Safe beliefs for propositional theories
type: Item
instance of: scholarly article
title: Safe beliefs for propositional theories
zbMATH Open document ID: 1074.03013
author: Mauricio Osorio
author: Juan Antonio Pérez
author: José Ramón Enrique Arrazola Ramírez
published in: Annals of Pure and Applied Logic
publication date: 2005-06-01T00:00:00Z
review text: The paper presents an extension of answer sets that are called safe beliefs. Safe beliefs allow for the use of arbitrary propositional theories as logic programs. The presented approach allows for the use of even modal or temporal logics as the underlying inference system to produce different semantic operators with additional or extended features. One of the main theorems of the paper shows that any propositional logic that is strictly weaker than classical logic and stronger than intuitionistic logic can be used in the definition of safe beliefs without modifying the resulting semantic operator. Another contribution of the paper is to present a translation that can be used to reduce any propositional theory into the class of augmented logic programs. Other translations can be used to provide a polynomial reduction of arbitrary propositional theories into disjunctive logic programs. Reviewer's remark: The 7th line of p. 66 contains a misprint: the atoms \(b_{m+1},\dots, b_{m+l}\) must be negated.
Mathematics Subject Classification ID: 03B70
Mathematics Subject Classification ID: 68N17
Mathematics Subject Classification ID: 68Q55
zbMATH DE Number: 2173066
zbMATH Keywords: logic programming
zbMATH Keywords: answer set semantics
zbMATH Keywords: safe beliefs
reviewed by: Nail Zamov
MaRDI profile type: Publication
full work available at URL: j.apal.2004.06.012
OpenAlex ID: W2170515813
cites work: Knowledge Representation, Reasoning and Declarative Problem Solving
cites work: A general theory of confluent rewriting systems for logic programming and its applications
cites work: Q4736516
cites work: Q4798001
cites work: Strongly equivalent logic programs
cites work: Nested expressions in logic programs
cites work: Q5586197
cites work: Q4808808
cites work: Q4812994
cites work: Applications of intuitionistic logic in Answer Set Programming
cites work: From here to there: Stable negation in logic programming
cites work: Stable inference as intuitionistic validity
cites work: Q4812975
cites work: Constructivism in mathematics. An introduction. Volume I
cites work: Logic and structure
cites work: Q4789450
DOI: 10.1016/J.APAL.2004.06.012
description: scientific article; zbMATH DE number 2173066