Open AccessProceedings Article
A model-theoretic counterpart of loop formulas
Joohyung Lee
- pp 503-508
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TLDR
"Externally supported" sets, defined in this paper, are a model-theoretic counterpart of loop formulas, and shows that they are related to assumption sets and to unfounded sets, invented many years earlier.Abstract:
In an important recent paper, Lin and Zhao introduced the concept of a loop formula, and showed that the answer sets for a logic program are exactly the models of Clark's completion of the program that satisfy the loop formulas. Just as supported sets are a model-theoretic account of completion, "externally supported" sets, defined in this paper, are a model-theoretic counterpart of loop formulas. This reformulation of loop formulas shows that they are related to assumption sets (Sacca and Zaniolo) and to unfounded sets (Van Gelder, Ross and Schlipf; Leone, Rullo and Scarcello), invented many years earlier. Other contributions of this paper includes a simplification of the definition of a loop, extending it to programs with classical negation and infinite programs, and a generalization of the definition of a loop formula.read more
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