CIS 1910 Lecture Notes - Lecture 5: Hypothetical Syllogism, Modus Tollens, Syllogism

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

Document Summary

Logical reasoning the language of logic allows us to formally establish the truth of logical statements, assuming that a set of hypotheses is true. Argument: is a sequence of propositions, called hypotheses, followed by a final proposition, called the conclusion. Validity of an argument: an argument is valid if the conclusion is true whenever the hypotheses are all true, otherwise the argument is invalid. 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. Theorem: an important proposition that can be proven. Lemma: a proposition helpful in the proof of a more important proposition. Corollary: a proposition that can be easily derived from another proposition. Conjecture: a statement that is believed to be true but for which no proof has been found yet.