On using Theorem Proving for Cognitive Agent-oriented Programming

The CADE ATP System Competition (CASC) is the annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-J10 was the twenty-fifth competition in the CASC series. Twenty-four ATP systems and system variants competed in the various competition divisions. This paper presents an outline of the competition design, and a commentated summary of the results.

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Retrieval System and Dynamic Algorithm Looking for Axioms of Notions Defined by Programs

Fundamenta Informaticae ◽

10.3233/fi-1993-193-404 ◽

1993 ◽

Vol 19 (3-4) ◽

pp. 275-301

Author(s):

Andrzej Biela

Keyword(s):

Theorem Proving ◽

Dynamic Process ◽

Functional Equations ◽

Automated Theorem Proving ◽

Retrieval System ◽

Formal System ◽

Dynamic Algorithm ◽

Algorithmic Logic ◽

Correctness Of Programs

In this paper we shall introduce a formal system of algorithmic logic which enables us to formulate some problems connected with a retrieval system which provides a comprehensive tool in automated theorem proving of theorems consisting of programs, procedures and functions. The procedures and functions may occur in considered theorems while the program of the above mentioned system is being executed. We can get an answer whether some relations defined by programs hold and we can prove functional equations in a dynamic way by looking for a special set of axioms /assumptions/ during the execution of system. We formulate RS-algorithm which enables us to construct the set of axioms for proving some properties of functions and relations defined by programs. By RS-algorithm we get the dynamic process of proving functional equations and we can answer the question whether some relations defined by programs hold. It enables us to solve some problems concerning the correctness of programs. This system can be used for giving an expert appraisement. We shall provide the major structures and a sketch of an implementation of the above formal system.

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Examples of automatic theorem proving a real geometry

Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94 ◽

10.1145/190347.190354 ◽

1994 ◽

Cited By ~ 2

Author(s):

Ahmed Guergueb ◽

Jean Mainguené ◽

Marie-Françoise Roy

Keyword(s):

Theorem Proving ◽

Automatic Theorem Proving ◽

Real Geometry ◽

Automatic Theorem

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Generalized Commutativity of Lattice-Ordered Groups

Mathematica Slovaca ◽

10.1515/ms-2015-0026 ◽

2015 ◽

Vol 65 (2) ◽

Cited By ~ 1

Author(s):

M. R. Darnel ◽

W. C. Holland ◽

H. Pajoohesh

Keyword(s):

Theorem Proving ◽

Natural Generalization ◽

Ordered Groups ◽

Lattice Ordered Groups ◽

Weak Commutativity

AbstractIn this paper we explore generalizations of Neumann’s theorem proving that weak commutativity in ordered groups actually implies the group is abelian. We show that a natural generalization of Neumann’s weak commutativity holds for certain Scrimger ℓ-groups.

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