Tabled Abduction in 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 mechanisms, are mature enough to facilitate the introduction of tabling abductive solutions (tabled abduction) into them. Our contributions are as follows: (1) We conceptualize tabled abduction for abductive normal logic programs, permitting abductive solutions to be reused, from one abductive context to another. The approach relies on a transformation into tabled logic programs that makes use of the dual transformation, and enables efficiently handling the problem of abduction under negative goals, by introducing dual positive counterparts for them. (2) We realize tabled abduction in TABDUAL, a system implemented in XSB Prolog, allowing dualization by-need only. (3) We refine the dual transformation in the context of TABDUAL to permit executing programs with variables and non-ground queries. (4) We foster pragmatic approaches in TABDUAL to cater to all varieties of loops in normal logic programs, now complicated by abduction. (5) We evaluate TABDUAL in practice by examining five variants, according to various evaluation objectives. (6) We detail how TABDUAL can be applied to declarative debugging and decision making. (7) Finally, we refer to related work, and discuss TABDUAL’s correctness, complexity, and features that could migrate to the engine level, in Logic Programming systems wanting to encompass tabled abduction.