A multi-dimensional terminological knowledge representation language

Franz Baader, Hans Juürgen Ohlbach
1995 Journal of Applied Non-Classical Logics  
An extension of the concept description language ALC used in KL-ONE-like terminological reasoning is presented. The extension includes multi-modal operators that can either stand for the usual role quantifications or for modalities such as belief, time etc. The modal operators can be used at all levels of the concept terms, and they can be used to modify both concepts and roles. This is an instance of a new kind of combination of modal logics where the modal operators of one logic may operate
more » ... logic may operate directly on the operators of the other logic. Different versions of this logic are investigated and various results about decidability and undecidability are presented. The main problem, however, decidability of the basic version of the logic, remains open. * This work was supported by the ESPRIT project 6471 MEDLAR, and the BMFT Projects Logo (ITS 9102) and TACOS (ITW 9201). A preliminary version has appeared in the Proceedings of the IJCAI-93. Definition 1.2 An interpretation = ( D, Σ ) for an n-dimensional M-ALC language L n consists of the Cartesian product D = D 1 × . . . × D n of n non-empty carrier sets (domains), and a signature interpretation Σ . The signature interpretation assigns successor functions to role names and n-place relations to concept names. To be more precise, a role name p of dimension i is interpreted as a function Σ (p) : D → 2 Di , and a concept name c as a set Σ (c) ⊆ D. The concept name is interpreted as D and ⊥ as the empty set. The interpretation of a role term q of dimension i is also a function (q) : D → 2 Di that is inductively defined as follows. Let r be a role name, p, q be role terms, and let j be the dimension of q. A satisfiability relation |= between an interpretation with actual point d and concept terms and concept equations is defined as follows. Let c be a concept name, e, f be concept terms, p be a role term of dimension i, and φ be a concept term or concept equation. An interpretation is a model of a T-Box iff for all actual points d and all equations φ of the T-Box one has , d |= φ. ¡
doi:10.1080/11663081.1995.10510854 fatcat:7k6b5lxufbhmpawzgr4hdbslfy