Sets, Logic and Maths for Computing pp 189-215 | Cite as

# Yea and Nay: Propositional Logic

## Abstract

We have been using logic on every page of this book – in every proof, verification and informal justification. In the first four chapters, we inserted some ‘logic boxes’; they gave just enough to be able to follow what was being done. Now we gather the material of these boxes together and develop their principles. Logic thus emerges as both a tool for reasoning and an object for study.

We begin by explaining different ways of approaching the subject and situating the kind of logic that we will be concerned with, then zooming into a detailed account of *classical propositional* logic. The basic topics there will be the *truth-functional connectives*, the family of concepts around *tautological implication*, the availability of *normal forms* and *unique minimalities* for formulae and the use of *semantic decomposition trees* as a shortcut method for testing logical status.

## Keywords

Propositional Logic Truth Table Truth Function Conjunctive Normal Form Decomposition Tree## Selected Reading

- Introductions to discrete mathematics tend to put their chapters on logic right at the beginning. In the order of nature, this makes good sense but it also makes it difficult to use tools like set, relation and function in the presentation. One computer science text that introduces logic after having presented those notions is:Google Scholar
- Hein J (2002) Discrete structures, logic and computability, 2nd edn. Jones and Bartlett, London, chapter 6 Google Scholar
- Five well-known books dedicated to elementary logic are listed below. The first is written specifically for students of computer science without much mathematics, the second for the same students but with more mathematical baggage, while the last three are aimed respectively at students of philosophy, linguistics and the general reader.Google Scholar
- Huth M, Ryan M (2000) Logic in computer science. Cambridge University Press, Cambridge, chapter 1Google Scholar
- Ben-Ami M (2001) Mathematical logic for computer science, 2nd edn. Springer, London/ New York, chapters 1–4Google Scholar
- Howson C (1997) Logic with trees. Routledge, London/New York, chapters 1–4Google Scholar
- Gamut LTF (1991) Logic, language, and meaning, vol I, Introduction to logic. University of Chicago Press, Chicago, chapters 1,2Google Scholar
- Hodges W (1977) Logic. Penguin, London, sections 1–25Google Scholar