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SMT Solving Modulo Tableau and Rewriting Theories
An automated theorem prover that combines an SMT solver with tableau calculus and rewriting, and Rewriting is introduced along the lines of deduction modulo theory, where axioms are turned into rewrite rules over both terms and propositions.
Centralizing equality reasoning in MCSAT
The topic of how to reason about equalities in a centralized way is broached, so that the theory reasoners can avoid replicating equality reasoning steps, and even benefit from a centralized implementation of equivalence classes of terms, which is based on a equality graph (Egraph).
Automated Deduction in the B Set Theory using Typed Proof Search and Deduction Modulo
- Guillaume Bury, D. Delahaye, Damien Doligez, Pierre Halmagrand, O. Hermant
- Computer ScienceLPAR
- 24 November 2015
We introduce an encoding of the set theory of the B method using polymorphic types and deduction modulo, which is used for the automated verication of proof obligations in the framework of theBWare…
Integrating Simplex with Tableaux
We propose an extension of a tableau-based calculus to deal with linear arithmetic. This extension consists of a smooth integration of arithmetic deductive rules to the basic tableau rules, so that…
First-Order Automated Reasoning with Theories: When Deduction Modulo Theory Meets Practice
- G. Burel, Guillaume Bury, Raphaël Cauderlier, D. Delahaye, Pierre Halmagrand, O. Hermant
- Computer ScienceJournal of Automated Reasoning
- 23 September 2019
This work describes two automated reasoning systems that have been built to extend other provers with Deduction modulo theory and describes the two backends of these systems to the Dedukti universal proof checker, which allows us to verify the proofs produced by these tools.
An Automation-Friendly Set Theory for the B Method
An automation-friendly set theory for the B method is proposed using first order logic extended to polymorphic types and rewriting along the lines of deduction modulo theory, where axioms are turned into rewrite rules over both propositions and terms.
Automated Deduction in the B Set Theory using Deduction Modulo ?
A new encoding of the set theory of the B method based on deduction modulo, an extension of predicate calculus that includes rewriting on both terms and propositions, which is well suited for proof search in axiomatic theories, as it turns many axioms into rewrite rules.
Implementing Polymorphism in Zenon
This paper discusses the implementation of polymorphism into the first-order tableau-based automated theorem prover Zenon, and modified some basic parts of the code, from the representation of expressions to the proof-search algorithm.
Dolmen: A Validator for SMT-LIB and Much More
- Guillaume Bury
- Computer ScienceSMT
Dolmen provides tools to parse, type, and validate input files used in automated deduction, such as problems written in the SMT-LIB language, but also other languages commonly used in theorem…
Integrating rewriting, tableau and superposition into SMT
- Guillaume Bury
- Computer Science
- 8 January 2019
This PhD thesis presents ArchSAT, an automated theorem prover with formal proof outputs, which is used to study the integration of some first-order reasoning methods into SMT solvers to speed up reasoning on problems whose axioms can be turned into rewrite rules.