AI 1st order logic

eric007 101 Aug 24, 2011 at 14:06

Hi all

i was wondering if anybody could explain/solve the folowing so i can understand:

What does it mean for a logical statement to be valid, and what does it mean for it to be satisfiable?
Which of the following statements are valid, satisfiable, or neither?

(a) fire => smoke
(:lol: Smoke => fire
(c) (fire => smoke) => (\~smoke => \~fire)

note:\~ refers to NOT, i could not draw the proper sign

any comment would be really appreciated


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tobeythorn 101 Aug 24, 2011 at 15:11

Not sure if this is a homework assignment, but so you know, this isn’t the place (and there shouldn’t be any place) to have other people do your homework for you.

Secondly, you must tell us what the => symbol means in this context.

I checked Wikipedia, and the pages are written from a retrospective and abstract perspective, rather than explaining things without assuming prior knowledge and experience, so I can’t make sense of it.

I’m guessing that valid means that a statement is consistent or correct. For example, 4+5 is valid, 4+/5 is not.

I’ll also guess that satisfiable means that the logical statement has at least one solution. For example, 2*3 = ? has a solution of 6. Infinity*zero = ? doesn’t necessarily have a solution.

alphadog 101 Aug 24, 2011 at 16:44

Seriously, have you ever heard of Google?

But, to get you started, “valid” means “satisfied under all possible instances” and “satisfied” applies to any one instance. IOW, valid means true for all instances, but you’d say a case satisfies the logic statement. (Keep in mind, “instances” are constrained to the domain the logic statement is about.)

“x is purple”
- If we substitute “eggplant” for x, then the statement is satisfied.
- I we substitute “Amy”, well, it’s not satisfied. Amy is not purple.

This is all basic stuff you’d find in any math book on predicate logic.