Abstract
Propositional logic is the study of propositions, where a proposition is a statement that is either true or false. Propositional logic may be used to encode simple arguments that are expressed in natural language, and to determine their validity. The validity of an argument may be determined from truth tables, or using the inference rules such as modus ponens to establish the conclusion. 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. The universal quantifier is used to express a statement such as that all members of the domain of discourse have property P, and the existential quantifier states that there is at least one value of x that has property P.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Basic truth tables were first used by Frege, and developed further by Post and Wittgenstein.
- 2.
This institution is now known as University College Cork and has over 20,000 students.
- 3.
This is stated more formally that if \({\text{H}} \cup \{ {\text{P}}\}\) ├ Q by a deduction containing no application of generalization to a variable that occurs free in P then H ├ \({\text{P}} \to {\text{Q}}\).
References
Kelly J (1997) The essence of logic. Prentice Hall
Gries D (1981) The science of programming. Springer, Berlin
Mendelson E (1987) Introduction to mathematical logic. Wadsworth and Cole/Brook. Advanced Books & Software
Dijkstra EW (1976) A disciple of programming. Prentice Hall
O’Regan G (2017) Concise guide to formal methods. Springer
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
O’Regan, G. (2021). Propositional and Predicate Logic. In: Guide to Discrete Mathematics. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-81588-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-030-81588-2_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-81587-5
Online ISBN: 978-3-030-81588-2
eBook Packages: Computer ScienceComputer Science (R0)