Integrating Simplex with Tableaux

Abstract

International audienceWe 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 there is a natural interleaving between arithmetic and regular analytic rules. The arithmetic rules rely on the general simplex algorithm to compute solutions for systems over rationals, as well as on the branch and bound method to deal with integer systems. We also describe our implementation in the framework of Zenon, an automated theorem prover that is able to deal with first order logic with equality. This implementation has been provided with a backend verifier that relies on the Coq proof assistant , and which can verify the validity of the generated arithmetic proofs. Finally, we present some experimental results over the arithmetic category of the TPTP library, and problems of program verification coming from the benchmark provided by the BWare project

Automated Deduction in the B Set Theory using Typed Proof Search and Deduction Modulo

“…In the first table, in addition to the regular version of Zenon, we present the extensions with (polymorphic) types, with types and arithmetic, with types and deduction modulo, and with types, deduction modulo, and arithmetic, which is currently the regular version of Zenon Modulo 2 . The arithmetic extension [12] handles linear arithmetic formulas, and relies on the simplex algorithm to compute solutions for systems over rationals, as well as on the branch and bound method to deal with integer systems [14]. As can be observed, the more extensions we plug, All Tools (12, the more POs we prove.…”

First-Order Automated Reasoning with Theories: When Deduction Modulo Theory Meets Practice

“…In the first table of Table 1, in addition to the regular version of Zenon, we present the extensions with (polymorphic) types (tagged with "T"), with types and arithmetic (tagged with "T" and "A"), with types and Deduction modulo theory (tagged with "T" and "M"), and with types, Deduction modulo theory, and arithmetic (tagged with "T", "M", and "A"), which is currently the regular version of Zenon Modulo 3 . The arithmetic extension [44] handles linear arithmetic formulas, and relies on the simplex algorithm to compute solutions for systems over rationals, as well as on the branch and bound method to deal with integer systems [49]. As can be observed, the more extensions we plug, the more POs we prove.…”

The CADE-27 Automated theorem proving System Competition – CASC-27

“…The problems are given to the ATP systems in TPTP format, in increasing order of TPTP difficulty rating. The problems for the LTB division were taken from publicly available problem sets: the HLL problem category used the HH7150 problem set 1 ; the HL4 problem category used the H4H13897 problem set 2 ; the ISA problem category used the SH5795 problem set 3 ; the MZR problem category used the MPTP2078 problem set 4 . The problems in each category have consistent symbol usage, and almost consistent axiom naming, between problems.…”