Inductive Theorem Proving by Consistency for First-Order Clauses

1992 ◽  
pp. 441-461 ◽  
Author(s):  
Harald Ganzinger ◽  
Jürgen Stuber
Keyword(s):  
Theorem Proving ◽  
First Order ◽  
Inductive Theorem Proving

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.

Refutational theorem proving for hierarchic first-order theories

1994 ◽  
Vol 5 (3-4) ◽  
pp. 193-212 ◽  
Author(s):  
Leo Bachmair ◽  
Harald Ganzinger ◽  
Uwe Waldmann
Keyword(s):  
Theorem Proving ◽  
First Order

scholarly journals Termination Analysis by Dependency Pairs and Inductive Theorem Proving

2009 ◽  
pp. 322-338 ◽  
Author(s):  
Stephan Swiderski ◽  
Michael Parting ◽  
Jürgen Giesl ◽  
Carsten Fuhs ◽  
Peter Schneider-Kamp
Keyword(s):  
Theorem Proving ◽  
Termination Analysis ◽  
Inductive Theorem Proving ◽  
Dependency Pairs

scholarly journals Inductive theorem proving based on tree grammars

2015 ◽  
Vol 166 (6) ◽  
pp. 665-700 ◽  
Author(s):  
Sebastian Eberhard ◽  
Stefan Hetzl
Keyword(s):  
Theorem Proving ◽  
Inductive Theorem Proving

scholarly journals Formalization of Linear Space Theory in the Higher-Order Logic Proving System

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Jie Zhang ◽  
Danwen Mao ◽  
Yong Guan
Keyword(s):  
Linear Space ◽  
Theorem Proving ◽  
Predicate Logic ◽  
Higher Order ◽  
Order Logic ◽  
First Order Logic ◽  
Space Theory ◽  
Higher Order Logic ◽  
First Order ◽  
Important Approach

Theorem proving is an important approach in formal verification. Higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and stronger semantics. Higher-order logic is more expressive. This paper presents the formalization of the linear space theory in HOL4. A set of properties is characterized in HOL4. This result is used to build the underpinnings for the application of higher-order logic in a wider spectrum of engineering applications.

Sign in / Sign up

Export Citation Format

Share Document