Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A theory of nonmonotonic rule systems I

A theory of nonmonotonic rule systems I We introduce here the study of generalnonmonotonic rule systems. These deal with situations where a conclusion is drawn from a “system of beliefs”S (and seen to be inS), basedboth on some “premises” being inS and on some “restraints” not being inS. In the monotone systems of traditional logic there are no restraints, conclusions are drawn solely based on premises being inS. Nonmonotonic rule systems capture the essential syntactic, semantic, and algorithmic features of many nonmonotone systems such as default logic, negation as failure, truth maintenance, autoepistemic logic, and also important combinatorial questions from mathematics such as the marriage problem. This reveals semantics and syntax and proof procedures and algorithms for computing belief sets in many cases where none were previously available and entirely uniformly. In particular, we introduce and study deductively closed sets, extensions and weak extensions. Semantics of nonmonotonic rule systems is studied in part II of this paper and extensions to predicate classical, intuitionistic, and modal logics are left to a later paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

A theory of nonmonotonic rule systems I

Download PDF
33 pages

Loading next page...
 
/lp/springer-journals/a-theory-of-nonmonotonic-rule-systems-i-5ZsShJtEkl

References (52)

Publisher
Springer Journals
Copyright
Copyright
Subject
Computer Science; Artificial Intelligence; Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/BF01531080
Publisher site
See Article on Publisher Site

Abstract

We introduce here the study of generalnonmonotonic rule systems. These deal with situations where a conclusion is drawn from a “system of beliefs”S (and seen to be inS), basedboth on some “premises” being inS and on some “restraints” not being inS. In the monotone systems of traditional logic there are no restraints, conclusions are drawn solely based on premises being inS. Nonmonotonic rule systems capture the essential syntactic, semantic, and algorithmic features of many nonmonotone systems such as default logic, negation as failure, truth maintenance, autoepistemic logic, and also important combinatorial questions from mathematics such as the marriage problem. This reveals semantics and syntax and proof procedures and algorithms for computing belief sets in many cases where none were previously available and entirely uniformly. In particular, we introduce and study deductively closed sets, extensions and weak extensions. Semantics of nonmonotonic rule systems is studied in part II of this paper and extensions to predicate classical, intuitionistic, and modal logics are left to a later paper.

Journal

Annals of Mathematics and Artificial Intelligence – Springer Journals

Published: Sep 1, 1990

There are no references for this article.