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Reasoning About Typicality in Description Logics: the Logic ALC + Tmin

Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca Pozzato

In our recent research we have proposed a nonmonotonic extension ALC +
Tmin of the Description Logic ALC for reasoning about prototypical properties
and inheritance with exception.
The logic ALC+Tmin is built upon a previously introduced (monotonic) logic
ALC + T [1], that is obtained by adding a typicality operator T to ALC. The
operator T is intended to select the “most normal” or “most typical” instances
of a concept, so that knowledge bases may contain subsumption relations of the
form “T(C) is subsumed by P”, expressing that typical C-members have the
property P. In order to perform nonmonotonic inferences, we define a “minimal
model” semantics ALC +Tmin for ALC +T. The intuition is that preferred, or
minimal models are those that maximise typical instances of concepts. By means
of ALC +Tmin we are able to infer defeasible properties of (explicit or implicit)
We are able to provide a decision procedure for checking satisfiability and va-
lidity in ALC +Tmin. Our decision procedure has the form of tableaux calculus,
with a two-step tableau construction. The idea is that the top level construc-
tion generates open branches that are candidates to represent minimal models,
whereas the auxiliary construction checks whether a candidate branch represents
indeed a minimal model. Our procedure can be used to determine constructively
an upper bound of the complexity of ALC+Tmin. Namely we obtain that check-
ing query entailment for ALC + Tmin is in co-NExpNP.


    author = {Laura Giordano and Valentina Gliozzi and Nicola Olivetti and Gian Luca Pozzato},
    title  ={Reasoning About Typicality in Description Logics: the Logic ALC + Tmin},
    year = {2008},
    editor = {Marco Gavanelli and Toni Mancini},
    booktitle = {R.i.C.e.R.c.A. 2008: RCRA Incontri E Confronti},