Sentential Logic Objectives Distinguish between simple and compound sentences and be able to identify the simple components of compound sentences Learn the definitions of sentential operator compound sentence and simple ID: 398941
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Slide1
The Structure of
Sentential
LogicSlide2
Objectives
Distinguish between simple and compound sentences and be able to identify the simple components of compound sentences.
Learn the definitions of sentential operator, compound sentence, and simple
sentence.
Learn five sentential operators and the symbols for
them.
Learn how compound formulas are constructed out of more elementary
parts.Slide3
Compound Sentence
It contains another complete declarative sentence as a component
Compound or not?
John loves Mary and Mary loves David.
The
person who ate the cake has a guilty conscience.
John went to New York and Mary went to New York.
Mary will be a good student or a good tennis player.Slide4
Compound Sentences
Sentences with compound subjects and/or compound predicates will be considered compound if they can be paraphrased into sentences that are explicitly compound.
One sentence contains another if it literally contains the other as a component or it can be paraphrased into an explicitly compound sentence. Slide5
Cases when you cannot tell whether the sentence is genuinely compound or just stating a relationship
John and Mary are married
The art of paraphrasing is not exactSlide6
The ff. Sentences are all simple
Jose is happy.
Dogs like bones.
Children fight a lot.
Keith likes bananas on his porridge.
The man standing by the door is a doctor.
The President liked to have complete silence during his many long, tedious speeches about the virtues of democratic
government.Slide7
The ff. Sentences are all compound
Jose and Maria like cats.
John likes cats and snakes.
Harvey thinks that the earth is flat.
If there are flying saucers, then fish live in trees.
Jose, Maria and Harvey like lobster and Big Macs.Slide8
A Sentential operator
Is an expression containing blanks such that, when the blanks are filled with complete sentences, the result is a sentence.
There are a lot of sentential operators in English, although we will be using only 5 in sentential logic.Slide9
A Sentential operator in Logic
Either _____ or _____
Neither _____ nor _____
_____ and _____
If _____, then _____
_____ if and only if _____
_____ unless _____
_____ after _____
_____ only if _____
_____ because _____Slide10
5 Sentential operators
Operator
Technical Name
Meaning
Example
or
Negation
Not
p Or p
, & or
Conjunction
And
p
q
V
Disjunction
Or
p
v q
or
V
Exclusive OR
XOR
p
q
, or
Conditional
Implication
If ___
then ____
p
q
, ,
iff
or
Biconditional
If and only if
p
qSlide11
5 Sentential operators
In p
q, p and q are called
conjuncts
.
In p v q, p and q are called
disjuncts
.
In p
q, p is the antecedent, q is the consequent
.We will use single capital letters to represent simple English sentences. Slide12
5 Sentential operators and ()
Let
P
be P-
Noy
is president,
B
be
Binay is vice-president. E be Erap
is president. M be Mar Roxas
is vice-president. Convert these into symbols:Binay is vice-president and P-
Noy
is president.
Erap
or P-
Noy
is president.
Binay
is vice-president if and only if P-
Noy
is president.
If
Binay
is vice-president, then P-
Noy
is president.
Erap
is not the president.
Not both
Erap
and P-
Noy
are president.
Either
Erap
is president and
Binay
is vice-president, or P-
Noy
is president and Mar
Roxas
is vice-president.
Mar
Roxas
is vice-president if and only if P-
Noy
is president.
The necessary use of parentheses in arithmetic is as important its use in logic
.Slide13
Some important terms
Sub-formula
– a meaningful formula that occurs as a part of another formula.
Major
operator/connective
– the operator that determines the overall form of the sentence, and is the operator introduced last in the process of constructing the formula from its more elementary components. Slide14
What is the major
operator?
((A
B) (C v D))
(((A
B) (C v D)) v ((E F) G))
(((A B) v ((C D) v F)) ((H E) v C))Slide15
Do Worksheet 1