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Discrete Structures, Logic, and Computability, 4th Edition by James L. Hein

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chapter 7Predicate Logic

Error of opinion may be tolerated where reason is left free to combat it.

—Thomas Jefferson (1743-1826)

We need a new logic if we want to describe arguments that deal with all instances or with some instance. In this chapter we’ll introduce the notions and notations of first-order predicate calculus. This logic will allow us to analyze and symbolize a wider variety of statements and arguments than can be done with propositional logic.

We begin by describing the syntax and semantics of formulas, the properties of validity, and the problem of deciding whether a formula is valid. Then we’ll study techniques to determine whether two formulas are logically equivalent, to transform a formula into prenex normal form, and to ...

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