Introductory logic phi 120
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Presentation: "Truth Tables – Validity vs. Soundness". Introductory Logic PHI 120. This PowerPoint Presentation contains a large number of slides, a good many of which are nearly identical. If you print this Presentation, I recommend six or nine slides per page. Homework.

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Introductory Logic PHI 120

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Introductory logic phi 120

Presentation: "Truth Tables – Validity vs. Soundness"

Introductory LogicPHI 120

This PowerPoint Presentation contains a large number of slides, a good many of which are nearly identical. If you print this Presentation, I recommend six or nine slides per page.


Homework

Homework

  • Study Allen/Hand Logic Primer

    • Sec. 1.1, p. 2: “soundness”

    • Sec. 2.2, p. 45, “incompatible premises”

  • Ex. 2.2: i-xii


Validity vs soundness

  • Validity: An argument is valid if and only if:

  • if all of its premises are true

  • its conclusion is true.

  • Corollary: It is impossible for a valid argument to have:

  • all true premises

  • false conclusion

P & Q, ~P ⊢ R

Validity vs. soundness


Validity vs soundness1

Validity vs. Soundness

Valid Argument

  • No invalidating assignment

    Criteria of a Sound Argument

  • argument is valid and

  • all premises are True.

Valid but Unsound

  • no invalidating assignment

  • not all premises true

Invalidating Assignment

(1) conclusion is False

(2) all premises are True


Incompatible premises

Incompatible Premises


Incompatible premises1

Incompatible Premises

Atomic statements MUST be written in alphabetical order


Incompatible premises2

Incompatible Premises


Incompatible premises3

Incompatible Premises


Incompatible premises4

Incompatible Premises


Incompatible premises5

Incompatible Premises


Incompatible premises6

Incompatible Premises


Incompatible premises7

Incompatible Premises


Incompatible premises8

Incompatible Premises


Incompatible premises9

Incompatible Premises


Incompatible premises10

Incompatible Premises


Incompatible premises11

Incompatible Premises


Incompatible premises12

Incompatible Premises


Incompatible premises13

Incompatible Premises


Incompatible premises14

Incompatible Premises


Incompatible premises15

Incompatible Premises


Incompatible premises16

Incompatible Premises


Incompatible premises17

Incompatible Premises

Testing for Validity:

Find the Invalidating Assignment


Incompatible premises18

Incompatible Premises


Incompatible premises19

Incompatible Premises


Incompatible premises20

Incompatible Premises


Incompatible premises21

Incompatible Premises


Incompatible premises22

Incompatible Premises


Incompatible premises23

Incompatible Premises

No Invalidating Assignment

So the argument is valid


Incompatible premises24

p. 45

Incompatible Premises


Validity vs soundness2

Validity vs. Soundness

Valid Argument

  • Impossible for conclusion to be False and all premises True

    Sound Argument

  • An argument is sound if and only if it is valid and all its premises are true.

Valid but Unsound

  • No invalidating assignment

  • Not all premises true


Sequents

Determine truth-values of:

  • atomic statements

  • negations of atomics

  • inside parentheses

  • negation of the parentheses

  • any remaining connectives

Truth Tables

Sequents


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

~P, R v ~P <-> P v Q ⊢ ~Q

First, identify the governing connectives.


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

~P, R v ~P <-> P v Q ⊢ ~Q

First, identify the governing connectives.


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

~P, R v ~P <-> P v Q ⊢ ~Q

First, identify the governing connectives.


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

~P, (R v ~P)<->(P v Q)⊢ ~Q

The second premise is a complex binary: Φ <-> Ψ


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

~P, R v ~P <-> P v Q ⊢ ~Q

The conclusion is a negation.


Construct the truth table

Truth Tables – Sequents

construct the truth table


Introductory logic phi 120

~P, R v ~P <-> P v Q ⊢ ~Q

Determine the number of rows for the sequent

23 simple statements = 8 rows


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid

Alphabetical Sequence!


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

(R v ~P)<->(P v Q)

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

(R v ~P)<->(P v Q)

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid

Testing for Validity:

Find the Invalidating Assignment


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

____

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

__

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

__

Invalid


Introductory logic phi 120

Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.

_ __

Valid

__

Invalid


Homework1

Homework

  • Study Allen/Hand Logic Primer

    • Sec. 1.1, p. 2: “soundness”

    • Sec. 2.2, p. 45, “incompatible premises”

  • Ex. 2.2: i-xii


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