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Logical Relations

Logical Relations. The most important idea in logic: Validity of an argument. Logical Relations. The most important idea in logic: Validity of an argument. Validity is a logical relation between statements that make up an argument. Logical Relations. The most important idea in logic:

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Logical Relations

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  1. Logical Relations The most important idea in logic: Validity of an argument.

  2. Logical Relations The most important idea in logic: Validity of an argument. Validity is a logical relation between statements that make up an argument.

  3. Logical Relations The most important idea in logic: Validity of an argument. Validity is a logical relation between statements that make up an argument. Namely that assuming premises are T the conclusion has to be T.

  4. Entailment Statement A entails statement B iff It is not possible for A to be T and B to be F.

  5. Entailment Statement A entails statement B iff It is not possible for A to be T and B to be F. iff The argument A | B has no counterexample.

  6. Entailment Statement A entails statement B iff It is not possible for A to be T and B to be F. iff The argument A | B has no counterexample. iff The argument A | B is valid.

  7. Entailment Statement A entails statement B iff It is not possible for A to be T and B to be F. iff The argument A | B has no counterexample. iff The argument A | B is valid. Summary: Entailment is “one premise” validity.

  8. Entailment More Generally: we can speak of a group of statements entailing another: A, B, C entails D iff A, B, C | D is a valid argument.

  9. Testing Entailment To show A entails B ... with a table: There is no A=T, B=F row. with a proof: Given A, prove B. with a tree: The tree for A, -B closes. For more click here

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