TF truth, falsity, and indeterminacy - PowerPoint PPT Presentation

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TF truth, falsity, and indeterminacy

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  1. TF truth, falsity, and indeterminacy P is truth-functionally true iff it has the value T for any truth-value assignment. P is truth-functionally false iff it has the value F for any truth-value assignment. P is tf-false iff ~P is tf-true P is truth-functionally indeterminate iff it has the value T for some truth-value assignments, and the value F for some other truth-value assignments. P is tf-indeterminate iff it is neither tf-true nor th-false.

  2. TF equivalence and consistency P and Q are truth-functionally equivalent iff P and Q do not have different truth-values for any truth-value assignment. A set of sentences is truth-functionally consistent iff there is a truth-value assignment that on which all the members of the set have the value T. A set of sentences is truth-functionally inconsistent iff it is not tf-consistent.

  3. TF entailment and validity A set  of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of  is true and P false.

  4. TF entailment and validity A set  of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of  is true and P false. An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false.

  5. TF entailment and validity A set  of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of  is true and P false. An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false. An argument of SL is truth-functionally invalid iff it is not tf-valid.

  6. TF entailment and validity A set  of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of  is true and P false. An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false. An argument of SL is truth-functionally invalid iff it is not tf-valid. An argument is tf-valid iff the premises tf-entail the conclusion.

  7. TF properties P is truth-functionally true iff it has the value T for any truth-value assignment. P is truth-functionally false iff ~P is tf-true. P is truth-functionally indeterminate iff P is neither tf-true nor tf-false. P and Q are truth-functionally equivalent iff P and Q do not have different truth-values for any truth-value assignment. A set of sentences is truth-functionally consistent iff there is a truth-value assignment that on which all the members of the set have the value T. A set  of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of  is true and P false. An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false.

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  50. shortened truth tables Show that ~B(B&~B) is not tf-true