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

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Presentation transcript:

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

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

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

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

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

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.

For more click here 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