Tabling with Answer Subsumption: Implementation, Applications and Performance

Tabled Logic Programming (TLP) is becoming widely available in Prolog systems, but most implementations of TLP implement only answer variance in which an answer A is added to the table for a subgoal S only if A is not a variant of any other answer already in the table for S. While TLP with answer variance is powerful enough to implement the well-founded semantics with good termination and complexity properties, TLP becomes much more powerful if a mechanism called answer subsumption is used. XSB implements two forms of answer subsumption. The first, partial order answer subsumption, adds A to a table only if A is greater than all other answers already in the table according to a user-defined partial order. The second, lattice answer subsumption, may join A to some other answer in the table according to a user-defined upper semi-lattice. Answer subsumption can be used to implement paraconsistent and quantitative logics, abstract analysis domains, and preference logics. This paper discusses the semantics and implementation of answer subsumption in XSB, and discusses performance and scalability of answer subsumption on a variety of problems.