Inductive Tight Semantics for Logic Programs

The Gelfond-Lifschitz operator fixed-point requirement by Stable Models induces asymmetry in dealing with Even Loops and Odd Loops Over Negation. We introduce a 2-valued semantics for Normal Logic Programs — the Inductive Tight semantics (ITS) — that generalizes SM semantics by dealing uniformly with Even and Odd loops. ITS conservatively extends the SM semantics, enjoys relevance and cumulativity, guarantees model existence, and respects the Well-Founded Model. The IT semantics relies on Layering, a generalization of Stratification, and is inductively defined on such layering: each model for a given layer must comply with some model for the whole set of layers below. Enjoying Relevance, the IT semantics is suitable top-down querying when complete models are unnecessary. The applications afforded by ITS are all those of Stable Models, which it generalizes, plus those employing OLONs for productively obtaining problem solutions, not just filtering them (like ICs).