CS 291 Exam Two Terms and Concepts
Hein Section 7.1 First-Order Predicate Calculus
- Understand predicates, existential
quantifiers and universal quantifiers over
a domain.
- Know what a well-formed formula (wff) is and all the standard
terminology associated with this idea.
- Be familiar with scope of quantified variables and
how to distinguish bound from free variables.
- Know the concepts of valid, unsatisfiable
and satisfiable as applied to wffs.
Hein Section 7.2 Equivalent Formulas
- Be familiar with the concept of logical
equivalence.
- Be able to do various manipulations to show that one logical
form is equivalent to another logical form.
- Know about prenex normal form and how to to through
the steps to put a wff into this form.
- Beyond this, be able to put wffs into disjunctive normal
form and conjunctive normal form.
- Be able to formalize English
sentences into wffs and find natural sounding English sentences
that are equivalent to wffs.
Hein Section 7.3 Formal Proofs in Predicate Calculus
- Know how to do formal conditional proofs in FOL using natural
deduction.
- Be familiar with universal instantiation
(UI), existential generalization
(EG), existential instantiation (EI),
and universal generalization (UG).
- Be able to take English sentences, translate them into formal
wffs and go through the process of doing a formal proof.
Hein Section 7.4 Equality
- There are various proofs in this section that I won't expect
you do do much with.
- You should know the Equal for Equals (EE) rule well
enough to use it in proofs.
- You should extend your ability to formalize English sentences
in FOL to include aspects of equality, as in the homework
problems.
Hein Section 8.1 Program Correctness
- You should understand the
{P} S {Q}
syntax used
in program correctness proofs.
- Know the Assignment Axiom and the Consequence
Rules and how to use them in proofs.
- Be familiar with the Composition Rule and
the If-Then Rule and If-Then-Else Rule and how
to use them in proofs. If I expected you to use any of these
three rules in proofs, I would give them to you on the exam.
- I do not expect you to be able to do correctness proofs
with the While Rule or any of the array assignment stuff
or program termination proofs.
Hein Section 8.2 Higher-Order Logics
- Nothing from this section.
Hein Section 8.3 Automatic Reasoning
- I expect you to be able to take logical wffs and put them in
clausal form, including Skolemization as
necessary. This includes being able to carefully
apply Skolem's Rule.
- You should be able to do resolution proofs, both with
propositional logic clauses and first-order logic clauses.
- Understand substitution and unification and
how they are used in resolution proofs.
- Be able to use Robinson's Unification Algorithm to
find most general unifiers (mgus).
- To restate, be able to do full blown first-order logic
resolution proofs from beginning to end.