A Language for Multi-dimensional Updates

Dynamic Logic Programming (DLP) was introduced to deal with knowledge about changing worlds, by assigning semantics to sequences of generalized logic programs, each of which represents a state of the world. These states permit the representation, not only of time, but also of specificity, strength of updating instance, hierarchical position of the knowledge source, etc. Subsequently, the Language of Updates LUPS was introduced to allow for the association, with each state, of a set of transition rules. It thereby provides for an interleaving sequence of states and transition rules within an integrated declarative framework. DLP (and LUPS), because defined only for a linear sequence of states, cannot deal simultaneously with more than a single dimension (e.g. time, hierarchies,…). To overcome this limitation, Multi-dimensional Dynamic Logic Programming (MDLP) was therefore introduced, so as to make it possible to organize states into arbitrary acyclic digraphs (DAGs). In this paper we now extend LUPS, setting forth a Language for Multi-dimensional Updates (MLUPS). MLUPS admits the specification of flexible evolutions of such DAG organized logic programs, by allowing not just the specification of the logic programs representing each state, but to the evolution of the DAG topology itself as well.