An ASP approach for reasoning in a concept-aware multipreferential lightweight DL

Abstract

In this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible concept inclusions. Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated. The construction of the concept-aware multipreference semantics is related to Brewka’s framework for qualitative preferences. We exploit Answer Set Programming (in particular, asprin) to achieve defeasible reasoning under the multipreference approach for the lightweight description logic ξ$\mathcal L_ \bot ^ + $.

A framework for a modular multi-concept lexicographic closure semantics

“…At one extreme, all the defeasible inclusions in D are put together in the same module, e.g., the module associated with concept ⊤. At the other extreme, which has been studied in [36], a module m i contains only the defeasible inclusions of the form T(C i ) ⊑ D, where C i is the subject of m i (and in this case, the inclusions T(C) ⊑ D with C subsumed by C i are not admitted in m i ). In this regard, the framework proposed in this paper could be seen as an extension of the proposal in [36] to allow coarser grained modules, while here we do not allow for user-defined preferences among defaults.…”

“…More precisely, preference < 5 should override preference < 2 when comparing PhDStudent-instances. This is the principle followed by Giordano and Theseider Dupré [36] to define a global preference relation, in the case when each module with subject C i only contains typicality inclusions of the form T(C i ) ⊑ D. A more sophisticated way to combine the preference relations < i into a global relation < is used to deal with this case with respect to Pareto combination, by exploiting the specificity relation among concepts. While we refer therein for a detailed description of this more sophisticated notion of preference combination, let us observe that this solution could be as well applied to the modular multi-concept knowledge bases considered in this paper, provided an irreflexive and transitive notion of specificity among modules is defined.…”

“…For the lightweight description logic EL + ⊥ , an Answer Set Programming (ASP) approach has been proposed [36] for defeasible inference in a miltipreference extension of EL + ⊥ , in the specific case in which each module only contains the defeasible inclusions T(C i ) ⊑ D for a single concept C i , where the ranking of defeasible inclusions is specified in the knowledge base, following the approach by Gerhard Brewka in his framework of Basic Preference Descriptions for ranked knowledge bases [14]. A specificity relation among concepts is also considered.…”

“…At one extreme, all the defeasible inclusions in D can be put together in a module associated with subject ⊤ (Thing). At the other extreme, which has been studied in [36], a module m i is a defeasible TBox containing only the defeasible inclusions of the form T(C j ) ⊑ D for some concept C i . In this paper we remove this restriction considering general modules, containing arbitrary sets of defeasible inclusions, intuitively pertaining some subject.…”

“…In [36], following Gerard Brewka's framework of Basic Preference Descriptions for ranked knowledge bases [14], we have assumed that a specification of the relative importance of typicality inclusions for a concept C i is given by assigning ranks to typicality inclusions. However, for a large module, a specification by hand of the ranking of the defeasible inclusions in the module would be awkward.…”