A Confluent Connection Calculus

This work is concerned with basic issues of the design of calculi and proof procedures for first-order connection methods and tableaux calculi. Proof procedures for these type of calculi developed so far suffer from not exploiting proof confluence, and very often unnecessarily rely on a heavily backtrack oriented control regime. As a new result, we present a variant of a connection calculus and prove its strong completeness. This enables the design of backtrack-free control regimes. To demonstrate that the underlying fairness condition is reasonably implementable we define an effective search strategy. We show that with the new approach the search space can be exponentially smaller than those of current, backtrackingoriented proof procedures based on weak completeness results.