Tableau-based theorem proving and synthesis of λ-terms in the intuitionistic logic

2005 ◽  
pp. 262-278 ◽  
Author(s):  
Oliver Bittel
Keyword(s):  
Theorem Proving ◽  
Intuitionistic Logic

scholarly journals Subformula Linking for Intuitionistic Logic with Application to Type Theory

2021 ◽  
pp. 200-216
Author(s):  
Kaustuv Chaudhuri
Keyword(s):  
Theorem Proving ◽  
Intuitionistic Logic ◽  
Type Theory ◽  
Linear Logic ◽  
Interactive Theorem Proving ◽  
Order Logic ◽  
First Order Logic ◽  
Direct Manipulation ◽  
First Order

AbstractSubformula linking is an interactive theorem proving technique that was initially proposed for (classical) linear logic. It is based on truth and context preserving rewrites of a conjecture that are triggered by a user indicating links between subformulas, which can be done by direct manipulation, without the need of tactics or proof languages. The system guarantees that a true conjecture can always be rewritten to a known, usually trivial, theorem. In this work, we extend subformula linking to intuitionistic first-order logic with simply typed lambda-terms as the term language of this logic. We then use a well known embedding of intuitionistic type theory into this logic to demonstrate one way to extend linking to type theory.

ON THE ALGORITHM TO REALIZE THEOREM PROVING AND SOLVING PROBLEM

1982 ◽  
Vol 2 (4) ◽  
pp. 459-464
Author(s):  
Xianchang Zeng
Keyword(s):  
Theorem Proving

Modal Theorem Proving,

1986 ◽  
Author(s):  
Martin Abadi ◽  
Zohar Manna
Keyword(s):  
Theorem Proving

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.

Generalized Commutativity of Lattice-Ordered Groups

2015 ◽  
Vol 65 (2) ◽  
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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