Elements of deductive inference : an introduction to symbolic logic
Elements of Deductive Inference is a introductory textbook in symbolic logic. Joe and I wrote this book because we could not find a logic text that appropriately balanced the need for a treatment of logic that is philosophically and formally sophisticated with a sensitivity to the fact that many of the students who take symbolic logic will enter their first course with only modest mathematical background and aptitude. The text covers statement logic and predicate logic with identity and functions. It allows the instructor a choice between natural deduction and truth-tree proof systems. It discusses basic metatheoretical issues, though it omits real proofs. Finally, it provides short introductions to extensions of predicate logic -- including modal logic, higher order logic, and free logic. For more information, visit the Elements of Deductive Inference web site (http://blue.butler.edu/~sglennan/InferenceEngine.html).
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Joseph Bessie and Stuart Glennan. Elements of deductive inference : an introduction to symbolic logic. Belmont, CA: Wadsworth Pub., 2000.