Intro to Symbolize Sent Ential Logic

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    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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    !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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    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).