Anyone know anything about Logic? (in the book sense)

[b0mbrman]

I normally wouldn't do this but I'm in a bind here...What the heck is this thing talking about? I know what valid, satisfiable, and unsatisfiable mean...but what is this "set of substitutions" business?

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Is this claim true?

If a schema is satisfiable but not valid, then by one set of substitutions we can get a valid schema from it, and by another set of substitutions we can get an unsatisfiable schema from it.

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[b0mbrman]

anyone?

 

[StormRider]

It's been too long since I took that type of logic course. But I vaguely remember bits and pieces of that course which are probably incorrect due to the effect of the passage of time on my memory.

Can you jog my memory a little by defining what schema, valid, satisfiable and unsatisfiable mean?

I'm probably making a fool out of myself but does this have something to do with the universal quantifier -- For All and the existential quantifier -- There exists?

For example, the sentence, x is divisible by 2 is a sentence that is neither true nor false. Once you substitute an integer for x (like 6) then it becomes a statement that is either true or false. In the case of 6, it is true. But if x was 7 then the statement is false.

But if you add a logical quantifier to it, like For all integers x, x is divisible by 2 -- then there is a set of "substitutions" (odd integers) that make this statement false and a set of substitutions (even integers) that make this statement true. So this statement is satisfiable but not valid.

Or is the book talking about something much more advanced? I have vague recollections of being a little lost near the end of the semester when the professor was talking about some deep logic theorems and I kind of remember terms like "satisfiability" and stuff.