Tight Semantics for Logic Programs

We define the Tight Semantics (TS), a new semantics for all NLPs complying with the requirements of: 2-valued semantics; preserving the models of SM; guarantee of model existence (even in face of odd loops over negation or infinite chains); relevance; cumulativity; and compliance with the Well-Founded Model. We also extend TS to adumbrate ELPs and Disjunctive LPs, though a full account of these is left to other papers. When complete models are unnecessary, and top-down querying (à la Prolog) is desired, TS provides the 2-valued option that guarantees model existence, as a result of its relevance property. Top-down querying with abduction by need is rendered available too by TS. The user need not pay the price of computing whole models, nor of generation all possible abductions, only to filter irrelevant ones subsequently. In a nutshell, a TS model of a NLP P is any minimal model M of P that further satisfies bP—the program remainder of P—in that each loop in bP has a minimal ...

• Type: Conference
• Year: 2010
• Where: ICLP
• Authors: Luís Moniz Pereira, Alexandre Miguel Pinto
• Keywords: Automated Reasoning, ICLP 2010, Minimal Models, Model Existence, TS Model