Efficient resolution mechanism for fuzzy temporal constraint logic

In this paper we describe a module, named Temporal Solving Module (TSM), for answering the queries sent to a data blackboard which must take into account fuzzy temporal constraints among blackboard variables. The TSM receives the queries written in an interaction language that is translated into a language of a reified [13] many-sorted [9] first-order logic, called Fuzzy Temporal Constraint Logic (FTCL). This logic has been formalized in previous works, together with a sound resolution principle for it [3] [4]. Now, we justify the search strategy used in the implementation of the unit resolution. The main results achieved in this work are the simplification criteria and the heuristic evaluation function given for improving the search process to achieve the refutation. First, we use the fuzzy number ordering functions proposed by Marin et al. [12] for obtaining a simplification on queries that imply an exhaustive search in the data blackboard. Secondly, in order to prune the tree, we use a function to check the possibility of obtaining a fuzzy temporal instant different to empty set, in the unification of two imprecise temporal variables.