Errata in lecture notes
-----------------------

Lecture 5

Slide 13: should be "(Ax.apple(x)) | (Ex.pear(x))"
(Although actually, Ax.(apple(x)|Ex.pear(x)) is logically equivalent to
(Ax.apple(x)) | (Ex.pear(x)). It is a good exercise for you to try to figure out why.)


Lecture 6

Slide 40: Second paragraph should say:
A sentence is satisfiable if and only if some interpretation is a model.
or:
A sentence is contingent if and only if some interpretation is a model and some interpretation isn't.


Lecture 7

Slide 3: "Infinitely many interpretations" -- the intention here is that even if you consider just a universe of discourse of 
size 2, there are infinitely many of those (i.e.: {circle,spot}, {1,2}, {%,6}, {!,@}, etc.); and then, there are universes 
with only 1 or 3 or more elements as well.

Notice however, if the discourse of universe is *a specific finite set* (e.g. {circle,spot}), and we consider only a finite 
number of symbols (object, function, and relation constants) in the language, then there are finitely many interpretations 
(though exponentially many) over this discourse of universe.


Lecture 8

Slide 15: should be "where phi contains no free variables other than v"

Slide 17: should add "where v and tau_1 .. tau_n are the only free variables in phi"

Slide 22: line 7 should have EI:2


Lecture 10

Slide 39: line 5: should be 1,4.