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Propositional and Predicate Logic

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Mathematics in Computing

Part of the book series: Undergraduate Topics in Computer Science ((UTICS))

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Abstract

This chapter provides an introduction to propositional and predicate logic. Propositional 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. 1.

    Basic truth tables were first used by Frege, and developed further by Post and Wittgenstein.

  2. 2.

    This institution is now known as University College Cork and has approximately 18,000 students.

  3. 3.

    This is stated more formally that if H ∪ {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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  • Kelly J (1997) The essence of logic. Prentice Hall

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  • Mendelson E (1987) Introduction to mathematical logic. Wadsworth and Cole/Brook, Advanced Books & Software

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Author information

Authors and Affiliations

  1. SQC Consulting, Mallow, Cork, Ireland

    Gerard O’Regan

Authors
  1. Gerard O’Regan
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Correspondence to Gerard O’Regan .

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O’Regan, G. (2020). Propositional and Predicate Logic. In: Mathematics in Computing. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-34209-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-34209-8_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34208-1

  • Online ISBN: 978-3-030-34209-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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