CSC165H1 Lecture Notes - Lecture 4: First-Order Logic

• School: UTSG
• Department: Computer Science
• Course: CSC165H1
• Professor: Tom Fairgrieve

Document Summary

For all there exists for all there exists. Read statements from predicate logic from left to right. There is some y that could depend on x that makes true x + y = 0 true of false for all this must be true. Consider h: the set of humans predicate loves(x, y): (cid:827)person x loves person y(cid:828), How to express in predicate logic the english statement (cid:827)everyone loves everyone(cid:828) , loves(x, y) (cid:827)someone loves someone(cid:828) (cid:827)everyone loves someone(cid:828) , loves(x, y) two people can love same person loves(tom, catherine) loves(diane, catharine) Q: is the last statement equivalent to loved by everyone(cid:828) express something completely di(cid:878)erent. We can conclude: for an arbitrary predicate p. When this is true does it follow that this is true? (cid:827)there is someone loved by everyone(cid:828) someone(cid:828) es (cid:827)everyone loves. Negation since to prove something true you could prove its negation false it"s negation i. e. some is such that p(x) is false is true so.