Depth-first Proof Search without Backtracking for Free-variable Clausal Tableaux

Depth-first Proof Search without Backtracking for Free-variable Clausal Tableaux

Depth-first Proof Search without Backtracking for Free-variable Clausal Tableaux

Depth-first proof search without backtracking for free-variable clausal tableaux

We analyse the problem of constructing a deterministic proof procedure for free variable clausal tableaux that performs depth-first proof search without backtracking; and we present a solution based on a fairness strategy. That strategy uses weight orderings and a notion of tableau subsumption to avoid proof cycles and it employs reconstruction steps to handle the destructiveness of free variab...

Incremental Closure of Free Variable Tableaux

This paper presents a technique for automated theorem proving with free variable tableaux that does not require backtracking. Most existing automated proof procedures using free variable tableaux require iterative deepening and backtracking over applied instantiations to guarantee completeness. If the correct instantiation is hard to find, this can lead to a significant amount of duplicated wor...

A Non-clausal Connection Calculus

A non-clausal connection calculus for classical first-order logic is presented that does not require the translation of input formulae into any clausal form. The definition of clauses is generalized, which may now also contain (sub-) matrices. Copying of appropriate (sub-)clauses in a dynamic way, i.e. during the actual proof search, is realized by a generalized extension rule. Thus, the calcul...