TY - GEN

T1 - Subnormal modal logics for knowledge representation

AU - Schwarz, Grigori

AU - Truszczynski, Miroslaw

PY - 1993

Y1 - 1993

N2 - Several widely accepted modal nonmonotonic logics for reasoning about knowledge and beliefs of rational agents with introspection powers are based on strong modal logics such as KD45, S4.4, S4F and S5. In this paper we argue that weak modal logics, without even the axiom K and, therefore, below the range of normal modal logics, also give rise to useful nonmonotonic systems. We study two such logics: the logic N, containing propositional calculus and necessitation but no axiom schemata for manipulating the modality, and the logic NT - the extension of N by the schema T. For the nonmonotonic logics N and NT we develop minimal model semantics. We use it to show that the nonmonotonic logics N and NT are at least as expressive as autoepistemic logic, reflexive autoepistemic logic and default logic. In fact, each can be regarded as a common generalization of these classic nonmonotonic systems. We also show that the nonmonotonic logics N and NT have the property of being conservative with respect to adding new definitions, and prove that computationally they are equivalent to autoepistemic and default logics.

AB - Several widely accepted modal nonmonotonic logics for reasoning about knowledge and beliefs of rational agents with introspection powers are based on strong modal logics such as KD45, S4.4, S4F and S5. In this paper we argue that weak modal logics, without even the axiom K and, therefore, below the range of normal modal logics, also give rise to useful nonmonotonic systems. We study two such logics: the logic N, containing propositional calculus and necessitation but no axiom schemata for manipulating the modality, and the logic NT - the extension of N by the schema T. For the nonmonotonic logics N and NT we develop minimal model semantics. We use it to show that the nonmonotonic logics N and NT are at least as expressive as autoepistemic logic, reflexive autoepistemic logic and default logic. In fact, each can be regarded as a common generalization of these classic nonmonotonic systems. We also show that the nonmonotonic logics N and NT have the property of being conservative with respect to adding new definitions, and prove that computationally they are equivalent to autoepistemic and default logics.

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M3 - Conference contribution

AN - SCOPUS:0027707102

SN - 0262510715

T3 - Proceedings of the National Conference on Artificial Intelligence

SP - 438

EP - 443

BT - Proceedings of the National Conference on Artificial Intelligence

T2 - Proceedings of the 11th National Conference on Artificial Intelligence

Y2 - 11 July 1993 through 15 July 1993

ER -