Logical Information Programming

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					   LOGIC
INFORMATION



       LOGIC INFORMATION
            Proportional LOGIC

Propositional logic is the basic sciences to study the
  algorithms and logic, a very important role in
  programming.
The process of computer work can not be separated from
  programs which will be translated by the system logic.
  With proportional logic methods, we will be able to
  determine the truth value (true or false) of many real
  sentences simply by testing or observing its forms.
  Proposition

. Is the composition of the basic logic
denoted by small letters (p, q, r, ....) which
has a truth value (true) and error (false)
can be represented by a declarative sentence

Declarative sentence is the sentence that contains
truth value true or false but it is not possible
have the score.
Example:
p: London is the capital of British-True
q: 9 plus 2 is 12 - False
  Proposition

The opposite of declarative sentences is open, ie
sentences were correct value can not be determined.
Example:
Who's Where did he go?
Whether in the year 2100 there will be a doomsday?
Is today the rain?
     Proportional RELATIONSHIP

To combine two or more propositions
  required so-called propositional connectives
  connectives are not, and, or, if-then, if-and-only-if, if-
  then-else.

      Proposition + propositional connectives =
        Sentences

To combine the propositions with
liaison is needed syntactics rule is rule
necessary to combine between propositions and
Propositional connectives to generate sentences
  SYNTACTICS RULE

Each proporsisi are sentences without any propositional connectives
  a. If p is a negation sentences, the sentences also note p
  b. If p and q is the conjunction of his sentences so that p and q are also
some sentences
  c. If p and q is the disjunction of his sentences is p or q is also a
sentences
  d. If p and q are sentences then the implication was that if p then q also
sentences
  e. If p and q are sentences then it is equivalent to p if and only if q is the
sentences
  f. If p, q and r is its conditional sentences so that if p then q else r is the
sentences
    INTERPRETATION


Is giving the truth value (true or false) on each
    symbolic logic proposition of a sentence
.
 Semantic Rule (Rule Semantics) is a rule that
 used to determine the "truth value" of a sentence
 from the interpretation of Proposition
    SEMANTIC RULE


Negative Rule (Rule of NOT)            Conjunction Rule (Rule of AND)

                                           P           q         p and q
       P             NOT p
                                          True       True         True
     True             False
                                          True      False         False
     False            True               False       True         False
                                          False     False         False

"Negation is true if the proposition       "Conjunction is true if every
is false, and vice versa negation is        proposition is true, if one
false if the proposition is true. "        proposition is false then the
                                              conjunction is false"
   SEMANTIC RULE


Disjunction Rule (Rule of OR)

  P            q          p OR q
 True        True           True
 True        False          True
 False       True           True
 False       False         False

    "disjunction is true if either
    proposition is true, if every
   proposition is false then the
         disjunction is false
        NATURE OF LOGIC ALGEBRA ^ and v



   Idempotent law            Distributive Law
    p p=p
      p p=p                    p(qr)= ( pq)  (pr)
    Legal cumulative           p(q r)= (pq)  (pr)
        p p q=q
    p q p=q                   Legal Identity
    Associative law            pFalse= p
     (p q) r = p (q
      r)                       pTrue = p
     (p q) r = p (q            pTrue = True
      r)
                               pFalse= False
          SIFAT LOGIKA ALJABAR ^ dan v



   Complement Law
    p no t p= False
    not(not p)= p
   De Morgan Law
    Negation of the conjunction
    and disjunction
    not (pq)= not p  not q
    not (pq)= not p  not q
     SEMANTIC RULE


        Implication Rule                Equivalence Rule
        (Rule IF-THEN)               (Rule IF –AND ONLY IF - )

     P         q      If p then q     p         q       If and only if
    True      True       True        True     True           True
    True      False      False       True     False         False
 False        True       True        False    True          False
 False        False      True        False   False           True
"The implication is false when the   "Evaluates to true if all the same
    antecedent true and the                 value proposition”
       consequent false"
     SEMANTIC RULE


           Conditional Rule
        (Rule of IF-THEN-ELSE)

 p        q        r     If p then q else r
True     True    True          True
True     True    False         True
True     False   True          False          "If p is true then q is true, if p is
True     False   False         False             false then the applicable r”
False    True    True          True
False    True    False         False
False    False   True          True
False    False   False         False
                                Example

• If (p and (not q)) then ((not p) or r), which is when the value
  p = true, q = false and r = false then set the value
  truth of the above sentence
.
   The value q = false, then not q = true
   The p-value = true and not q = true then
   Value (p and (not q)) = true
   The p-value = true, then not p = false
   The value r = false then ((not p) or r) = false




              Result : (p and (not q)) = true
                 ((not p) or r)  false
           so If (p and (not q)) then ((not p) or r) false
Metode Truth Tabel:
  P   q    r   ~p      ~q   p ^ (~ q)   (~ p) or r   If A Then B
                               |A|         |B|

  T   T    T       F   F       F            T                T

  T   T    F       F   F       F            F                T

  T   F    T       F   T       T            T                T

  T   F    F       F   T       T            F        False
  F   T    T       T   F       F            T        T

  F   T    F   T       F       F            T                T

  F   F    T       T   T       F            T                T

  F   F    F       T   T       F            T                T
                                      QUIZ


     Determine the truth value of logic about the first sentence the
     following note p = T, q = T, r = F, s = F if


1. ((if p then q) and (if q then p)) if and only if (q or not
   p)

                   Use a truth table for about two :

2. (p and (if r then s)) if and only if ((if r then (not s))
   and p)
TO .…. BE ..... CONTINUE

				
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