The resolution principle for ω+-valued logic

1979 ◽  
Vol 2 (1) ◽  
pp. 1-15
Author(s):  
Ewa Orłowska
Keyword(s):  
Theorem Proving ◽  
Resolution Principle ◽  
Herbrand Theorem

A resolution-style theorem proving system for the ω+-valued Post logic is developed. The soundness and the completeness of the system are proved. The two versions of the Herbrand theorem for the logic considered are given.

Resolution systems and their applications I

1980 ◽  
Vol 3 (2) ◽  
pp. 235-268
Author(s):  
Ewa Orłowska
Keyword(s):  
Theorem Proving ◽  
Sufficient Conditions ◽  
Predicate Calculus ◽  
Resolution Method ◽  
First Order ◽  
Deductive Systems ◽  
Resolution System ◽  
Resolution Principle ◽  
Necessary And Sufficient ◽  
Classical Predicate

The central method employed today for theorem-proving is the resolution method introduced by J. A. Robinson in 1965 for the classical predicate calculus. Since then many improvements of the resolution method have been made. On the other hand, treatment of automated theorem-proving techniques for non-classical logics has been started, in connection with applications of these logics in computer science. In this paper a generalization of a notion of the resolution principle is introduced and discussed. A certain class of first order logics is considered and deductive systems of these logics with a resolution principle as an inference rule are investigated. The necessary and sufficient conditions for the so-called resolution completeness of such systems are given. A generalized Herbrand property for a logic is defined and its connections with the resolution-completeness are presented. A class of binary resolution systems is investigated and a kind of a normal form for derivations in such systems is given. On the ground of the methods developed the resolution system for the classical predicate calculus is described and the resolution systems for some non-classical logics are outlined. A method of program synthesis based on the resolution system for the classical predicate calculus is presented. A notion of a resolution-interpretability of a logic L in another logic L ′ is introduced. The method of resolution-interpretability consists in establishing a relation between formulas of the logic L and some sets of formulas of the logic L ′ with the intention of using the resolution system for L ′ to prove theorems of L. It is shown how the method of resolution-interpretability can be used to prove decidability of sets of unsatisfiable formulas of a given logic.

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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