SUO: Re: Critique Of Non-Functional Reason
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| A. Automated Reasoning (AR)
|
| The standard will be suitable for automated logical inference
| to support knowledge-based reasoning applications.
| B. Inter-Operability (IO)
|
| The standard will provide a basis for achieving Inter-Operability
| among various software and database applications.
[A]
Before we go any further in our reading of Quine,
let me summarize as succinctly as I possibly can
several important themes in what has gone before.
To do this I will introduce an ad hoc collection
of "grammatical category markers", as follows:
NP = grammatical category of Noun Phrases, or names.
VP = grammatical category of Verb Phrases, or predicates.
SC = grammatical category of Sentential Clauses, or statements.
For the purposes of the present discussion, interrested more in the
bare computational bones and the articulated logical skeletons than
the fully fleshed out corse of natural language processing, it will
be convenient to allow for "distributed constructions", for example,
in the sentence, "Othello loves Desdemona in the worst way", we may
parse the ordered pair <"Othello", "Desdemona"> as a distributed NP
and the sequence <"loves", "in the worst way"> as a distributed VP.
Expressed in terms of "grammar rules" (GR's) that constrain the
assembly of lexical strings as they fall under these categories,
Quine calls attention to the following rules of logical grammar:
| To say that a city or a word has a given property, e.g.
| populousness or disyllabism, we attach the appropriate
| predicate to a name of the city or word in question.
| To say that a statement has a given property, e.g.
| the phonetic property of being a hexameter or the
| semantic property of truth or falsehood, we attach
| the appropriate predicate to a name of the statement
| in question -- not to the statement itself.
| In order to say that two objects stand in a given relation, e.g.
| hate, or remoteness, one puts an appropriate binary predicate
| (transitive verb) between names of the objects.
| To say that two statements stand in a given relation, whether the
| phonetic relation of rhyming or the semantic relation of implication,
| we put the appropriate binary predicate between names of the statements --
| not between the statements themselves.
| "Is true" and "is false" attach to names
| of statements precisely because, unlike "~",
| they are predicates by means of which we speak
| 'about' statements. Whereas statement connectives
| ("~", "&", "v", "=>", "<=>") attach to statements
| to form statements, a predicate is an expression
| which attaches to names to form statements.
| The verb "implies" belongs between names of statements precisely because,
| unlike "=>" or "if-then", it expresses a relation between statements;
| it is a binary predicate by means of which we talk 'about' statements.
We may summarize the instructions on how to use a predicate
to say that anything has a given property, or to say that
any two things stand in a given relation, as follows:
GR 1. If q is a VP, then q : NP -> SC,
not! q : SC -> SC.
We may write this as "VP : NP -> SC",
so long as we remember what it means.
The distinction between "connective" and "predicate"
has the following array of grammatical consequences:
GR 2. Constraints applying to connectives:
GR 2.1 ~ : SC -> SC
GR 2.2 & : SC x SC -> SC
GR 2.3 v : SC x SC -> SC
GR 2.4 => : SC x SC -> SC
GR 2.5 <=> : SC x SC -> SC
GR 3. Constraints applying to predicates (VP's):
GR 3.1 "is true" : NP -> SC
GR 3.2 "is false" : NP -> SC
GR 3.4 "implies" : NP x NP -> SC
Of course, there may be additional constraints, to be enunciated.
For instance, the binary predicate "implies" does not make sense
when it is plied between any two NP's, but only when it is plied
between those NP's that are construed as the names of statements.
SubCatcha Later,
Jon Awbrey
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