Bidirectional Answer Set Programs with Function Symbols

Current Answer Set Programming (ASP) solvers largely build on Datalog, which, unlike general logic programming, lacks function symbols. This limitation makes ASP decidable, but greatly complicates the modeling of indefinite time, recursive data structures (e.g., lists), and infinite processes and objects in general. Recent research thus aims at finding decidable fragments of ASP with function symbols and studying their complexity. We identify bidirectional ASP programs as an expressive, but yet decidable, language that is useful, e.g., for reasoning about actions involving both the future and the past. We tightly characterize the computational complexity of bidirectional programs and some of their subclasses, addressing the main reasoning tasks. Our results also show that the recently introduced FDNC programs can be extended by inverse rules while retaining decidability, but computational costs are unavoidably higher.

Thomas Eiter, Mantas Simkus