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7/25/2019 Module02 Predicate Logic
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COMP 1805Predicate Logic
Carleton University
Winter 2016
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Propositional Logic
Predicate Calculus
Set TeoryMate!atical "easoning and Proo#s
$%nctionsSe&%ences and S%!s
Co!ple'ity o# (lgorit!s
)nd%ction
*raps
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Predicates
Consider eac o# te #ollo+ing state!ents
So!eone is la%ging
,veryone is appy
- . /
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Predicates
( predicate is a property tat an oect can
ave
We can +rite a predicate as a propositional
function +ic ret%rns tr%e or #alse depending
on te val%e tat te oect as
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Predicates
)s a propositional #%nction a proposition4
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Predicates
o+ do +e say so!eting lie
So!eone lies tea
,veryone lies tea
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Universe o# 7isco%rse
Wic oects are +e taling ao%t4
Te universe of discourse or domain o#ten denoted
y UUUU is te speci#ic set o# oects +e are concerned+it in a given prole!
Ly9 is te predicate :y lies star tre;
,veryone lies star tre
L'19
L'29
L'/9
%anti#ication
Te existential quantification o# te propositional#%nction () is te proposition :tere e'ists an
ele!ent in te %niverse o# disco%rse s%c tat
() is tr%e;
()
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,'istential >%anti#ication
Wen is an existential quantification tr%e?#alse4
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,'istential >%anti#ication
So!e astrona%ts +ant to go to space
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Ainding Bariales
( variale is bound +en
( val%e is assigned to it or
( &%anti#ier is %sed on it
Te scope o# a &%anti#ier is te part o# te
e'pression tat te &%anti#ier is applied to
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Ainding Bariales
Consider
()
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Translations
: not
: and %t also
: or : i!plies i#ten onlyi# necessary
s%##icient +enever %anti#iers
,veryone lies to s!ile
So!eone lies to dance
1=
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Degating >%anti#iers
= ,
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Degating >%anti#iers
()
()
1@
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Dested >%anti#iers
$'y9 is :' and y are #riends;
,
,
,
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,'a!ple
,very CS !aor in tis class no+s at least one CS!aor tat is taing COMP 1305
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,'a!ple
,veryone in tis class no+s e'actly one person tatgoes to %Otta+a
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