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LPL 10.2 lecture

LPL 10.2 lecture - First-order validity and consequence In...

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First-order validity and consequence In the preceding chapters we have discussed the notions of logical truth, logical consequence, and logical equivalence. We also discussed the notions of tautology, tautological consequence, and tautological truth. In this chapter we want to discuss the notions of first-order validity, first-order consequence, and first-order equivalence. But first, a review of the earlier terms: A logical truth (logical necessity) is a sentence that is a logical conseqence of any set of premises, even the empty set. It is impossible for a logical truth to be falsified. a = a SameShape(a, a) SameSize(b, b) Logical consequence describes a situation in which a sentence is true in virtue of a given set of premises. If a sentence is a logical consequence of some set of premises, then it is impossible for that sentence to be false if all the premises are true. SameShape(a, b) Cube(a) Cube(b) Logical equivalence describes a situation in which two sentences have the same truth- value in all possible circumstances. If two sentences are logically equivalent, it will be impossible for one to be true while the other is false. LeftOf(a, b) RightOf(b, a) BackOf(c, d) FrontOf(d, c) There is no precise method to test for logical truth, consequence, and equivalence.

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LPL 10.2 lecture - First-order validity and consequence In...

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