Success Ontology Models

Sets of Models for Ax and C - Some Examples

Satisfiable (SAT): Some interpretations are models of Ax, and some models of Ax are models of C. CounterSatisfiable (CSA): Some interpretations are models of Ax, and some models of Ax are models of ¬C. EquivalentTheorem (ETH): Some, but not all, interpretations are models of Ax, all models of Ax are models of C, and all models of C are models of Ax. Tautology (TAU): All interpretations are models of Ax, and all interpretations are models of C. WeakerTautologousConclusion (WTC): Some, but not all, interpretations are models of Ax, and all interpretations are models of C. WeakerTheorem (WTH): Some interpretations are models of Ax, all models of Ax are models of C, some models of C are not models of Ax, and some interpretations are not models of C. TautologousConclusionContradictoryAxioms (TCA): No interpretations are models of Ax, and all interpretations are models of C. WeakerConclusionContradictoryAxioms (WCA): No interpretations are models of Ax, and some, but not all, interpretations are models of C. UnsatisfiableConclusionContradictoryAxioms (UCA): No interpretations are models of Ax, and all interpretations are models of ¬C. WeakerUnsatisfiableConclusion (WUC): Some, but not all, interpretations are models of Ax, and all interpretations are models of ¬C. Unsatisfiable (UNS): All interpretations are models of Ax, and all interpretations are models of ¬C.