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8/18/2019 Intro to Symbolize Sent Ential Logic
1/3
SYMBOLIC LOGICTRANSLATING INTO SENTENTIAL LOGIC
Translations from natural languages into logical formulas have certain
properties.
• They are concerned only with truth values
• They miss out on subtleties of communication (for example, we
translate ‘but’, ‘although,’ and ‘despite the fact that’ as ‘and’).
Atomic Claims: Represent each simple claim with a capital letter that
corresponds to the sentence (to mae it easier to remember). !orexample, represent the sentence "ara got her hair cut with the letter #.
Sentence Connectives: Represent (truth functional) sentence
connectives as follows$ % (&'T), (&*), + ('R) and ⊃ (!-T/&,
012/3) and 4 (! &* '&25 !).
n conjunctions, the left con6unct goes to the left of the connective and the
right con6unct to the right. #on6unction symbols must have a formula on
each side.
Example$/nglish$ "ara got her hair dyed and cut.
3entential 2ogic$ * #
n isjunctions, the left dis6unct goes to the left of the connective and the
right dis6unct to the right. #on6unction symbols must have a formula on
each side.
Example$/nglish$ "ara got her hair either dyed or cut.
3entential 2ogic$ * + #
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8/18/2019 Intro to Symbolize Sent Ential Logic
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!a"ent#eses can be used to control the order of processing. !or example,
if you wanted to translate the sentence 7f you either attend enough classes
or go to a presentation you will get a good attendance grade,8 then you
would use parentheses to show that the antecedent is made up of two
dis6uncts enclosed in parentheses, as follows$ ( + 1) ⊃ 9
n ne$ations the &'T symbol goes to the left of the formula.
Example$/nglish$ "ara didn’t get her hair dyed.
3entential 2ogic$ %*
f you want the negation to affect a compound formula (and not 6ust the
atomic sentence immediately to its right) you need parentheses.
Example$/nglish$ t’s not true that "ara got her hair dyed and cut.
3entential 2ogic$ %(* #) this means 7not both8
n conitionals, the antecedent is connected to the conse:uent with the ⊃
symbol, with the antecedent to the left of it and the conse:uent to its right.
Example$/nglish$ f "ara got her hair dyed then she got cut.
3entential 2ogic$ * ⊃ #
NOTE$ 5ou must get the antecedent and conse:uent in the right order
around the connective since it says something different to have it the other
way.
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8/18/2019 Intro to Symbolize Sent Ential Logic
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TRANSLATING %ROM ENGLIS& TO SENTENTIAL LOGIC
;. dentify and circle each sentence connective in the /nglish sentence
(and, or, if-then, not, if and only if).