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Extensional Crisis and Proving Identity [chapter]

Ashutosh Gupta, Laura Kovács, Bernhard Kragl, Andrei Voronkov
2014 Lecture Notes in Computer Science  
We illustrate this by running the VAMPIRE theorem prover with extensionality resolution on a number of set theory and array problems.  ...  Extensionality axioms are common when reasoning about data collections, such as arrays and functions in program analysis, or sets in mathematics.  ...  S11410-N23), and the WWTF PROSEED grant ICT C-050.  ... 
doi:10.1007/978-3-319-11936-6_14 fatcat:fj7nwcr54rhhfjgnbqtypfb3zy

Coming to terms with quantified reasoning

Laura Kovács, Simon Robillard, Andrei Voronkov
2017 Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages - POPL 2017  
However, as the theory of finite term algebras is not finitely axiomatizable, reasoning about quantified properties over term algebras is challenging.  ...  In this paper we address full first-order reasoning about properties of programs manipulating term algebras, and describe two approaches for doing so by using first-order theorem proving.  ...  the EPSRC grant ReVeS: Reasoning for Verification and Security.  ... 
doi:10.1145/3009837.3009887 fatcat:26soclwzs5gkbkc5ao2t42vg7m

Coming to Terms with Quantified Reasoning [article]

Laura Kovacs, Simon Robillard, Andrei Voronkov
2016 arXiv   pre-print
However, as the theory of finite term algebras is not finitely axiomatizable, reasoning about quantified properties over term algebras is challenging.  ...  In this paper we address full first-order reasoning about properties of programs manipulating term algebras, and describe two approaches for doing so by using first-order theorem proving.  ...  the EPSRC grant ReVeS: Reasoning for Verification and Security.  ... 
arXiv:1611.02908v1 fatcat:gfxm4sj7prgcrdpl3ymffnhp4m

System Description: SPASS-FD [chapter]

Matthias Horbach
2011 Lecture Notes in Computer Science  
Using a constrained superposition calculus and a disunification procedure, it is possible to employ superposition-based first-order reasoners for reasoning not only about all models of a first-order theory  ...  In this paper, I describe the tool Spass-FD, an extension of the firstorder prover Spass that equips Spass with disunification and with fixed domain and minimal model theorem proving capabilities.  ...  reasoning with a saturation-based first-order prover.  ... 
doi:10.1007/978-3-642-22438-6_25 fatcat:jk55poh3pngizejzvn2j55ihfy

Visualizing Data Saturation Process in Mapping Site Amplification of Earthquake Ground Motions

Anirban CHAKRABORTY, Hiroyuki GOTO
2020 Journal of Natural Disaster Science  
Using information theory, we propose a parameter that measures the incremental information gain as maps are updated with new data over time.  ...  However, we cannot ascertain whether the amount of available data is sufficient, and we have no guidelines to draw the maps based on the available data consistent with the data accumulation.  ...  Sumio Sawada from the Disaster Prevention and Research Institute, Kyoto University, Japan for his valuable comments and insights on the manuscript.  ... 
doi:10.2328/jnds.40.14 fatcat:s5xs4hc4ezbtflsytmqd3r3aji

Layered Clause Selection for Theory Reasoning [article]

Bernhard Gleiss, Martin Suda
2020 arXiv   pre-print
Explicit theory axioms are added by a saturation-based theorem prover as one of the techniques for supporting theory reasoning.  ...  The strategy refines a recently proposed two-layer-queue clause selection and combines it with a heuristical measure of the amount of theory reasoning in the derivation of a clause.  ...  Introduction Thanks to recent advances, saturation-based theorem provers are increasingly used to reason about problems requiring quantified theory-reasoning [6, 4] .  ... 
arXiv:2001.09705v3 fatcat:lamgodl3e5fnxnonoydvmrv5ya

Proofs by Deduction [chapter]

2017 Logic and Language Models for Computer Science  
Nonetheless, the seminar was especially timely given recent activities in deduction and applications, and it enabled researchers from different subcommunities to communicate with each other towards exploiting  ...  Many use models as certificates for satisfiability to extract feasible program executions; others use proof objects as certificates for unsatisfiability in the context of highintegrity systems development  ...  The theory of arrays is one of the most relevant theories for software verification, this is the reason why current research in automated reasoning dedicated so much effort in establishing decision and  ... 
doi:10.1142/9789813229211_0003 fatcat:cqpgqtobz5gx3db5bq54gxrd4m

Layered Clause Selection for Theory Reasoning [chapter]

Bernhard Gleiss, Martin Suda
2020 Lecture Notes in Computer Science  
Explicit theory axioms are added by a saturation-based theorem prover as one of the techniques for supporting theory reasoning.  ...  The strategy refines a recently proposed two-layer-queue clause selection and combines it with a heuristic measure of the amount of theory reasoning in the derivation of a clause.  ...  Introduction Thanks to recent advances, saturation-based theorem provers are increasingly used to reason about problems requiring quantified theory-reasoning [4, 6] .  ... 
doi:10.1007/978-3-030-51074-9_23 fatcat:xnv6ppimzvci5om6nd7isha4me

On theorem proving for program checking

Maria Paola Bonacina
2010 Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '10  
This article is a survey of recent results, related works and new challenges in automated theorem proving for program checking.  ...  The aim is to give some historical perspective, albeit necessarily incomplete, and highlight some of the turning points that made crucial advances possible.  ...  Reasoning with equality and more generally theory reasoning are essential to reasoning about programs.  ... 
doi:10.1145/1836089.1836090 dblp:conf/ppdp/Bonacina10 fatcat:mh3666vskfcxvgnisxp7hnwvi4

Decision Procedures for Region Logic [chapter]

Stan Rosenberg, Anindya Banerjee, David A. Naumann
2012 Lecture Notes in Computer Science  
This fragment combines sets and (functional) images with the theories of arrays and partial orders.  ...  Region logic is Hoare logic for object-based programs. It features local reasoning with frame conditions expressed in terms of sets of heap locations.  ...  Thanks to Nikolaj Bjørner and Leonardo de Moura for help with Z3 integration and feedback on the implementation. Thanks to Clark Barrett for studying proofs of soundness and completeness of tableaux.  ... 
doi:10.1007/978-3-642-27940-9_25 fatcat:d5rc6es2sbhh5byheba6cmzm3a

Unification with Abstraction and Theory Instantiation in Saturation-Based Reasoning [chapter]

Giles Reger, Martin Suda, Andrei Voronkov
2018 Lecture Notes in Computer Science  
We make a new contribution to the field by providing a new method of using SMT solvers in saturation-based reasoning.  ...  This utilises the power of SMT solvers for theory reasoning with non-ground clauses, reasoning which is currently achieved by the addition of often prolific theory axioms.  ...  Introduction Reasoning in quantifier-free first-order logic with theories, such as arithmetic, is hard. Reasoning with quantifiers and first-order theories is very hard.  ... 
doi:10.1007/978-3-319-89960-2_1 fatcat:qmvu5nhrdzdevgqlyq7eckcplu

Engineering DPLL(T) + Saturation [chapter]

Leonardo de Moura, Nikolaj Bjørner
2008 Lecture Notes in Computer Science  
Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrated theory reasoning.  ...  The most efficient SMT solvers rely on refutationally incomplete methods for incorporating quantifier reasoning. We describe a calculus and a system that tightly integrates Superposition and DPLL(T).  ...  Conclusion We have introduced a calculus that tightly integrates inference rules used in saturation based provers with the DPLL(T) calculus.  ... 
doi:10.1007/978-3-540-71070-7_40 fatcat:sdrbygml4fbadde76qhbsxmtju

Case Studies on Invariant Generation Using a Saturation Theorem Prover [chapter]

Kryštof Hoder, Laura Kovács, Andrei Voronkov
2011 Lecture Notes in Computer Science  
Automatic understanding of the intended meaning of computer programs is a very hard problem, requiring intelligence and reasoning.  ...  used in the experiments.  ...  Kryštof Hoder is supported by the School of Computer Science at the University of Manchester and by an EPSRC Pathfinder grant.  ... 
doi:10.1007/978-3-642-25324-9_1 fatcat:ht36kixdvvgzvbdoeohs24v5bm

First-Order Theorem Proving and Vampire [chapter]

Laura Kovács, Andrei Voronkov
2013 Lecture Notes in Computer Science  
Further, we also cover more recent topics and features of VAMPIRE designed for advanced applications, including satisfiability checking, theory reasoning, interpolation, consequence elimination, and program  ...  We discuss the superposition calculus and explain the key concepts of saturation and redundancy elimination, present saturation algorithms and preprocessing, and demonstrate how these concepts are implemented  ...  This work was partially done while the first author was affiliated with the TU Vienna.  ... 
doi:10.1007/978-3-642-39799-8_1 fatcat:bhabf63t35h3fdvmqb23d3w2jq

Layered Clause Selection for Saturation-based Theorem Proving

Bernhard Gleiss, Martin Suda
2020 Zenodo  
In this work, we investigate this framework in depth and introduce, in addition to a previously presented feature (based on the amount of theory reasoning in the derivation of a clause), three new features  ...  We implemented the resulting clause selection heuristics in the state-of-the-art saturation-based theorem prover Vampire and present an evaluation of these new clause-selection strategies and their combinations  ...  Acknowledgements We thank the anonymous reviewers for their useful comments and suggestions. We also thank Sibylle Ortner for a careful proofreading of a preliminary version of this paper.  ... 
doi:10.5281/zenodo.4584799 fatcat:gzosonxhsbgi3pmxeme6expmzq
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