# Propositional and Predicate Logic

• Gerard O’Regan
Chapter
Part of the Undergraduate Topics in Computer Science book series (UTICS)

## 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 inference rules such as modus ponens to establish the conclusion via deductive steps. 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 has property P.

## References

1. 1.
J. Kelly, The Essence of Logic (Prentice Hall, Englewood Cliffs NJ, 1997)Google Scholar
2. 2.
D. Gries, The Science of Programming (Springer, Berlin, 1981)Google Scholar
3. 3.
4. 4.
G. O’ Regan, Guide to Discrete Mathematics (Springer, Switzerland, 2016b)Google Scholar
5. 5.
E.W. Dijkstra, A Disciple of Programming (Prentice Hall, Englewood Cliffs, NJ, 1976)Google Scholar