Logic, Language, And Meaning, Volume 1 by L.T.F. Gamut
Introduction to Logic
A clear, systematic introduction to formal logic that develops the syntax, proof theory, and model-theoretic semantics of propositional and first-order languages and shows how these tools can be used to analyze and formalize aspects of natural language; it explains truth conditions, quantification, identity, logical consequence, and methods of formal proof and translation, and it uses examples and exercises to connect abstract formalism to linguistic meaning and everyday reasoning.
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