leanTAP: Lean tableau-based deduction

Theorem proving for conditional logics: CondLean and GOALDUCK

“…CondLean is inspired by the "lean" methodology, introduced by Beckert and Posegga (Beckert et al, 1995) and analyzed by Fitting (Fitting, 1998). In (Beckert et al, 1995) an efficient and elegant first-order theorem prover, called leanT A P, is presented. leanT A P is a very short Prolog program consisting of only five clauses, and makes use of Prolog's search mechanism and backtracking as much as possible.…”

“…It is a SICStus Prolog program inspired by the "lean" methodology introduced by leanT A P ( (Beckert et al, 1995;Fitting, 1998)). The program CondLean comprises a set of clauses, each one of them represents a sequent rule or axiom.…”

“…Proof search is provided for free by the mere depth-first search mechanism of Prolog, without any meta-level algorithm of search strategy. In this way, the philosophy underlaying the "lean" methodology is "to achieve maximal efficiency from minimal means" (Beckert et al, 1995), that is to say to write short programs and exploit the power of Prolog's engine as much as possible.…”

“…CondLean follows to a certain extent the "lean" methodology (Beckert et al, 1995;Fitting, 1998). The program implements a predicate prove, and each clause of this predicate represents a sequent rule or axiom.…”

Nested sequent calculi and theorem proving for normal conditional logics: The theorem prover NESCOND

“…The program, called NESCOND, is inspired by the methodology introduced by the system leanT A P [5], even if it does not fit its style in a strict sense. The basic idea is that each axiom or rule of the nested sequent calculi is implemented by a Prolog clause of the program.…”