w4

L1        (L2)

roll
exam return and comments...

 

Next Exam: two weeks! (through chapter four...so we'll get a jump on that chapter this week)

 

I. Table review:

A. The idea...one row at a time like in 3.1 and...

  1. review the truth table definitions of the connectives,
  2. think about truth functionality , then...









  3. do a couple problems, and
  4. note how these simple tables lead to the full tables.

B. Full Tables

  1. Do some, and
  2. think about table length.

 

II. Concepts and Tables

A. Possibility

  1. It's key to our deductive logic concepts.
  2. On a table, we list possibilities, each row corresponds to a possibility.
  3. Definition: Truth value assignments and partial tvas.

    We need to think about possibilities in terms of ways things could be. For this, we need to give meaning to our language so that sentences can be true or false given a possibility: we'll call these interpretations.

































B. Logical Truth

  1. First,


  2. Next,






  3. Think about:
    • Bob will be a student only if he gets a loan, (B>L), and
    • If he doesn't get a loan, he won't be a student. (~L>~B).
    • There are 4 possible ways that things could go...










  4. Logical Truth...the definition revisited:
    • The old definition?
















    • Let's apply this. To test to see if ~L>~B is logically true, what do we do?














C. Other concepts...

  1. Logically False? Indeterminate? Problems!

  2. Logical Equivalence

    For a sentence to be logically equivalent to another means?





    Now, let's see the definition in SL:








  3. Here's how to do one (test to see if 'A=B' is l.equiv. to 'B>(A&B):
















  4. You do:
    • ~L>~B   vs.   B>L
    • AvC   vs.   ~Av~C

(overheads)

 

roll

exam returns
next exam!

Don't forget:

  • The reference manual
  • And other printable pages...under results track.
  • But you really need to work through the tutorials.
  • Things get more complicated each week. We'll see complicated symbolizations this week and complications of a new way of doing logic very soon (Chapter 5)
  • NO VACATIONS!

 

III Review

  1. Possibility and Logic










  2. Logical Truth, Falsity, Indeterminacy: A sentence which is...
    • Logically True is true on every   ________

    • Logically False is   _______________

    • Logically Indeterminate is   __________





  3. Try some: Which of the following are l.t., l.f. or l.i.?
    • ~(A>(A&B))
    • (C=L)&~(Cv~L)
    • J&(K&~U)



      (overhead)


  4. Something New: Short-cut tables.














  5. Logical Equivalence... the definition in SL:








  6. Are the following l.e.?


    WvS , ~S>W


 

IV. The final concepts

  1. Validity

























    We do...














    You do...









    (overheads)









  2. Consistency





















  3. Let's work some...





















    (note this row...)


    You do...








    (overheads)



 

 

 

 

V. Symbolizations

  1. "or" revisited.
    •   P Q PvQ
      row one: T T ???
      row two: T F T
      row three: F T T
      row four: F F F

    • inclusive 'or' vs. exclusive 'or'


    • Some people say that English 'or' is usually exclusive (witness "she's ten or eleven)

    • But, here's a reductio...




























      Complex Symbolizations: (From the reference manual)
































































































    • Let's do some symbolizations for review

 

 

 

 

 

 

 

 

 

 

 

W5?

VI. Informal Proofs: Do each of the following using deductive concepts for SL. (That is, when thinkng about validity, think about valid-in-SL; there is no tva making premises true and conclusion false.)

 

A. If P entails Q (i.e., P/Q is valid) then P>Q is logically true (l.t.).



B. If P&Q is l.t., then so is P.      1,2,3,4,5,6


 

 

C. PvQ can be logically true while both P and Q are logically indeterminate.