Formal test for validity
This presentation is the property of its rightful owner.
Sponsored Links
1 / 53

Formal Test for Validity PowerPoint PPT Presentation


  • 38 Views
  • Uploaded on
  • Presentation posted in: General

Formal Test for Validity. evaluations. Evaluations. An evaluation is an assignment of truth-values to sentence letters. For example: A = T B = T C = F D = T E = F. Evaluating WFFs. To evaluate a WFF is to determine whether it is true or false according to an evaluation.

Download Presentation

Formal Test for Validity

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Formal test for validity

Formal Test for Validity


Evaluations

evaluations


Evaluations1

Evaluations

An evaluation is an assignment of truth-values to sentence letters. For example:

  • A = T

  • B = T

  • C = F

  • D = T

  • E = F

  • ...


Evaluating wffs

Evaluating WFFs

To evaluate a WFF is to determine whether it is true or false according to an evaluation.

Let’s consider ((Q & ~P) → R)

Here’s our evaluation: Q = T, P = T, R = F.


Evaluation stage 1

Evaluation: Stage 1

Write down sentence letters.


Evaluation stage 11

Evaluation: Stage 1

Insert truth-values from evaluation.


Evaluation stage 2

Evaluation: Stage 2

Copy down the formula to evaluate.


Evaluation stage 3

Evaluation: Stage 3

Copy the truth-values of each variable.


Evaluation stage 31

Evaluation: Stage 3

Copy the truth-values of each variable.


Evaluation stage 32

Evaluation: Stage 3

Copy the truth-values of each variable.


Evaluation stage 4

Evaluation: Stage 4

Find a connective to evaluate.


Evaluation stage 41

Evaluation: Stage 4

Need these truth values.


Evaluation stage 42

Evaluation: Stage 4

Need these truth values.


Evaluation stage 43

Evaluation: Stage 4

Need this truth value.


Evaluation stage 44

Evaluation: Stage 4

Need this truth value.


Evaluation stage 45

Evaluation: Stage 4

Need these truth values.


Evaluation stage 46

Evaluation: Stage 4

Need these truth values.


Evaluation stage 47

Evaluation: Stage 4

Need these truth values.


Evaluation stage 48

Evaluation: Stage 4

Need these truth values.


In class exercises

In-Class Exercises

Evaluation: P = F, Q = F, R = T

  • ~(~P & ~Q)

  • ~(P → ~Q)

  • ((P & ~Q) & R)


Full truth tables

Full truth-tables


Possibilities for one sentence letter

Possibilities for One Sentence Letter


Possibilities for two sentence letters

Possibilities for Two Sentence Letters


Possibilities for three sentence letters

Possibilities for Three Sentence Letters


Formal test for validity

~(~P & ~Q)


Copy whole column

Copy Whole Column


Copy whole column1

Copy Whole Column


Evaluate each row

Evaluate Each Row


Evaluate each row1

Evaluate Each Row


Formal test for validity

~(~P & ~Q)


Formal test for validity

~(~P & ~Q)


P q p v q

(~(~P & ~Q) ↔ (P v Q))

So “~(~P & ~Q)” has the same truth-table as “(P v Q).” Why is that?

Suppose I say: “you didn’t do your homework and you didn’t come to class on time.” When is this statement false? When either you did your homework or you came to class on time.


In class exercise

In-Class Exercise

Write a full truth-table for:

~(P → ~Q)


Formal test for validity

~(P → ~Q)


Formal test for validity

~(P → ~Q)


Formal test for validity

~(P → ~Q)


Formal test for validity

~(P → ~Q)


Formal test for validity

~(P → ~Q)


P q p q

(~(P → ~Q) ↔ (P & Q))

So “~(P → ~Q)” has the same truth-table as “(P & Q).” Why is that?

Suppose I say: “If you eat this spicy food, you will cry.” You might respond by saying “No, that’s not true: I will eat the spicy food and I will not cry.”


In class exercise1

In-Class Exercise

Write a full truth-table for:

(P & (~Q & R))


P q r

(P & (~Q & R))


P q r1

(P & (~Q & R))


P q r2

(P & (~Q & R))


P q r3

(P & (~Q & R))


P q r4

(P & (~Q & R))


P q r5

(P & (~Q & R))


Truth tables and validity

Truth-tables and validity


The truth table test for validity

The Truth-Table Test for Validity

We know that an argument is deductively valid when we know that if it is true, then its conclusion must be true.

We can use truth-tables to show that certain arguments are valid.


The test

The Test

Suppose we want to show that the following argument is valid:

(P → Q)

~Q

Therefore, ~P

We begin by writing down all the possible truth-values for the sentence letters in the argument.


Write down all the possibilities

Write Down All the Possibilities


Write truth table for premises

Write Truth-Table for Premises


Write truth table for conclusion

Write Truth-Table for Conclusion


Look at lines where premises are true

Look at Lines Where Premises are True


  • Login