Model-Guided Proof Debugging

In automated deduction, the final goal is to achieve a fully automatic proof system: given a logical specification of a problem, take a high-performance theorem prover, and let it do the work. Unfortunately, this does not work in practice, not only because theorem provers often lack finding the proof within reasonable time, but also because the specification is error-prone. For the latter, in the literature several methods are proposed for detecting and verifying errors in logic programs. In order to enable such analyses, usually termination of computation is presupposed. In this paper, we introduce techniques which are also applicable in the case of nontermination. One important aspect is the use of a natural language interface for inspecting even intermediate results of the proof search. By this, we are able to investigate the given specification wrt. critical properties: correctness wrt. an intended model, completeness, and sufficiency for answering given queries. For this, we employ tableau-based calculi, especially hyper-tableaux because of its model-building capability that is very helpful for debugging axiomatizations. 1 Motivation: The Deduction Life Cycle Automated deduction makes life easy: given a logical specification of your problem, take a highperformance theorem prover and let it do the work. Unfortunately, this is only a dream. In some cases it works for benchmark suites like the TPTP library [24]. There, a huge number of problems is given in form of a logical specification and the interesting question is, whether a prover can solve the problems—in most cases they have been solved by many other provers before—, and if it can, how fast? In real life, however, the problem is to find the appropriate logical formalization of the given problem. Once a formalization is found, the capabilities of theorem provers can be used to process the logical formulae—and usually one finds out, that the formalization was not as intended: either it was inconsistent or it did not meet the requirements. Our paper takes such a situation as the starting point.