Single Quantifier, Multiple Predicates

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# Single Quantifier, Multiple Predicates - PowerPoint PPT Presentation

Single Quantifier, Multiple Predicates. some S tudent R espects Jay. there is some one. who is a student. AND. who respects Jay. there is some x. x is a student. AND. x respects Jay.  x. Sx. (. . Rxj. ).  x ( Sx  Rxj ). Single Quantifier, Multiple Predicates.

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Single Quantifier, Multiple Predicates

some Student Respects Jay

there is some one

who is a student

AND

who respects Jay

there is some x

x is a student

AND

x respects Jay

x

Sx

(

Rxj

)

x ( SxRxj )

Single Quantifier, Multiple Predicates

every Student Respects Kay

no matter who you are

IF

you are a student

THEN

you respect Kay

no matter who x is

IF

x is a student

THEN

x respects Kay

Sx

Rxk

)

x

(

x ( Sx  Rxk )

Single Quantifier, Multiple Predicates

Jay Respects no Student

there is no one

who is a student

AND

whom Jay respects

there is no x

x is a student

AND

Jay respects x

Rjx

)

x

Sx

(

x ( SxRjx )

Multiple Quantifiers, Multiple Predicates

every Student Respects someone or other

no matter who you are

IF

you are a student

THEN

you respect someone

no matter who x is

IF

x is a student

THEN

x respects someone

x

Sx

(

x respects someone

)

x ( Sxx respects someone )

Multiple Quantifiers, Multiple Predicates

x ( Sx 

x R's someone

)

there is someone

whom x R's

there is some y

x R's y

y

Rxy

x ( Sx y Rxy )

Multiple Quantifiers, Multiple Predicates

no-one Respects every Politician

there is no one

who respects every politician

there is no x :

x respects every politician

x

x (x respects every politician)

Multiple Quantifiers, Multiple Predicates

x

x Respects every Politician

no matter who you are

IF

you are P

THEN

x R’s you

no matter who y is

IF

y is P

THEN

x R’s y

Rxy

)

Py

y

(

x y ( Py  Rxy )

Multiple Quantifiers, Multiple Predicates

there is a Politician whom no-one Respects

there is some one

who is a politician

AND

whom no-one respects

there is some x

x is a politician

AND

no-one respects x

(

)

x

Px

no-one R's x

x ( Pxno-one R's x )

Multiple Quantifiers, Multiple Predicates

x ( Px &

no one R's x

)

there is no one

who R’s x

there is no y

y R's x

y

Ryx

x ( Pxy Ryx )

Multiple Quantifiers, Multiple Predicates

there is a Politicianwho Respects every Citizen

there is some one

who is a politician

AND

who respects every C

there is some x

x is a politician

AND

x respects every C

x

Px

(

x respects every C

)

x ( Pxx respects every C )

Multiple Quantifiers, Multiple Predicates

x ( Px

x R's every C

)

no matter who you are

IF

you are C

THEN

x R’s you

no matter who y is

IF

y is C

THEN

x R’s y

Rxy

)

y

Cy

(

x ( Pxy ( Cy Rxy ) )

Multiple Quantifiers, Multiple Predicates

every CitizenRespects some Politician (or other)

no matter who you are

IF

you are a citizen

THEN

you respect some P

no matter who x is

IF

x is a citizen

THEN

x respects some P

Cx

(

x

x respects some P

)

x ( Cxx respects some P )

Multiple Quantifiers, Multiple Predicates

x ( Cx 

x R's some Politician

)

there is someone

who is a P

AND

whom x R's

there is some y

y is a P

AND

x R's y

y

(

Py

Rxy

)

x ( Cxy ( PyRxy ) )

Multiple Quantifiers, Multiple Predicates

there is a Politicianwhom every Citizen Respects

there is some one

who is a politician

AND

whom every C respects

there is some x

x is a politician

AND

every C respects x

x

(

)

Px

every C respects x

x (Pxevery C respects x )

Multiple Quantifiers, Multiple Predicates

x ( Px

every C R's x

)

no matter who you are

IF

you are C

THEN

you R x

no matter who y is

IF

y is C

THEN

y R’s x

(

y

)

Cy

Ryx

x (Pxy ( Cy Ryx ) )

Multiple Quantifiers, Multiple Predicates

there is a Citizen who Respects no Politician

there is some one

who is a citizen

AND

who respects no P

there is some x

x is a citizen

AND

x respects no P

x

Cx

(

x respects no P

)

x ( Cxx respects no P )

Multiple Quantifiers, Multiple Predicates

x ( Cx

x R's no P

)

there is no-one

who is P

AND

whom x R's

there is no y

y is P

AND

x R’s y

y

Py

Rxy

(

&

)

x ( Cxy ( PyRxy ) )