1. CT214 – Logical Foundations of Computing Darren Doherty Rm. 311 Dept. of Information Technology NUI Galway Email:darren.doherty@nuigalway.iedarren.doherty@nuigalway.ie http://netserver.it.nuigalway.ie/darrendoherty/ct214.html

2.  Course 12 weeks  1 Lecture per week -10am Thurs in IT125G  Section B of Exam paper – Answer 2 out of 3 questions  Email: darren.doherty@nuigalway.iedarren.doherty@nuigalway.ie  http://netserver.it.nuigalway.ie/darrendoherty/ct214.html

3. 1. Propositional calculus (using properties of connectives to manipulate logical expressions without using truth tables) (3 weeks) 2. Writing proofs in propositional calculus using the rules of inference (modus ponens, modus tollens, disjunctive syllogism, etc.) (3 weeks) 3. Introduction to predicate calculus (if get time, discuss how it can map to a programming language ) (4 weeks) 4. Revision lecture (1 week)

4. Contradiction – a logical incompatibility between two or more propositions e.g. paul plays tennis AND paul does not play tennis (P ^ ¬P) Tautology – a propositional formula that is true under any possible valuation of its propositional variables e.g. paul plays tennis OR paul does not play tennis (P v ¬P) Contingency – a propositional formula that is not logically necessarily true or false

5. Argument – a sequence of one or more declarative sentences (premises) followed by a conclusion Inductive argument – truth of conclusion is supported by the premises Deductive argument – truth of conclusion is a logical consequence of the premises P 1 ^ P 2 ^ P 3 ^ … ^ P N -> C