Solving open questions with an automated theorem-proving program

2005 ◽  
pp. 1-31 ◽  
Author(s):  
L. Wos
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Open Questions

The complexity of analytic tableaux

2006 ◽  
Vol 71 (3) ◽  
pp. 777-790 ◽  
Author(s):  
Noriko H. Arai ◽  
Toniann Pitassi ◽  
Alasdair Urquhart
Keyword(s):  
Lower Bound ◽  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Relative Complexity ◽  
Analytic Tableaux ◽  
Open Questions ◽  
Tree Resolution

AbstractThe method of analytic tableaux is employed in many introductory texts and has also been used quite extensively as a basis for automated theorem proving. In this paper, we discuss the complexity of the system as a method for refuting contradictory sets of clauses, and resolve several open questions. We discuss the three forms of analytic tableaux: clausal tableaux, generalized clausal tableaux, and binary tableaux. We resolve the relative complexity of these three forms of tableaux proofs and also resolve the relative complexity of analytic tableaux versus resolution. We show that there is a quasi-polynomial simulation of tree resolution by analytic tableaux; this simulation is close to optimal, since we give a matching lower bound that is tight to within a polynomial.

The 10th IJCAR automated theorem proving system competition – CASC-J10

2021 ◽  
pp. 1-15
Author(s):  
Geoff Sutcliffe
Keyword(s):  
Theorem Proving ◽  
Classical Logic ◽  
Automated Theorem Proving ◽  
Fully Automatic

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.

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

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.

Verifying B proof rules using deep embedding and automated theorem proving

2013 ◽  
Vol 14 (1) ◽  
pp. 101-119 ◽  
Author(s):  
Mélanie Jacquel ◽  
Karim Berkani ◽  
David Delahaye ◽  
Catherine Dubois
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Proof Rules ◽  
Deep Embedding
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