CENG 385
Mathematical Logic
Using propositional, predicate and temporal logics, in order to logically analyse, specify and solve complex problems.
Course Contents
1.Specify in mathematical logics sentences given in natural languages
2.Infer mathematical conclusions from specifications given in mathematical logics
3.Specify mathematically uncertainty, multi-valence interpretation and temporal change of complex problems
4.Solve sample complex problems using automated reasoning applications
Recommended or Required Reading
Mendelson, Elliott; 1997; “Introduction to mathematical logic”; Chapman& Hall; ISBN 0-412-80830-7 ,Bell,J.L.; 1997; “A course in mathematical logic”; 1997; N.H.; ISBN 0-7204-2844-0 ,Kelly, John; 1997; “The Essence of Logic”; ISBN 0-13-396375-6 ,Enderton, Herbert B.; 2001; “A mathematical introduction to logic”; Academic Press; ISBN 0-12-238452-0 ,Gabbay, Dov M.; 2000; “Temporal logic:mathematical foundations and computational aspects”; Oxford: Clarendon press; ISBN 0-19-853768-9
Learning Outcomes
1. Resolve ambiguities in natural language sentences
2. Specifies problems in mathematical logics
3. Explains mechanisms for automated reasoning
4. Develops logical systems
| Topics |
| Overview |
| Propositions in Propositional Logic |
| Normal Forms in Propositional Logic |
| Semantics of Propositional Logic |
| Inference in Propositional Logic |
| Syntaxt and Semantics of Predicate Logic |
| Satisfiability of Predicate Logic |
| Formal Systems of Predicate Logic |
| Completeness of Predicate Logic |
|
Undecidability and Incompleteness of Predicate Logic
|
| Summary |
| Higher-Order Predicate Logics |
| Advanced Topics |
| Fuzzy Logic |
Grading
Midterm: 24%
Quiz: 6%
Homework: 10%
Presentation: 30%
Final: 30%