NoMoRe: A System for Non-Monotonic Reasoning under Answer Set Semantics

The Intelligent Grounder of DLV

“…Answer Set Programming (ASP) [18,19,11,32] is a powerful logic-based programming language which is enjoying increasing interest within the scientific community also thanks to the availability of a number of efficient implementations [27,15,23,29,30,2]. DLV [27] is one of the most successful and widely used ASP systems, which has stimulated some interest also in industry.…”

Logic programming with infinite sets

“…More generally, our next result will show that various questions about the least model of an arbitrary recursive ESB Horn program are 1 1 hard. Note that theorem 2.4 allowed us to prove that the least model of a ESB Horn program is r.e.…”

“…Given a recursive ESB Horn program P , there is a 0 1 monotone operator such that the least model M of P is the closure of started on the empty set, which is automatically 1 1 by the classical result of Spector [38]. For the completeness, we will define a recursive ESB Horn program P with recursive constraints and least fixed point M such that Now consider the one-step provability operator T P for P .…”

“…(b) The predicate "R is the least fixed point of P " is 1 1 -complete. (c) The predicate "P has a recursive stable model" is 1 1 -complete.…”

“…For example, for any arithmetic set A, we shall construct a recursive ESB Horn program P A with recursive constraints such that the degree of the least model of P A is A. We also show that the least model of a recursive ESB Horn program P with recursive constraints is always 1 1 and that there is a recursive ESB Horn program P with recursive constraints whose least model is 1 1 -complete. Moreover we show the question of whether ω is the least model of a recursive ESB Horn program P with recursive constraints is 1 1 -complete, as is the question of whether a recursive ESB Horn program P with recursive constraints has a recursive least model.…”