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656/556 2003 1w 09 predicates LPC
Assigned work:
Do the exercise on the "Algorithm Apply" Handout to
generate x.y+ (-x).(-y) from x.y and (-x).(-y) and
check that the result is x<->y.

Predicate Logic= LPC=
Propositional operations +
predicates  + quantifiers + terms

Book
2.1 Need for a richer language
Jackson handout

Common patterns
for all x( P -> Q)
for some x ( P and Q)
for no x(P and Q) = not for some(P and Q).
for one x(P and Q)
Uncommon patterns (be suspicious of these)
for all x (P and Q)
for some x ( P->Q)
2.2 LPC Syntax
Terms
WFF
not and or implies
for all
for some
priorities
free and bound variables
Substitution   \phi[t/x]
2.3 Proof Theory
Natural deduction
Rules for =  (its algebra!)
Rules for "for all"
Rules for "for some"
if it is true for t then it is true for something.
if any value implies P and there is a value then P.
Equivalences

discounts case study (again)
abbreviations
D(d,p,n):= discount on day d for person p is n%.
T(d):= d is a Tuesday.
C(p):= p has a club card.
S(p):= p is a senior.
10,5,0: terms.
formulas
(r1): for all p,d( C(p) /\T(d) -> D(d,p,10)).
(r2): for all p,d( C(p) /\ - T(d) -> D(d,p,5)).
(r3): for all p,d( S(p) /\ C(p) -> D(d,p,10)).
(r4): for all p,d(-C(p) /\  S(p) -> D(d,p,5)).
(r5): for all p,d( -C(p) /\ - S(p) -> D(d,p,0)).

Expressed in Prolog
http://ftp.csci.csusb.edu/dick/cs656/prolog/discounts.plg

Penguin example

Introduction to Prolog
Handout on Semantic Tableaux
Chapter 2, section 2.4

lab
http://www.csci.csusb.edu/dick/cs656/prolog/lab1.html

Next
Complete study of chapter 2.
Concentrate on the Semantics (section 2.4)
You need to know the results shown in section 2.5
but not how to prove them in this class.
http://www.csci.csusb.edu/dick/cs656/class/10.html