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| Note: This schedule is subject to change, but not without notice. Any changes will be announced in class and reflected on these pages. Be sure to check regularly. |
| Dates | Topics | Readings |
| Mar 29 [Tu] |
Basics of set theory Notation, definitions Some laws and equalities |
Ch. 1 |
| Apr 1 [Th] |
Relations and functions Ordered pairs, Cartesian products Composition, inverses |
Ch. 2 |
| Apr 6 [Tu] |
Properties of relations Transitivity etc. Equivalence relations Orderings |
Ch. 3 |
| Apr 8 [Th] |
Propositional logic Syntax Truth assignments, truth tables Equivalence, consequence, validity |
Ch. 5; 6.1-5 |
| Apr 13, 15 [Tu,Th] |
First-order predicate logic Syntax Models, variable assignments Quantifiers |
Ch. 7; 8.1-2; 8.5.1-6; 8.6 |
| Apr 20, 22 [Tu,Th] |
Algebra Algebras and operations Maps and morphisms Boolean algebra and propositional logic |
Ch. 9, 12.1 Bach (1986) |
| Apr 27, 29 [Tu,Th] |
Lattices Posets, orderings, operations Morphisms Filters and ideals Heyting algebra, intuitionistic logic |
Ch. 11, 12.4-5 |
| May 4, 6 [Tu,Th] |
Languages I Trees and grammars Regular languages and finite-state automata Pumping lemma for regular languages English |
Ch. 16, 17 |
| May 11, 13 [Tu,Th] |
Languages II Context-free languages and pushdown automata Pumping lemmas for context-free languages Natural languages |
Ch. 18 |
| May 18, 20 [Th,Tu] |
Probability I Mathematical Basics Relationship to propositional logic and Boolean algebra Bayesian inference |
Manning and Schütze (1999), Ch. 2.1 |
| May 25, 27 [Tu,Th] |
Probability II Weighted automata Hidden Markov Models Probabilistic context-free grammars |
Bod (2003), Manning (2003) |
| May 31 - Jun 04 | Reading Week | |
| June 07 [Mo] |
Final take-home exam due | |
Bach, E. 1986. The algebra of events. Linguistics and Philosophy 9:5-16.
Bod, R. 2003. Introduction to elementary probability theory and formal stochastic language theory. In Bod et al. (2003), 11-37.
Bod, R., J. Hay, and S. Jannedy. 2003. Probabilistic Linguistics. MIT Press.
Manning, C. Probabilistic syntax. In Bod et al. (2003), 289-341.
Manning, C. and H. Schütze. 1999. Foundations of Statistical Natural Language Processing. MIT Press.
Sagey, E. 1988.
On the ill-formedness of crossing association lines.
Linguistic Inquiry 19:109-118.