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CS486 Spring 1997
Lecture 2 Thursday, Jan. 23, 1997
- Reading: Please read Smullyan Chapter II §1.
- Grelling antinomy-``hetrological'' is hetrological iff it is not.
- Collect data from students.
- Boolean valuations, assignments, truth-tables, evaluations, ``short-circuit evaluations.''
Assignment 
eval 
(Form 
Assignment) 
definition of 
as a computable function.
- Tautologies, satisfaction, falsification-leftover from lecture 1.
- Induction on recursive types, (also see Smullyan p.8).
Let 
, recall
Given some property 
of formulas,
to prove that for all formulas 
, is true (symbolized as 
,
we can first show that for in Var and in Constants, is true,
and also show that for 
in Form, if and 
are true,
then so are
and 
for 
- Full binary decision tree, as a proof.
- Truth-tables-with no-goal, with goal, with subgoals, as proofs-see handout given in class.
- Binary decision diagrams (BDD's)-decorated and undecorated-see handout given in class.
- Consistency and completeness of truth-tables and BDD's.
Completeness: If formula 
is a tautology, then there is a proof (BDD or
truth-table).
Consistency: If is proved by a BDD or a truth-table then is a tautology.
These are immediate facts about these simple ``proof systems''.