Note on truth-tables

Abstract

In this paper a method will be described which is intended to exhibit some relationships between sets of tautologies determined by truth-tables. This method is an attempt to form an algebra of truth-tables. The results sketched below are restricted to sets of tautologies determined by truth-tables with a finite number of elements and involving a single binary connective Δ. However, most of the results can be easily extended to the case of Tarski's logical matrix and even to a more general case. We denote by S ( ) the set of all tautologies ( -tautologies) according to a given truth-table . Let describe a binary connective Δ. Then Δ( )( x, y ) stands for the truth-value of ΔPQ, when P has the truth-value x and Q has the truth-value y . If no ambiguity may arise we write Δ( x, y ) or Δ( ) for Δ( )( x, y ).