SET THEORY FOR KNOWLEDGE REPRESENTATION

The decision problem in set theory has been intensively investigated in the last decades, and decision procedures or proofs of undecidability have been provided for several quantified and unquantified fragments of set theory. In this thesis we study the decision problem for three novel quantified fragments of set theory, which allow the explicit manipulation of ordered pairs. We present a decision procedure for each language of this family, and prove that all of these procedures are optimal (in the sense that they run in nondeterministic polynomial-time) when restricted to formulae with quantifier nesting bounded by a constant. The expressive power of languages of this family is then measured in terms of set-theoretical constructs they allow to express. In addition, these languages can be profitably employed in knowledge representation, since they allow to express a large amount description logic constructs.

Grantor dc:publisher

Università degli studi di Catania

Year dc:date

2011

Author dc:creator

• LONGO, CRISTIANO

Contributors dc:contributor

• CANTONE, Domenico

• Set,Theory,knolwedge,representation,NP-completeness

Statement dc:rights

• info:eu-repo/semantics/openAccess
• license:PUBBLICO - Pubblico con Copyright
• license uri:iris.PUB02

Language dc:language

eng

Handle dc:identifier

https://hdl.handle.net/20.500.11769/594343

OAI identifier oai:identifier

oai:www.iris.unict.it:20.500.11769/594343