CIS 1910 Lecture Notes - Lecture 5: Luiza, Propositional Calculus, Validity

• School: University of Guelph
• Department: Computing and Information Science
• Course: CIS 1910
• Professor: Luiza Antonie

Document Summary

The language of logic allows us to formally establish the truth of logical statements, assuming that a set of hypotheses are true. An argument is a sequence of propositions, called hypotheses, followed by a nal proposition, called the conclusion. An argument is valid if the conclusion is true whenever the hypotheses are all true, otherwise the argument is invalid. Propositions and proofs: proposition: a statement that can be shown to be true, a premise, proof: a valid argument that establishes the truth of the proposition. It is a logically valid and complete argument that establishes the truth of the proposition. Dr. luiza antonie: for clear communication of logical arguments in any domain, proofs are essential in both maths and computer sciences, applications of proofs: Showing that system speci cations are consistent: proving a theorem allows us to rely upon its correctness even in the most critical scenarios. Rules of inference are building blocks for proofs.