APPLICATIONS OF LYNDON HOMOMORPHISM THEOREMS TO THE THEORY OF MINIMAL MODELS
Marek A. Suchenek · International Journal of Foundations of Computer Science · 1990
This paper contains, among others, a concise proof (proof 6.2) of the following fact (theorem 2.7): For every ∀∪Neg-theory Σ and every positive sentence φ, [Formula: see text] It is demonstrated in this paper (corollary 5.2) that the necessary and sufficient condition for φ, guaranteeing the truthfulness of the above equivalence for every Σ⊆∀, is that φ is equivalent to a sentence which does not contain in a scope of negation an occurrence of a relation symbol other than the equality symbol. The proofs have been constructed using classical model-theoretic tools, thus supporting the thesis that classical logic is adequate for expressing and investigating non-monotonic reasoning patterns.