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Re: [ontolog-forum] Anthropology of Colour

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Tue, 18 Mar 2008 10:01:57 -0500
Message-id: <p06230909c405884219fd@[]>
At 6:03 PM -0500 3/17/08, Christopher Menzel wrote:
>Ed Barkmeyer wrote:
>>  I wrote:
>>>>  That is the point I thought should not be lost: Formalization turns
>>>>  adjectives, including colour attribution, into predicates ("verbs").
>>  Pat Hayes wrote:
>>>  I wouldn't say for a second that predicates in FOL have any clear
>>>  connection with verbs in English.
>>  Upon reflection, I have to agree.  Logical predicates seem to
>>  represent nouns, adjectives, verbs and adverbs without prejudice.
>Not adverbs, typically.  In a standard logical language, sentences like
>(1) John buttered the toast
>(2) John buttered the toast slowly
>would have to be represented using completely different predicates, one
>for "buttered" and another for "slowly buttered", e.g., "Bjt" and "Sjt"
>or "Buttered(john,thetoast)" and "SlowlyButtered(john,thetoast)".  This
>is very unsatisfactory, however, as sentence (1) obviously follows from
>(2), whereas "Bjt" obviously does not follow from "Sjt".
>This observation was Davidson's motivation for arguing that the logical
>form of "action sentences" like (1) and (2) involved quantification over
>events.  Thus, if we represent the logical form of (1) and (2) as
>(1')  (Ex)(Event(e) & Buttering(e) & Agent(e,j))
>(2')  (Ex)(Event(e) & Buttering(e) & Agent(e,j) & Slow(e))
>respectively, it is obvious that (1') now follows from (2') by simple
>predicate logic.    (01)

I expect you mean to bind e rather than x    (02)

>Others (e.g., Harman) have argued that Davidson's logical forms for
>sentences like (1) and (2) are too remote from their surface grammatical
>forms to serve as satisfying logical forms.  Rather, adverbs seem to
>function much more as operators on predicates.  Capturing the logical
>forms of action sentences like (1) and (2) on this approach thus require
>augmenting the usual apparatus of first-order logic with formal
>predicate operators and the addition of new logical principles to govern
>their behavior, e.g., for operator S and unary predicate P, that S[P](x)
>entails P(x).
>The two options here nicely illustrate a frequent trade-off in the
>semantics of natural language: Increase ontological commitments and keep
>the necessary logical apparatus simple (Davidson) or avoid the
>ontological commitments and make the logical apparatus more complex
>(Harman).    (03)

You might have pointed out that Common Logic already allows the 
"Harman" constructions without extending the language. This is legal 
CLIF:    (04)

(forall ((S HarmanOperator) P x)(if ((S P) x) (P x)))    (05)

However, for all that, I prefer the Davidson way of writing things:    (06)

(forall ((S HarmanOperator) P x)(if
                ((S P) x)
                (exists ((e Event))(and (P e)((Davidize S) e) (agent e x) ))
))    (07)

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