Studying for this test should be pretty straightforward.
First, everything in this class is cumulative, so you should look back at the review
sheet for the last test (and at the last test) and make sure you are on top of all that
material. In particular, the first study sheet contains a list of terms whose
definitions you should be prepared to supply. Make sure you can supply any of
those definitions.
As you study for the second test in this course, it’s important to keep in mind that
the techniques we’ve been studying are in service of the central topic of this course:
validity. [Validity is officially defined as a property of arguments, but we can also
apply it to sentences. That is, we say that a sentence is valid just in case it’s logically
true, or true in all interpretations.] Validity is a semantic notion and one of our aims
is to develop a syntactic system for showing that valid arguments are valid. In
particular, this is not a bad time to think again about the notions of soundness and
completeness and why they are so interesting for our purposes.
Here are some other questions that you (still!) need to be able to answer (some of
the answers are given, indented, below the question):
What is an inductive definition?
What is an ordered pair and how can you determine whether ordered pairs are
identical?
What is a set and how can you determine whether sets are identical?
What is an interpretation?
[An interpretation is an ordered pair consisting of a non-empty set (a
domain) and a function]
How is an interpretation different from a dictionary?
What does the function that is the second member of an interpretation take as
arguments? And what kind of values does the function give for each argument?
What kind of thing is a c-variant of an interpretation?
[An interpretation. Note: given an interpretation, be prepared to give a c-
variant (or, a-variant or b-variant, etc.) if asked.]
What are soundness and completeness?
[Remember: These are properties of systems for evaluating inferences.
A system is sound iff whenever the system tells us that an inference is valid,
it is valid
A system is complete iff whenever an inference is valid, the system tells us it
is valid.]
You can expect to have to answer questions about these notions. The questions may
resemble homework questions or they may not.
What about the material since the first test? Here is a list of some of the things we
have been doing and that you should make sure you can do on the test.
1) More complicated trees. In particular, trees in which there are sentences
with nested quantification.
