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arXiv · 1405.3365

A Well-Founded Semantics for FOL-Programs

Yi Bi·Jia-Huai You·Zhiyong Feng
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Abstract

An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with description logics. In this paper, we define a well-founded semantics for FOL-programs based on a new notion of unfounded sets on consistent as well as inconsistent sets of literals, and study some of its properties. The semantics is defined for all FOL-programs, including those where it is necessary to represent inconsistencies explicitly. The semantics supports a form of combined reasoning by rules under closed world as well as open world assumptions, and it is a generalization of the standard well-founded semantics for normal logic programs. We also show that the well-founded semantics defined here approximates the well-supported answer set semantics for normal DL programs.

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Yi Bi, Jia-Huai You, Zhiyong Feng. 2014-05-14. A Well-Founded Semantics for FOL-Programs. https://arxiv.org/abs/1405.3365

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