Abstract
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.
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References
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]).
In Tarski [1930], [1930a], theories are called ‘deductive systems’.
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.
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© 1988 Springer Science+Business Media Dordrecht
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Wójcicki, R. (1988). Basic Concepts. In: Theory of Logical Calculi. Synthese Library, vol 199. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-6942-2_2
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DOI: https://doi.org/10.1007/978-94-015-6942-2_2
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