Reasoning about Minimal Belief and Negation as Failure

Journal of Artificial Intelligence Research

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic.


Minimal Revision of Logical Specification Using Extended Logic Programming: Preliminary Report Ken Satoh

AAAI Conferences

In software engineering, there are several proposals of logical treatment of "inconsistency" of software specification (Borgida 1985; Balzer 1991; Finkelstein et al. 1994). A survey of these approaches is found in (Nuseibeh 1996).


Pearce

AAAI Conferences

As a doxastic counterpart to epistemic logic based on S5 we study the modal logic KSD that can be viewed as an approach to modelling a kind of objective and fair belief. We apply KSD to the problem of minimal belief and develop an alterna- tive approach to nonmonotonic modal logic using a weaker concept of expansion.


A Knowledge Representation Framework Based on Autoepistemic Logic of Minimal Beliefs

AAAI Conferences

In this paper we introduce a simple nonmonotonic knowledge representation framework which isomorphically contains all of the above mentioned nonmonotonic formalisms and semantics as special cases and yet is significantly more expressive than each one of these formalisms considered individually.


Reasoning about Minimal Belief and Negation as Failure

arXiv.org Artificial Intelligence

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic.