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 (OLONs) or infinite chains; relevance cumulativity; and compliance with the Well-Founded Model.

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 that of generating all possible abductions, only to filter irrelevant ones subsequently.

A TS model of a NLP P is any minimal model M of P that further satisfies P^---the program remainder of P---in that each loop in P^ has a MM contained in M, whilst respecting the constraints imposed by the MMs of the other loops so-constrained too.

The applications afforded by TS are all those of Stable Models, which it generalizes, plus those permitting to solve OLONs for model existence, plus those employing OLONs for productively obtaining problem solutions, not just filtering them (like Integrity Constraints).