Day 10: Discrete Math

Last Time: Problems from 1.4:
- 12/18 - Message: Before you try to prove a wff valid, make sure that it makes sense to you! Perhaps it's not valid, and you should find an interpretation in which it's false!
- 21/28 - Message: Make sure that you get the translation right! You can waste a lot of time trying to prove the wrong wff....
Exercise 17/23 requires a temporary hypothesis: let's look at that one.
New Today:
- Return homework 1.3:
  - 15/18(a,b,c)
    1. Both sides are true exactly when A(x,y) hold for all x,y pairs.
    2. Both sides are true exactly when some x,y pair satisfies A(x,y).
    3. If there is a single x that is in relation P to all y, then for every y an x exists (this same x) that is in relation P to y.
  - 16/19(a,c)
    1. domain is the integers, A(x) is "x is even", B(x) is "x is odd"
    3. domain is the positive integers, P(x) is "x>4", Q(x) is "x>2"
  Note: Homeworks must be turned in at the beginning of class (or before)!
- Section 1.5: Logic Programming
Next Time: Problems from 1.5

Some prolog links:

SWI-Prolog: a freely available version of prolog (here's a local copy of version 5.09 for Windows; Mac OS-X version and linux versions are available from the website above).
Concerning the Mac OS X version of SWI-Prolog, we have this from class member Phil Ulrich:
"You might want to make a note somewhere on your webpage to users of Mac OS X (I'm probably the only one, but you can never tell). Basically, just downloading their distribution of SWI-Prolog for OS X DOES NOT WORK, even if you install XDarwin (XFree86 on OS X). There's a conflict between some things SWI-Prolog expects to be defined that OS X doesn't actually define. However, it works fine if you download the full source code and compile it that way."
Phil also notes that it's possible to get rid of the warning from my version of mat385.swi:
```
To get rid of that warning that shows up after compiling, the one
about "singleton variable: Preditor" (which I changed to Predator; no
offense, but the spelling was bugging me ;)), I changed your prey rule
to this:

prey(Animal) :-
        eat(Predator,Animal),
        animal(Predator),
        animal(Animal).

This also makes sure that in the event that someone makes up some
strange relation where grass or algae winds up eating something, that
something is still not its prey.
```
Demo file for SWI-Prolog using class example 37/39.
Demo file for SWI-Prolog using class practice 28/29, p. 64/66.
An on-line Prolog programming book (which helped me to write the demo file above).
Screen shots of SWI-Prolog:
- Example37/39
- Which are prey?

Website maintained by Andy Long. Comments appreciated.