Semantics of nonmonotonic reasoning in logic programming

We give an overview of the multifaceted relationship between nonmonotonic logics and preferences. We discuss how the nonmonotonicity of reasoning itself is closely tied to preferences reasoners have on models of the world or, as we often say here, possible belief sets. Selecting extended logic programming with the answer-set semantics as a "generic" nonmonotonic logic, we show how that logic defines preferred belief sets and how preferred belief sets allow us to represent and interpret normative statements. Conflicts among program rules (more generally, defaults) give rise to alternative preferred belief sets. We discuss how such conflicts can be resolved based on implicit specificity or on explicit rankings of defaults. Finally, we comment on formalisms which explicitly represent preferences on properties of belief sets. Such formalisms either build preference information directly into rules and modify the semantics of the logic appropriately, or specify preferences on belief sets independently of the mechanism to define them.

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Logic Programming and Nonmonotonic Reasoning

10.1007/978-3-030-20528-7 ◽

2019 ◽

Cited By ~ 1

Keyword(s):

Logic Programming ◽

Nonmonotonic Reasoning

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Approximation Fixpoint Theory for Non-Deterministic Operators and Its Application in Disjunctive Logic Programming

10.24963/kr.2021/32 ◽

2021 ◽

Author(s):

Jesse Heyninck ◽

Ofer Arieli

Keyword(s):

Logic Programming ◽

Nonmonotonic Reasoning ◽

Default Logic ◽

Autoepistemic Logic ◽

Algebraic Framework ◽

Nonmonotonic Logics

Approximation fixpoint theory (AFT) constitutes an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to non-deterministic constructs such as disjunctive information. This is done by generalizing the main constructions and corresponding results to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.

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