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    Type Semantics Summary PT 1

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    Qarliddh
    An easy-going summary of the course discussion on Type Semantics as taught at Jadavpur University for its Masters Programme in Linguistics.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Type Semantics Summary PT 1

    Uploaded by

    Qarliddh
    50 views4 pages
    An easy-going summary of the course discussion on Type Semantics as taught at Jadavpur University for its Masters Programme in Linguistics.

    Original Title

    Type Semantics Summary Pt 1

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    © © All Rights Reserved

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    PDF, TXT or read online from Scribd

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    An easy-going summary of the course discussion on Type Semantics as taught at Jadavpur University for its Masters Programme in Linguistics.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    50 views4 pages

    Type Semantics Summary PT 1

    Uploaded by

    Qarliddh
    An easy-going summary of the course discussion on Type Semantics as taught at Jadavpur University for its Masters Programme in Linguistics.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    You are on page 1of 4

    ARKA BANERJEE

    @ welearnbetter Type Semantics


    6th April '20
    SHUBHARUP.COM

    TYPE t

    Something is of type "t" if you're mainly


    concerned about
    its truth value.
    CAT(X)
    e.g. "The cat
    is fat." Now let us construct a procedure by which we
    check for the "catness" of a given object -
    "Nicolo has a blue-tshirt." the procedure yields certainty regarding

    these are either true or false. whether the object is a cat


    Hence sentences always have type "t". (in which case t = "True")
    or not (t = "False").

    In computer speak the value False is given the


    DONT GET LOST
    number 0 and True is assigned 1.

    The procedure checked whether x is a So it could also be that t = 1 or t = 0,


    cat and returned 0 or 1. That's respectively.
    Cat(x).
    We could call this procedure "is-cat".
    But for brevity we'll call it Cat.

    We write an empty space beside the name of a


    procedure to convey the group of objects which
    MORE TYPES
    work with it or makes sense together.

    So the output of the procedure is clearly a Thus we refer to the procedure in our
    truth value, and so of type t. Cat(x) as a discussion as
    procedure can work on "things", right?
    Cat(x), where x denotes an empty space.
    Cat(Building) is not a well-formed formula.
    Cat(x) is a wff.

    So the input in the blank space "x" can be a


    type of "thing" - an object, an entity.
    "Things" are type e.

    Thus the input type of cat is e.


    A QUESTION . . .

    Thus cat takes as input something of type What is the type of "fat cat"?
    e and outputs something
    (some value) of type t.

    We convey that understanding


    in saying that
    Cat is of type <e , t>
    input e, output t
    We've established the type of
    "cat" to be <e,t>
    LET'S
    Now fat, as an adjective, is DIG1 M / 3 FT
    begging for a Noun.
    IN
    Thus Fat
    ...
    takes as input
    something of type <e , t>
    e.g. Cat

    Cat takes objects as input.


    The objects are of type e.

    In particular, it cannot take any


    Common Noun (CN) of type <e,t>.

    [[Cat(buildings)]] is not a wff.

    But Fat, as an attributive adjective,


    takes CNs as one of its arguments.

    shubharup.com
    Source: World Health Organization
    Is Fat a function?

    [[Fat]] = λPλx.[Fat(x) & P(x)]

    Thus,

    Fat
    has two argument places
    and so takes a one-place predicate P
    of type <e,t>

    and an individual x,
    of type e

    as arguments.
    It returns 1 iff that individual x is P and Fat.

    shubharup.com
    Fat has its type <<e,t>,<e,t>>
    and behaves like a function valued function
    i.e. a function which outputs another
    function when one argument place has
    been filled e.g. Fat Cat

    Fat Cat

    is a one-place function
    and so takes an individual x
    of type e

    as argument
    to yield output
    of type t.

    Thus Fat Cat has its type <e,t>

    shubharup.com

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