Note on truth-tables
Jan Kalicki · Journal of Symbolic Logic · 1950
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).