Abstract
The well-founded semantics (WFS) for logic programs is one of the few major paradigms for closed-world reasoning. With the advent of the Semantic Web, it is being used as part of rule systems for ontology reasoning, and also investigated as to its usefulness as a semantics for hybrid systems featuring combined open- and closed-world reasoning. Even in its most basic form, however, the WFS is undecidable. In fact, it is not even semi-decidable, which means that it is a theoretical impossibility that sound and complete reasoners for the WFS exist.
Surprisingly, however, this matter has received next to no attention in research, although it has already been shown in 1995 by John Schlipf [1]. In this paper, we present several conditions under which query-answering under the well-founded semantics is decidable or semi-decidable. To the best of our knowledge, these are the very first results on such conditions.
This work is partially supported by the German Federal Ministry of Education and Research (BMBF) under the SmartWeb project (grant 01 IMD01 B), by the Deutsche Forschungsgemeinschaft (DFG) under the ReaSem project and by the EU in the IST project NeOn (IST-2006-027595), http://www.neon-project.org/
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Cherchago, N., Hitzler, P., Hölldobler, S. (2007). Decidability Under the Well-Founded Semantics. In: Marchiori, M., Pan, J.Z., Marie, C.d.S. (eds) Web Reasoning and Rule Systems. RR 2007. Lecture Notes in Computer Science, vol 4524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72982-2_21
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DOI: https://doi.org/10.1007/978-3-540-72982-2_21
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