LiU Electronic Press
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Author:
Gabbay, Dov (Warsaw University)
Szalas, Andrzej (Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab) (Linköping University, The Institute of Technology)
Title:
Annotation Theories over Finite Graphs
Department:
Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab
Linköping University, The Institute of Technology
Publication type:
Article in journal (Refereed)
Language:
English
Publisher: Springer
Status:
Published
In:
Studia Logica: An International Journal for Symbolic Logic(ISSN 0039-3215)(EISSN 1572-8730)
Volume:
93
Issue:
2-3
Pages:
147-180
Year of publ.:
2009
URI:
urn:nbn:se:liu:diva-65966
Permanent link:
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-65966
Subject category:
Engineering and Technology
SVEP category:
TECHNOLOGY
Keywords(en) :
argumentation theory - labeled graphs - annotations - semantics of logic programs - second-order quantifier elimination
Abstract(en) :

In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph’s nodes. Such theories, which we call annotation theories, can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying problem, specification of preferred models and model checking problem. We show that most of considered problems are NPTime- or co-NPTime-complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of annotation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2, 28, 21].

Available from:
2011-02-28
Created:
2011-02-28
Last updated:
2012-02-13
Statistics:
12 hits