Open Answer Set Programming With Guarded Programs

Open Answer Set Programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program's constants. The authors define a Fixed Point Logic (FPL) extension of Clark's completion such that open answer sets correspond to models of FPL formulas and identify a syntactic subclass of programs, called (loosely) guarded programs. Whereas reasoning with general programs in OASP is undecidable, the FPL translation of (loosely) guarded programs falls in the decidable (loosely) guarded fixed point logic (µ(L)GF). Moreover, they reduce normal closed ASP to loosely guarded OASP, enabling for the first time, a characterization of an answer set semantics by µLGF formulas.