model-theoretic-formalization-paradox-free-minimal-models
IN premise — summaries/2026/08/24/wiki-Non-monotonic_logic.md
Created 2026-08-24T17:11:19+00:00
Model-theoretic formalization of non-monotonic logics restricts a monotonic logic's semantics to special models (e.g., minimal models) to derive sound and complete inference rules, eliminating paradoxes present in proof-theoretic (fixed-point) approaches; first-order circumscription, CWA, and autoepistemic logic were all successfully reformulated this way.
Summary
Instead of letting non-monotonic reasoning systems derive their own rules through iterative self-reference (which tends to produce contradictions and paradoxes), this approach fixes the meaning by restricting which interpretations of the world count as valid — typically the most conservative or "smallest" ones. This gives a clean, paradox-free foundation for practical systems like circumscription and the closed-world assumption, and it works in practice, not just on paper, since several major reasoning frameworks have been successfully rebuilt on this principle.