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
>
>and
>
>(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))
>
>and
>
>(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)
Pat
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