Basic Concepts

  • Ryszard Wójcicki
Part of the Synthese Library book series (SYLI, volume 199)


A propositional language S is an absolutely free algebra (S,i 1,...,i n ) where S is the set of all formulas of S and i 1,..., i n are the connectives of S. Endomorphisms of S are called substitutions. Sb(X) is the set of all substitution instances of the set of formulas X.


Classical Logic Propositional Calculus Logical Truth Logical Constant Consequence Operation 
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  1. 4.
    A paradigm of such a framework is Alfred Tarski’s semantic of formalized languages he set out as part of his conception of truth (see Tarski [1933]). Another exemplary development in this area is Richard Montague’s work on ‘universal grammar’ (Montague [1970]).Google Scholar
  2. 6.
    In Tarski [1930], [1930a], theories are called ‘deductive systems’.Google Scholar
  3. 8.
    One of the eminent predecessors of Tarski was Bernard Bolzano. For a short account of Bolzano’s idea of consequence operation see van Benthem [19851.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1988

Authors and Affiliations

  • Ryszard Wójcicki
    • 1
  1. 1.Section of Logic, Institute of Philosophy and SociologyPolish Academy of SciencesPoland

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