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Csce 625 - Artificial Intelligence

Pure logic: Sentential logic and first-order logic, culminating in the proof of Gödel's Completeness, theorem (not to be confused with Gödel's Incompleteness, theorems). 2. Basic model theory: Applications of the Completeness Theorem, including the Löwenheim-Skolem Theorems, the Compactness Theorem; and a discussion of elementary equivalence.

1. The truth tables for propositional connectives apply to evaluate the value of aND oR ( implies and (NOT ). 2. for all, is true if is true for any element of as value of at free occurrences of in. Final Exam, solution to 5b, 5c, click here to download the course handout. Previous midterms: 1 2, previous second midterms: 1 2. The main objective of this course is to introduce you to mathematical logic through the study of two of its aspects: 1. The ability to formulate mathematical proofs. For this reason, you should have had some exposure to proof-writing before taking this course. Some knowledge of linear algebra or abstract algebra would also be useful, but is not strictly necessary. Week, date, topic, reading, lectures, homework, homework Solutions 1 9/8, propositional Logic I 1.0 - 1.4 ps pdf ps(4up) pdf(4up review sheet: ps pdf ps pdf ps pdf 2 9/15. Propositional Logic II 1.5, 1.7 ps pdf ps(4up) pdf(4up) ps pdf ps pdf 3 9/22, propositional Logic: Applications 1.7, abstract dpll (pp. Please feel free to contact me if you'd like to take this course, but are unsure whether you have the right preparation. There will be a problem set assigned every week. A formula whose truth table contains only false in any interpretation is called unsatisfiable. The Löwenheim-Skolem theorem establishes that any satisfiable formula of first-order logic is satisfiable in an (aleph-0) domain of interpretation. Otherwise, is false. 3. there exists an such that is true if is true for at least one element of as value of at free occurrences of in. Otherwise, is false.