Forward Chaining for Hybrid ASP

Abstract

In this paper, we define an analogue of the Forward Chaining (FC) algorithm due to Marek, Nerode, and Remmel [12] for Hybrid Answer Set Programming (H-ASP). The FC algorithm for normal logic programs takes as an input a well ordering ≺ of the non-Horn clauses of a normal logic program P and produces a stable model D ^≺ for a subprogram A ^≺ of P. It is the case that for every stable model M of P, there is a well ordering ≺ such that D ^≺ = M and A ^≺ = P. Thus the search for a stable model of P becomes a search for a well ordering ≺ such that A ^≺ = P. We show that a similar result hold in case of FC for H-ASP. H-ASP is an extension of normal logic programming or Answer Set Programming (ASP), introduced by the authors in [2] that allows users to combine ASP type rules and numerical algorithms. The MFC algorithm, introduced by the authors in [1] is a Monte Carlo algorithm that combines the FC algorithm and the Metropolis-Hastings algorithm to search for stable models of normal logic programs. We shall briefly discuss how one can produce an analogue of the MFC algorithm to search for stable models of H-ASP programs.