Automated Theorem Proving with Extensions of First-Order Logic

Automated theorem provers are computer programs that check whether a logical conjecture follows from a set of logical statements. The conjecture and the statements are expressed in the language of some formal logic, such as first-order logic. Theorem provers for first-order logic have been used for automation in proof assistants, verification of programs, static analysis of networks, and other purposes. However, the efficient usage of these provers remains challenging. One of the challenges is the complexity of translating domain problems to first-order logic. Not only can such translation be cumbersome due to semantic differences between the domain and the logic, but it might inadvertently result in problems that provers cannot easily handle.The work presented in the thesis addresses this challenge by developing an extension of first-order logic named FOOL. FOOL contains syntactical features of programming languages and more expressive logics, is friendly for translation of problems from various domains, and can be efficiently supported by existing theorem provers. We describe the syntax and semantics of FOOL and present a simple translation from FOOL to plain first-order logic. We describe an efficient clausal normal form transformation algorithm for FOOL and based on it implement a support for FOOL in the Vampire theorem prover. We illustrate the efficient use of FOOL for program verification by describing a concise encoding of next state relations of imperative programs in FOOL. We show a usage of features of FOOL in problems of static analysis of networks. We demonstrate the efficiency of automated theorem proving in FOOL with an extensive set of experiments. In these experiments we compare the performance of Vampire on a large collection of problems from various sources translated to FOOL and ordinary first-order logic. Finally, we fix the syntax for FOOL in TPTP, the standard language of first-order theorem provers

Initial Experiments with TPTP-style Automated Theorem Provers on ACL2 Problems

This paper reports our initial experiments with using external ATP on some corpora built with the ACL2 system. This is intended to provide the first estimate about the usefulness of such external reasoning and AI systems for solving ACL2 problems.Comment: In Proceedings ACL2 2014, arXiv:1406.123

12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser

This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto

The Vampire and the FOOL

This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions. We argue that presented extensions facilitate reasoning-based program analysis, both by increasing the expressivity of first-order reasoners and by gains in efficiency