Tabdual: a tabled abduction system for logic programs

Abduction has been on the back burner in logic programming, as abduction can be too difficult to implement, and costly to perform, in particular if abductive solutions are not tabled. On the other hand, current Prolog systems, with their tabling mecha- nisms, are mature enough to facilitate the introduction of tabling abductive solutions (tabled abduction) into them. Our contributions are as follows. First, we conceptualize a tabled abduction technique for abductive normal logic programs, permitting abductive solutions to be reused, from one abductive context to another. The approach is underpinned by the theory of ABDUAL and relies on a transformation into tabled logic programs. It particularly makes use of the dual transformation of ABDUAL that enables efficiently handling the prob- lem of abduction under negative goals, by introducing dual positive counterparts for them. Second, we realize this tabled abduction technique in TABDUAL, a system implemented in XSB Prolog. The implementation poses several challenges to concretely realize the abstract theory of ABDUAL, e.g., by taking care of all varieties of loops (positive loops and loops over negation) in normal logic programs, now complicated by tabled abduction. Other challenges are pertinent to optimizations, by benefitting from XSB features, e.g., constructing dual rules by need only. Third, we evaluate TABDUAL with respect to various standpoints. The evaluations employ cases from declarative debugging, and also touch upon tabling nogoods of subproblems in the context of abduction. The techniques introduced in TABDUAL intends to sensitize a general audience of users, and of implementers of various LP systems, to the potential benefits of tabled abduction, where a number of its techniques are also adaptable and importable into LP systems that afford tabling mechanisms, other than XSB Prolog.