In mathematical logic sentences are represented by formulas. Those investigations which only depend on the formal structure of logical formulas and fixed formal rules of deduction are said to be syntactic. On the other hand those which depend on model-theoretic interpretations are said to be semantic. Syntactic investigations, which feature predominantly in proof theory, are usually carried out constructively whilst the semantic ones can only be carried out with constructive concepts and proof procedures in the simplest part of logic, that is, in the sentential (or propositional) calculus.
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