negative introspection in autoepistemic reasoning is proposed. The scheme is formulated proof-theoretically in terms of enumerations of formulae. The resulting sets of conclusions, cautious expansions, are a generalization of Moore style stable expansions such that each set of premises has a cautious expansion. A finitary characterization is provided for the cautious expansions. Excluding weakly grounded expansions, i.e. considering only xxN-grounded cautious expansions, is shown to imply attractive properties not present in, e.g., Moore style autoepistemic logic. For every set of premises, the intersection of the xxN-grounded cautious expansions is a cautious expansion which is the unique least xxN-grounded cautious expansion under a natural partial order of expansions. The least xxN-grounded cautious expansion can be constructed as the least fixed point of a monotonic operator. Using the finitary characterization the decidability of decision problems related to cautious expansions is established and the decision problems are related to the polynomial time hierarchy. A comparison indicates that the new principle is stronger than other similar proposals and than that used in the well-founded semantics.
Ilkka Niemelä gratefully acknowledges the support from the following foundations: Emil Aaltonen Foundation, Foundation of Technology, Heikki and Hilma Honkanen Foundation, Alfred Kordelin Foundation, Jenny and Antti Wihuri Foundation.
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Janhunen, T., Niemelä, I. (1993). A scheme for weakened negative introspection in autoepistemic reasoning. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022570
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DOI: https://doi.org/10.1007/BFb0022570
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