mbnf


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.


Only-Knowing: Taking It Beyond Autoepistemic Reasoning

AAAI Conferences

The idea of only-knowing a collection of sentences has been previously shown to have a close connection with autoepistemic logic. Here we propose a more general account of only-knowing that captures not only autoepistemic logic but default logic as well. This allows us not only to study the properties of default logic in terms of an underlying model of belief, but also the relationship among different forms of nonmonotonic reasoning, all within a classical monotonic logic characterized semantically in terms of possible worlds.


Reasoning with minimal negation as

AAAI Conferences

The logic of minimal belief and negation as failure (A03NF) (Lifschitz 1994) is one of the most expressive formalisms for nonmonotonic reasoning. Roughly speaking, such a logic is built by adding to first-order logic two distinct modalities, a "minimal belief" modality



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.


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.