Abstract
This chapter provides an introduction to propositional and predicate logic. Propositonal logic may be used to encode simple arguments that are expressed in natural language and to determine their validity. The nature of mathematical proof is discussed, and we present proof by truth tables, semantic tableaux, and natural deduction. Predicate logic allows complex facts about the world to be represented, and new facts may be determined via deductive reasoning. Predicate calculus includes predicates, variables, and quantifiers, and a predicate is a characteristic or property that the subject of a statement can have.
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Notes
- 1.
Basic truth tables were first used by Frege and developed further by Post and Wittgenstein.
- 2.
This is stated more formally that if H \(\cup\) {P} ├ Q by a deduction containing no application of generalization to a variable that occurs free in P, then H ├ P → Q.
References
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Mendelson E (1987) Introduction to mathematical logic. Wadsworth and Cole/Brook, Advanced Books & Software
Dijkstra EW (1976) A disciple of programming. Prentice Hall
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O’Regan, G. (2023). Propositional and Predicate Logic. In: Mathematical Foundations of Software Engineering. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-031-26212-8_10
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DOI: https://doi.org/10.1007/978-3-031-26212-8_10
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