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Logical Relations: Validity of Arguments

Understand the essential concept in logic - validity of an argument, where the conclusion must be true if the premises are true. Explore entailment and how one statement implies another. Discover how entailment equates to the validity of arguments involving multiple statements. Learn how to test entailment using tables, proofs, and trees.

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Logical Relations: Validity of Arguments

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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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