Concrete Results on Abstract Rules

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Markus Krötzsch, Despoina Magka, Ian Horrocks

Concrete Results on Abstract Rules



Abstract. There are many different notions of “rule” in the literature. A key feature and main intuition of any such notion is that rules can be “applied” to derive conclusions from certain premises. More formally, a rule is viewed as a function that, when invoked on a set of known facts, can produce new facts. In this paper, we show that this extreme simplification is still sufficient to obtain a number of useful results in concrete cases. We define abstract rules as a certain kind of functions, provide them with a semantics in terms of (abstract) stable models, and explain how concrete normal logic programming rules can be viewed as abstract rules in a variety of ways. We further analyse dependencies between abstract rules to recognise classes of logic programs for which stable models are guaranteed to be unique.

Published at LPNMR 2013 (Conference paper)

Download PDF (last update: 18 September 2013)

Citation details

Remarks

The above is a preprint of the conference paper. Some additional proofs can be found in the extended technical report of the same title.

You can view the presentation in any modern browser. It was prepared using Sozi and Inkscape; many thanks to these projects.

Topics

Rule languages, nonmonotonic reasoning, stable models

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