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