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Tuesday, 25 September 2018

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Pubblication Details
Authors:Laura Giordano
Alberto Policriti
Title:Power (set) Description Logic
Published on:TR-INF-2018-02-02-UNIPMN
Publisher:DiSIT, Computer Science Institute, UPO
Year:2018
Tipo Pubblicazione:Technical Report
URL:http://www.di.unipmn.it...R-INF-2018-02-02-UNIPMN.pdf
Abstract:We explore the relationships between Description Logics and Set Theory. The study is carried on using, on the set-theoretic side, a very rudimentary axiomatic set theory Ω, consisting of only four axioms characterizing binary union, set difference, inclusion, and the power-set. The approach is then completed defining ALCΩ, an extension of ALC, in which concepts are naturally interpreted as sets living in Ω-models. In ALCΩ not only membership between concepts is allowed—even admitting circularity—but also the power-set construct is exploited to add metamodeling capabilities. We conclude providing a polynomial translation of ALCΩ in ALCOI and proving its basic traits, among which the validity of the finite model property.