Refinements of Theory Model Elimination and a Variant without Contrapositives

Theory Reasoning means to build-in certain knowledge about a problem domain into a deduction system or calculus, which is in our case model elimination. Several versions of theory model elimination (TME) calculi are presented and proven complete: on the one hand we have highly restricted versions of total and partial TME. These restrictions allow (1) to keep fewer path literals in extension steps than in related calculi, and (2) discard proof attempts with multiple occurrences of literals along a path (i.e. regularity holds). On the other hand, we obtain by small modifications to TME versions which do not need contrapositives (a la Near-Horn Prolog). We show that regularity can be adapted for these versions. The independence of the goal computation rule holds for all variants. Comparative runtime results for our PTTP-implementations are supplied.