Multi-dimensional Logic Programming

According to the paradigm of Dynamic Logic Programming, knowledge is given by a set of theories (encoded as logic programs) representing different states of the world. Different states may represent time (as in updates), specificity (as in taxonomies), strength of the updating instance (as in the legislative domain), hierarchical position of knowledge source (as in organizations), etc. The mutual relationships extant between different states are used to determine the semantics of the combined theory composed of all individual theories. Although suitable to encode one dimension (e.g. time, hierarchies, domains,...), Dynamic Logic Programming cannot deal with more than one such dimension simultaneously because it is only defined for a linear sequence of states. To overcome this limitation, we introduce, in this paper, the notion of Multi-dimensional Dynamic Logic Programming, which generalizes Dynamic Logic Programming by allowing collections of states represented by arbitrary acyclic digraphs. In this setting, Multi-dimensional Dynamic Logic Programming assigns semantics to sets and subsets of logic programs, depending on how they stand in relation to one another, these relations being defined by the acyclic digraph that represents the states. By dint of such natural generalization, Multi-dimensional Dynamic Logic Programming affords extra expressiveness, thereby 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 possibilities, some of which will be expounded in this paper.