Non-Deterministic Approximation Fixpoint Theory and Its Application in Disjunctive Logic Programming
This work addresses the problem of handling indefinite information in nonmonotonic logics for researchers in logic programming and formal semantics, but it is incremental as it builds upon the existing AFT framework.
The authors extended Approximation Fixpoint Theory (AFT) to handle non-deterministic constructs for indefinite information, such as disjunctive formulas, by generalizing its constructions to operators with set ranges, and demonstrated its applicability in disjunctive logic programming.
Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.