scholarly journals A verified decision procedure for the first-order theory of rewriting for linear variable-separated rewrite systems

2021 ◽  
Author(s):  
Alexander Lochmann ◽  
Aart Middeldorp ◽  
Fabian Mitterwallner ◽  
Bertram Felgenhauer
Keyword(s):  
Decision Procedure ◽  
Order Theory ◽  
Rewrite Systems ◽  
First Order ◽  
First Order Theory

scholarly journals Certifying Proofs in the First-Order Theory of Rewriting

2021 ◽  
pp. 127-144
Author(s):  
Fabian Mitterwallner ◽  
Alexander Lochmann ◽  
Aart Middeldorp ◽  
Bertram Felgenhauer
Keyword(s):  
Decision Procedure ◽  
Order Theory ◽  
Proof Assistant ◽  
Tree Automata ◽  
Decision Tool ◽  
Rewrite Systems ◽  
First Order ◽  
Decidable Theory ◽  
First Order Theory ◽  
Isabelle Proof Assistant

AbstractThe first-order theory of rewriting is a decidable theory for linear variable-separated rewrite systems. The decision procedure is based on tree automata techniques and recently we completed a formalization in the Isabelle proof assistant. In this paper we present a certificate language that enables the output of software tools implementing the decision procedure to be formally verified. To show the feasibility of this approach, we present , a reincarnation of the decision tool with certifiable output, and the formally verified certifier .

Implementing the cylindrical algebraic decomposition within the Coq system

2007 ◽  
Vol 17 (1) ◽  
pp. 99-127 ◽  
Author(s):  
ASSIA MAHBOUBI
Keyword(s):  
Programming Language ◽  
Decision Procedure ◽  
Order Theory ◽  
Decomposition Algorithm ◽  
Proof Assistant ◽  
Real Numbers ◽  
First Order ◽  
Cylindrical Algebraic Decomposition ◽  
First Order Theory ◽  
Automation Tools

The Coq system is a Curry–Howard based proof assistant. Therefore, it contains a full functional, strongly typed programming language, which can be used to enhance the system with powerful automation tools through the implementation of reflexive tactics. We present the implementation of a cylindrical algebraic decomposition algorithm within the Coq system, whose certification leads to a proof producing decision procedure for the first-order theory of real numbers.

scholarly journals A first-order theory of Ulm type

Computability ◽  
2019 ◽  
Vol 8 (3-4) ◽  
pp. 347-358
Author(s):  
Matthew Harrison-Trainor
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory

scholarly journals Quasi-decidability of a Fragment of the First-Order Theory of Real Numbers

2015 ◽  
Vol 57 (2) ◽  
pp. 157-185 ◽  
Author(s):  
Peter Franek ◽  
Stefan Ratschan ◽  
Piotr Zgliczynski
Keyword(s):  
Order Theory ◽  
Real Numbers ◽  
First Order ◽  
First Order Theory

The spectrum of resplendency

1990 ◽  
Vol 55 (2) ◽  
pp. 626-636
Author(s):  
John T. Baldwin
Keyword(s):  
Homogeneous Model ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Uncountable Cardinal ◽  
Recursive Theory ◽  
Finite Language

AbstractLet T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least min(2λ, ℶ2) resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, 2ω} there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ.

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