A progression semantics for first-order logic programs

摘要

In this paper, we propose a progression semantics for first-order normal logic programs, and show that it is equivalent to the well-known stable model (answer set) semantics. The progressional definition sheds new insights into Answer Set Programming (ASP), for instance, its relationships to Datalog, First-Order Logic (FOL) and Satisfiability Modulo Theories (SMT). As an example, we extend the notion of boundedness in Datalog for ASP, and show that it coincides with the notions of recursion-freeness and loop-freeness under program equivalence. In addition, we prove that boundedness precisely captures first-order definability for normal logic programs on arbitrary structures. Finally, we show that the progressional definition suggests an alternative translation from ASP to SMT, which yields a new way of implementing first-order ASP.