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.
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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 approximately 20,000 students.
- 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
J. Kelly, The Essence of Logic (Prentice Hall, Englewood Cliffs NJ, 1997)
D. Gries, The Science of Programming (Springer, Berlin, 1981)
E. Mendelson, Introduction to Mathematical Logic (Wadsworth and Cole/Brook, Advanced Books & Software, 1987)
G. O’ Regan, Guide to Discrete Mathematics (Springer, Switzerland, 2016b)
E.W. Dijkstra, A Disciple of Programming (Prentice Hall, Englewood Cliffs, NJ, 1976)
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O’Regan, G. (2017). Propositional and Predicate Logic. In: Concise Guide to Formal Methods. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-64021-1_6
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DOI: https://doi.org/10.1007/978-3-319-64021-1_6
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