A survey of the logical foundations of mathematics: development of propositional calculus and quantification theory, the notions of a proof and of a model, the completeness theorem, Gödel's incompleteness theorem.

This course is offered as both CSE 371 and MAT 371.

CSE 150 or CSE 215 or MAT 200

• Present the systems of classical propositional and predicate logic, including a full development of syntax, semantics, and proof techniques.
• Discuss the connection between semantic and syntactic concepts, e.g., truth versus proof, by exploring the soundness and completeness of calculi for these logics.
• Enhance the students abstract reasoning skills through experience with formal proofs.
• Examine some non classical logics and their use in Computer Science together with basic automated proving methods and formal systems.

• Anita Wasilewska, Logic for Computer Science, Chapters 1- 15, Distributed to Students.
• A Friendly Introduction to Mathematical Logic, Christopher Leary, Prentice Hall 2000

• Syntax and Semantics for Classical and various non-classical propositional logics.
• Two proofs of Completeness Theorem for classical propositional Logic.
• Automated Theorem proving systems for classical, intuitioinistic amd modal S4, S5 logics.
• Constructive Completeness Theorem proofs.
• First Order Classical Logic; syntax and semantics.
• Proof of Completeness Theorem.
• Formal Theories based on first order logic; Peano Arithmetic.
• Discussion of Godel Incompleteness and Inconsistency results.

Not applicable since it is a theory course.