Complexity of Nested Circumscription and Nested Abnormality Theories
نویسندگان
چکیده
Circumscription has been recognized as an important principle for knowledge representation and common-sense reasoning. The need for a circumscriptive formalism that allows for simple yet elegant modular problem representation has led Lifschitz (AIJ, 1995) to introduce nested abnormality theories (NATs) as a tool for modular knowledge representation, tailored for applying circumscription to minimize exceptional circumstances. Abstracting from this particular objective, we propose LCIRC, which is an extension of generic propositional circumscription by allowing propositional combinations and nesting of circumscriptive theories. As shown, NATs are naturally embedded into this language, and are in fact of equal expressive capability. We then analyze the complexity of LCIRC and NATs, and in particular the effect of nesting. The latter is found to be a source of complexity, which climbs the Polynomial Hierarchy as the nesting depth increases and reaches PSPACE-completeness in the general case. We also identify meaningful syntactic fragments of NATs which have lower complexity. In particular, we show that the generalization of Horn circumscription in the NAT framework remains coNP-complete, and that Horn NATs without fixed letters can be efficiently transformed into an equivalent Horn CNF, which implies polynomial solvability of principal reasoning tasks. Finally, we also study extensions of NATs and briefly address the complexity in the first-order case. Our results give insight into the “cost” of using LCIRC (resp. NATs) as a host language for expressing other formalisms such as action theories, narratives, or spatial theories.
منابع مشابه
Nested Abnormality Theories
We propose a new approach to the use of circumscription for representing knowledge. Nested abnormality theories are similar to simple abnormality theories introduced by McCarthy, except that their axioms may have a nested structure , with each level corresponding to another application of the circumscription operator. The new style of applying circumscription sometimes leads to more economical ...
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ورودعنوان ژورنال:
- CoRR
دوره cs.AI/0207072 شماره
صفحات -
تاریخ انتشار 2002