scholarly journals Single axioms in the implicational propositional calculus

2005 ◽  
pp. 710-713 ◽  
Author(s):  
Frank Pfenning
Keyword(s):  
Propositional Calculus ◽  
Single Axioms

Corrections for "On the lengths of proofs in the propositional calculus preliminary version"

1974 ◽  
Vol 6 (3) ◽  
pp. 15-22 ◽  
Author(s):  
Stephen Cook ◽  
Robert Reckhow
Keyword(s):  
Propositional Calculus ◽  
Preliminary Version

scholarly journals Preface

2011 ◽  
Vol 21 (4) ◽  
pp. 671-677 ◽  
Author(s):  
GÉRARD HUET
Keyword(s):  
Mathematical Logic ◽  
Computer Science ◽  
20Th Century ◽  
Theorem Proving ◽  
Propositional Calculus ◽  
Interactive Theorem Proving ◽  
Predicate Calculus ◽  
Special Issue ◽  
Mathematical Structures ◽  
Infinite Domains

This special issue of Mathematical Structures in Computer Science is devoted to the theme of ‘Interactive theorem proving and the formalisation of mathematics’.The formalisation of mathematics started at the turn of the 20th century when mathematical logic emerged from the work of Frege and his contemporaries with the invention of the formal notation for mathematical statements called predicate calculus. This notation allowed the formulation of abstract general statements over possibly infinite domains in a uniform way, and thus went well beyond propositional calculus, which goes back to Aristotle and only allowed tautologies over unquantified statements.

A Lattice-Diagram for the Propositional Calculus

1962 ◽  
Vol 46 (356) ◽  
pp. 119 ◽  
Author(s):  
John Evenden
Keyword(s):  
Propositional Calculus

On simple, weak and strong models of propositional calculi

1973 ◽  
Vol 74 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Ronald Harrop
Keyword(s):  
Simple Model ◽  
Propositional Calculus ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
Finite Structure ◽  
Propositional Calculi ◽  
Simple Models

In this paper we will be concerned primarily with weak, strong and simple models of a propositional calculus, simple models being structures of a certain type in which all provable formulae of the calculus are valid. It is shown that the finite model property defined in terms of simple models holds for all calculi. This leads to a new proof of the fact that there is no general effective method for testing, given a finite structure and a calculus, whether or not the structure is a simple model of the calculus.

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