A Multi-Context System Computing Modalities

The system description presents the conception and a prototypical implementation of a multi-context system, used for computing and implementing temporal modalities within given data without the use of modal operators. Instead, an external constraint based rule system is used for computing the corresponding temporal relations, making use of the way a multi-context system works for transporting the needed information between contexts and knowledge bases. 1 Point of Departure and Problem Statement Introducing new modalities should involve no more fuss than introducing a new predicate. [1] The above quotation, taken from John McCarthy’s paper “Modality, Si! Modal Logic, No!”, addresses a point quite well-known to description logicians and people working with systems for knowledge representation, based on DL. Real world applications often demand for the use of modalities (e.g. to express statements about time), or using McCarthy again: In particular, human-level AI requires that programs be able to introduce modalities when this is appropriate, e.g. have function taking modalities as values. [1] Nevertheless, allowing for the unrestricted use of modal operators within a description logic framework (given the not very probable case that this may be possible), major problems concerning decidability, completeness and computability arise. Even if only some modal operators shall be incorporated into a standard DL framework (as e.g. SHOIN (D), corresponding to the widely used OWL DL V1.0 language, or SROIQ(D) for OWL DL V2.0), a large part of the “pleasant” properties of the original formalism gets lost. Thus, we decided to build a working and applicable implementation of modalities (in the following we will use time as an example modality) without the use of modal operators, thereby following the basic idea lined out in McCarthy’s paper. We managed to do so by using concepts from the field of multi-context systems (MCS), mainly based on the results presented in [2] and [3]. Proc. 23rd Int. Workshop on Description Logics (DL2010), CEUR-WS 573, Waterloo, Canada, 2010.