[Index] || [Contents] || [Grades] Mon Mar 3 14:43:01 PST 2003

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 Assigned work: Read 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