Complexity of nested circumscription and abnormality theories

Authors:
Marco Cadoli;Thomas Eiter;Georg Gottlob
Affiliations:
Dipartimento di Informatica e Sistemistica, Università di Roma "La Sapienza", Roma, Italy;Institut für Informationssysteme, Technische Universität Wien, Wien, Austria;Institut für Informationssysteme, Technische Universität Wien, Wien, Austria
Venue:
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Year:
2001

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Abstract

We propose LCirc, an extension of circumscription by allowing propositional combinations and nesting of circumscriptive theories. As shown, Lifschitzs nested abnormality theories (NATs, introduced in AIJ, 1995) are naturally embedded into this language. We analyze the complexity of LCirc and NATs, and in particular the effect of nesting. The latter is found a source of complexity, as both formalisms are proved to be PSPACE-complete. We identify cases of lower complexity, including a tractable case. Our results give insight into the cost of using LCirc resp. NATs as a host language for expressing other formalisms, such as narratives.