35,511 research outputs found
Towards Ranking Geometric Automated Theorem Provers
The field of geometric automated theorem provers has a long and rich history,
from the early AI approaches of the 1960s, synthetic provers, to today
algebraic and synthetic provers.
The geometry automated deduction area differs from other areas by the strong
connection between the axiomatic theories and its standard models. In many
cases the geometric constructions are used to establish the theorems'
statements, geometric constructions are, in some provers, used to conduct the
proof, used as counter-examples to close some branches of the automatic proof.
Synthetic geometry proofs are done using geometric properties, proofs that can
have a visual counterpart in the supporting geometric construction.
With the growing use of geometry automatic deduction tools as applications in
other areas, e.g. in education, the need to evaluate them, using different
criteria, is felt. Establishing a ranking among geometric automated theorem
provers will be useful for the improvement of the current
methods/implementations. Improvements could concern wider scope, better
efficiency, proof readability and proof reliability.
To achieve the goal of being able to compare geometric automated theorem
provers a common test bench is needed: a common language to describe the
geometric problems; a comprehensive repository of geometric problems and a set
of quality measures.Comment: In Proceedings ThEdu'18, arXiv:1903.1240
Automated Deduction – CADE 28
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions
Proof Certification in Zenon Modulo: When Achilles Uses Deduction Modulo to Outrun the Tortoise with Shorter Steps
International audienceWe present the certifying part of the Zenon Modulo automated theorem prover, which is an extension of the Zenon tableau-based first order automated theorem prover to deduction modulo. The theory of deduction modulo is an extension of predicate calculus, which allows us to rewrite terms as well as propositions, and which is well suited for proof search in axiomatic theories, as it turns axioms into rewrite rules. In addition, deduction modulo allows Zenon Modulo to compress proofs by making computations implicit in proofs. To certify these proofs, we use Dedukti, an external proof checker for the λΠ-calculus modulo, which can deal natively with proofs in deduction modulo. To assess our approach, we rely on some experimental results obtained on the benchmarks provided by the TPTP library
Automated Deduction in the B Set Theory using Typed Proof Search and Deduction Modulo
International audienceWe 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 project. Deduction modulo is an extension of predicate calculus with rewriting both on terms and propositions. It is well suited for proof search in theories because it turns many axioms into rewrite rules. We also present the associated automated theorem prover Zenon Modulo, an extension of Zenon to polymorphic types and deduction modulo, along with its backend to the Dedukti universal proof checker, which also relies on types and deduction modulo, and which allows us to verify the proofs produced by Zenon Modulo. Finally, we assess our approach over the proof obligation benchmark of BWare
Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers
We prove decidability of univariate real algebra extended with predicates for
rational and integer powers, i.e., and . Our decision procedure combines computation over real algebraic
cells with the rational root theorem and witness construction via algebraic
number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated
Deduction, 2015. Proceedings to be published by Springer-Verla
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