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.
KeywordsClassical Logic Propositional Calculus Logical Truth Logical Constant Consequence Operation
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- 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 ). Another exemplary development in this area is Richard Montague’s work on ‘universal grammar’ (Montague ).Google Scholar
- 6.In Tarski , [1930a], theories are called ‘deductive systems’.Google Scholar
- 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