Multi-dimensional Dynamic Knowledge Representation

According to Dynamic Logic Programming (DLP), knowledge may be given by a sequence of theories (encoded as logic programs) representing different states of knowledge. These may represent time (e.g. in updates), specificity (e.g. in taxonomies), strength of updating instance (e.g. in the legislative domain), hierarchical position of knowledge source (e.g. in organizations), etc. The mutual relationships extant among states are used to determine the semantics of the combined theory composed of all the individual theories. Although suitable to encode a single dimension (e.g. time, hierarchies...), DLP cannot deal with more than one simultaneously because it is defined only for a linear sequence of states. To overcome this limitation, we introduce the notion of Multidimensional Dynamic Logic Programming (MDLP), which generalizes DLP to collections of states organized in arbitrary acyclic digraphs representing precedence. In this setting, MDLP assigns semantics to sets and subsets of such logic programs. By dint of this natural generalization, MDLP affords extra expressiveness, in effect enlarging the latitude of logic programming applications unifiable under a single framework. The generality and flexibility provided by the acyclic digraphs ensures a wide scope and variety of application possibilities.