Syntax Syllabus

Course Outline

Linguistics 522

The table below gives an approximate schedule of classes, assignments, and lectures for this course. On days that are shaded gray, class does not meet. Days shaded gray before the last day of classes are either holidays, cancelled classes, or furlough days.

Days shaded gray after the last day of classes represent content that would have been covered in class in a normal semester.






Tue Aug 28   Assignment 1 Lecture  
Tue Sep 04 Chapter 2: Relations, functions. The main point: Defining sets. Predicates. Necessary and sufficient conditions.

Recursive definitions of sets.

Assignment 2 Predicate definitions and Russell's Pair of docks Recursion slides. Relations Slides. Functions Lecture (ctd).  
Tue Sep 11 Chapter 3: Equivalence relations Assignment: Chapter 3, Ex 1,2,3, Think about 4. Lecture Equivalence relations slides  
Tue Sep 18   Assignment. Ch. 6. P128. Exercises. 1a,c,d,e,f,g,h,i. 2a,b,c,e,f[!]. (Note: '!' means: watch out! Tricky!). 3a,b,c. 6[all] (use truth tables to decide!) 8a. Read but discuss later: Basic concepts of Logic. Chapter 5

Chapter 6, statement logic Logic lecture Laws of logic (ps, pdf). Logical laws and linguistic intuitions.

Tue Sep 25 Chapter 6. Proofs in statement logic Assignment. Ch. 6. (ctd) 9a,b,e,f. 10a, c, e    
Tue Oct 02 Chapter 7. Predicate logic: Assignment (pp 174-177):
  1. 1a,d,e,f,l,m,,r,x, y.
  2. 2a, c, d, e,f,h
  3. 3e.
  4. 7a,b,d
  5. 8a,b
Lecture slides.  
Tue Oct 09 Chapter 8. Mathematical logic. Mathematical study of logical "languages." Axioms. Models. Consistency. Soundness. Completeness. Godel's Theorem. What does all this tell us about language?      
Tue Oct 16 Chapter 9 (which is short), focusing on 9.1, 9.2, 9.3. Algebra. Also read 10.1, which introduces groups by way of symmetries of the square.   Extended Examples: Symmetries of the Square.

Lecture slides.

Extra! Don't read it unless you're a real geek! Groups and Cryptography (ps, pdf).
Tue Oct 23 Chapter 10 ctd. Midterm (pdf).    
Tue Oct 30 Chapter 11 (skipping 11.3, 11.4). Posets. Examples with sets, logic. Distributivity. Graphs. Groups assignment (this document summarizes the assignment given in class). Lecture (ps, pdf) Lecture.  
Tue Nov 06 Chapter 11 continued. Lattices. Lattice assignment (with [a few] feature structures). lattices. Linguistic applications

Lecture 3 on lattices:Feature structures (revised 10/15). Diagrams of feature structure lattices.

Tue Nov 13 Chapter 16, 17 Languages, grammars, automata. Finite-state automata. Introduction. What is an ATM? Finite-state languages. Regular languages. Using set theory on strings.

Recursive definition of regular languages.

Assignment (pp 480-484):
  1. (1a)
  2. (3b,c,d)
  3. (4a,b,c)
  4. Construct a regular expression which accepts the same language as the automaton on p. 4, Fig.3, here.
  5. (11c,e,f)
Tue Nov 20   Assignment: Ch 17: 8(all); 12e [construct the FSA for 11e]; Ch 18 1 (all); 3a; 7;8 Chapter 17.

Limitations of finite-state languages. The pumping lemma. Regular language intro Lecture on Regular languages, FSAs.

Tue Nov 27 Chapter 17. Finite-state grammars and Linguistics. Chomsky's arguments against the adequacy of finite-state languages. Mathematical status of phonological and morphological rules. Modern applications in phonology and morphology.      
Tue Dec 04     Context free grammars and pda's. anbn, recursion versus iteration. Lecture on Everett on recursion.
Tue Dec 11   Final (pdf). Lecture (Are human languages context-free?). Review.