Abstract
AbstractLogic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational meaning of ordered disjunction is clear, there exists an important open issue regarding its semantics. In particular, there does not exist a purely model-theoretic approach for determining the most preferred models of an LPOD. At present, the selection of the most preferred models is performed using a technique that is not based exclusively on the models of the program and in certain cases produces counterintuitive results. We provide a novel, model-theoretic semantics for LPODs, which uses an additional truth value in order to identify the most preferred models of a program. We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs. Moreover, the new approach can be used to define the semantics of a natural class of logic programs that can have both ordered and classical disjunctions in the heads of clauses. This allows programs that can express not only strict levels of preferences but also alternatives that are equally preferred.
Highlights
Logic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing ordered alternatives in the heads of program rules
We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs
We propose a new semantics for LPODs which uses an additional truth value in order to select as most preferred models those in which a top preference fails only if it is impossible to be satisfied
Summary
Logic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing ordered alternatives in the heads of program rules. To our knowledge, the second phase (namely the selection of the most preferred answer sets), has never been justified model-theoretically We consider this as an important shortcoming in the theory of LPODs. Apart from its theoretical interest, this question carries practical significance, because, as we are going to see, the present formalization of the second phase produces in certain cases counterintuitive (and in our opinion undesirable) results. We define a natural class of such programs and demonstrate that all our results about LPODs transfer, with minimal modifications, to this new class In this way we provide a clean semantics for a class of programs that can express strict levels of preference and alternatives that are preferred. The proofs of all results have been moved to corresponding appendices
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