Annotation Theories over Finite Graphs
Gabbay, Dov Szalas, Andrzej
2009 (English)In: Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, E-ISSN 1572-8730, Vol. 93, no 2-3, 147-180Article in journal (Refereed) Published
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].
argumentation theory - labeled graphs - annotations - semantics of logic programs - second-order quantifier elimination
National CategoryEngineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-65966DOI: 10.1007/s11225-009-9220-3OAI: oai:DiVA.org:liu-65966DiVA: diva2:400675