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Zhou

AAAI Conferences

Reiter's original proposal for default logic is unsatisfactory for open default theories because of Skolemization and grounding. In this paper, we reconsider this long-standing problem and propose a new world view semantics for first-order default logic. Roughly speaking, a world view of a first-order default theory is a maximal collection of structures satisfying the default theory where the default part is fixed by the world view itself. We show how this semantics generalizes classical first-order logic and first-order answer set programming, and we discuss its connections to Reiter's semantics and other related semantics. We also argue that first-order default logic under the world view semantics provides a rich framework for integrating classical logic based and rule based formalisms in the first-order case.


Complexity of Prioritized Default Logics

arXiv.org Artificial Intelligence

In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example specificity in inheritance reasoning can be handled this way, or they may be given abstractly as an ordering on the default rules. In this article we investigate formalizations of the latter approach in Reiter's default logic. Our goal is to analyze and compare the computational properties of three such formalizations in terms of their computational complexity: the prioritized default logics of Baader and Hollunder, and Brewka, and a prioritized default logic that is based on lexicographic comparison. The analysis locates the propositional variants of these logics on the second and third levels of the polynomial hierarchy, and identifies the boundary between tractable and intractable inference for restricted classes of prioritized default theories.


ropositional its

AAAI Conferences

We characterize the complexity of several typical problems in propositional default logics. In particular, we examine the complexity of extension membership, extension existence, and extension entailment problems. We show that the extension existence problem is X; complete, even for semi-normal theories, and that the extension membership and entailment problems are X; complete and II; complete respectively, even when restricted to normal default theories. These results contribute to our understanding of the computational relationship between propositional default logics and other formalisms for nonmonotonic reasoning, e.g., autoepistemic logic and McDermott and Doyle's NML, as well as their relationship to problems outside the realm of nonmonotonic reasoning.


Complexity of Prioritized Default Logics

Journal of Artificial Intelligence Research

In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example specificity in inheritance reasoning can be handled this way, or they may be given abstractly as an ordering on the default rules. In this article we investigate formalizations of the latter approach in Reiter's default logic. Our goal is to analyze and compare the computational properties of three such formalizations in terms of their computational complexity: the prioritized default logics of Baader and Hollunder, and Brewka, and a prioritized default logic that is based on lexicographic comparison. The analysis locates the propositional variants of these logics on the second and third levels of the polynomial hierarchy, and identifies the boundary between tractable and intractable inference for restricted classes of prioritized default theories.