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Register a new userSubsumption Demodulation in First-Order Theorem Proving
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Added by
Bernhard Gleiss
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Motivated by applications of first-order theorem proving to software analysis, we introduce a new inference rule, called subsumption demodulation, to improve support for reasoning with conditional equalities in superposition-based theorem proving. We show that subsumption demodulation is a simplification rule that does not require radical changes to the underlying superposition calculus. We implemented subsumption demodulation in the theorem prover Vampire, by extending Vampire with a new clause index and adapting its multi-literal matching component. Our experiments, using the TPTP and SMT-LIB repositories, show that subsumption demodulation in Vampire can solve many new problems that could so far not be solved by state-of-the-art reasoners.
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To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem provers can be used to prove program properties efficiently. However, in the TPTP language, the input language of automated first-order theorem provers, the use of the boolean sort is limited compared to other sorts, thus hindering the use of first-order theorem provers in program analysis and verification. In this paper, we present an extension FOOL of many-sorted first-order logic, in which the boolean sort is treated as a first-class sort. Boolean terms are indistinguishable from formulas and can appear as arguments to functions. In addition, FOOL contains if-then-else and let-in constructs. We define the syntax and semantics of FOOL and its model-preserving translation to first-order logic. We also introduce a new technique of dealing with boolean sorts in superposition-based theorem provers. Finally, we discuss how the TPTP language can be changed to support FOOL.
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This volume of EPTCS contains the proceedings of the Seventh Workshop on Proof Exchange for Theorem Proving (PxTP 2021), held on 11 July 2021 as part of the CADE-28 online conference in Pittsburgh, USA. The PxTP workshop series brings together researchers working on various aspects of communication, integration, and cooperation between reasoning systems and formalisms, with a special focus on proofs. The progress in computer-aided reasoning, both automated and interactive, during the past decades, made it possible to build deduction tools that are increasingly more applicable to a wider range of problems and are able to tackle larger problems progressively faster. In recent years, cooperation between such tools in larger systems has demonstrated the potential to reduce the amount of manual intervention. Cooperation between reasoning systems relies on availability of theoretical formalisms and practical tools to exchange problems, proofs, and models. The PxTP workshop series strives to encourage such cooperation by inviting contributions on all aspects of cooperation between reasoning tools, whether automatic or interactive.
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