Detection of First Order Axiomatic Theories
Automated theorem provers for first-order logic with equality have become very powerful and useful, thanks to both advanced calculi — such as superposition and its refinements — and mature implementation techniques. Nevertheless, dealing with some axiomatic theories remains a challenge because it gives rise to a search space explosion. Most attempts to deal with this problem have focused on specific theories, like AC (associative commutative symbols) or ACU (AC with neutral element). Even detecting the presence of a theory in a problem is generally solved in an ad-hoc fashion. We present here a generic way of describing and recognizing axiomatic theories in clausal form first-order logic with equality. Subsequently, we show some use cases for it, including a redundancy criterion that can be applied to some equational theories, extending some work that has been done by Avenhaus, Hillenbrand and Löchner.
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