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Re: [ontolog-forum] Ontology-based database integration

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: rick <rick@xxxxxxxxxxxxxx>
Date: Sun, 18 Oct 2009 09:34:52 -0400
Message-id: <4ADB197C.5050208@xxxxxxxxxxxxxx>
Chris, Thanks for your comments. You definitely pointed me in the right
direction with the Konyndyk book a while back. So I am an eager student,
of course with a cautious analysis of the facts and an all too painful 
reminder of the frailty of language. See below for specifics.    (01)

Christopher Menzel wrote:
> On Oct 9, 2009, at 3:29 PM, rick wrote:
>> Christopher Menzel wrote:
>>> And model theoretic semantics is entirely silent on those questions.
>>
>> Sounds like model theoretic semantics is overdue for an update 
>> because the rich discussion of meaning is still ongoing in philosophy. 
> 
> I believe this betrays a misunderstanding of what model theoretic 
> semantics is about.  Your comment suggests that you think that, because 
> it contains the word "semantics", model theoretic semantics purports to 
> be all there is to semantics.    (02)

Quite the contrary, I think model theoretic semantics (MTS) should
become more than good old fashioned model theory. I use this term as it
has been used by Harold Simmons here ...    (03)

http://www.cs.man.ac.uk/~hsimmons/BOOKS/ModelTheory.pdf    (04)

Is MTS perceived as a closed subject in academia? I can see where
classical first order logic may be perceived as closed, but I've seen
recent work in MTS that leads me to believe that's not the case.
Diaconescu's Institution Independent Model Theory is one example.    (05)

http://www.springer.com/birkhauser/mathematics/book/978-3-7643-8707-5    (06)

> To the contrary, model theoretic 
> semantics one rather small, though vital, niche in the body of research 
> that constitutes semantics generally.  The point of my remark above was 
> precisely to highlight the limitations of model theoretic semantics 
> vis-a-vis the broader semantical enterprise.    (07)

Agreed and thanks for the excellent summary below.    (08)

> Let me give it another shot.
> 
> The typical purpose of a model theoretic semantics is threefold:
> 
> 1. /To provide precise meanings to those lexical items in a given class 
> of formal languages that are considered *logical* and hence whose 
> meanings are held constant across all interpretations./ 
> 
> In the languages of classical first-order logic, for example, these 
> include the boolean operators and the quantifiers.  Extensions of 
> classical logic might include temporal operators, modal operators, 
> epistemic operators, etc.
> 
> 2. /To provide formal representations of the *kinds* of meanings to be 
> assigned to the basic non-logical lexical categories of a given language./
> 
> In classical first-order model theory, for example, individual constants 
> are assigned objects within a given domain of discourse and n-place 
> predicates are assigned sets of n-tuples of members of the domain  the 
> latter constituting the classical "extensional" representation of 
> properties and relations.  The development of possible world semantics 
> by Kripke led to very creative (and controversial) representations of 
> properties and relations.  These ideas were extended to other semantic 
> objects and applied to more and more kinds of syntactic constructs by, 
> most notably, Montague, whose work in turn has generated a /huge/ body 
> of research in linguistics on the semantics of natural language.  Well 
> known non-Montagovian developments in model theoretic semantics include 
> Kamp's Discourse Representation Theory and the information theoretic 
> semantics of Barwise and Seligman that arose out of situation semantics 
> and which draws not only the the heritage of classical model theory but 
> also category theory to model basic semantic categories.  (I should note 
> that Barwise and Seligman's work is also concerned with a lot more than 
> simply providing a semantics for formal languages.)
> 
> There is an important qualification here: One might /apply/ a model 
> theoretic semantics to define a specific /intended/ interpretation for a 
> given language  e.g., one might specify that the /intended 
> /interpretation for the language of arithmetic is the usual natural 
> number structure, or that the /intended/ interpretation of a language 
> designed to represent employee information is a specific company and its 
> actual employees and their relevant properties and relations.  The task 
> of identifying and defining intended interpretations is what I 
> called /applied/ /semantics/, wherein a given model theoretic semantics 
> is being /used/ to provide a specific interpretation for a specific 
> language, and that of course is a very important activity; but it is not 
> itself part of model theoretic semantics proper.  That is the point I 
> was making by saying that "model theoretic semantics is entirely silent 
> on those questions", i.e., on the question of the precise meaning of a 
> /specific/ name or predicate.    (09)

Agreed and I understand your use of the term applied semantics and your
distinction between it and your description of model theoretics proper.    (010)

But this raises a question. Do you agree that there are patterns or
idioms from applied semantics that are language independent?    (011)

> If you design a language for employee 
> information, model theoretic semantics cannot tell you what the intended 
> interpretation for that language is; it cannot tell you what the meaning 
> of the name "CEO" or the predicate "WorksInDept" are.  It can only tell 
> you that "CEO" denotes a member of the domain of the interpretation and 
> that "WorksInDept" picks out a set of pairs of members of the domain.    (012)

If the patterns or idioms from applied semantics do exist can a theory
of meaning be established based on them? Where in this case meaning is
both denotation and interpretation, whether intended or unintended.    (013)

> 3. /To provide a rigorous account of how the meanings assigned to a 
> complex expression are determined systematically by the meanings 
> assigned to their immediate, semantically significant syntactic parts 
> and, ultimately, by the meanings assigned to its logical connectives and 
> the items in its basic non-logical lexical categories./
> 
> This last feature of a semantics is known as /compositionality/. 
>  Compositionality is critical, as it provides a finite definition of 
> meaning for languages with infinitely many expressions.  Our own 
> semantical knowledge, it seems, must take some sort of compositional 
> form.  For there seems no other adequate explanation for how it is that 
> we, with our finite intellects, have the ability to interpret an 
> unbounded number of sentences that we have never heard before.  Pretty 
> clearly, our knowledge must consist in some finite set of semantic 
> principles that enable us to assign meanings to complex sentences in 
> terms of the meanings of their semantically significant parts and, 
> ultimately, in terms of our knowledge of individual words.    (014)

Good point and yes, I'm aware of compositionality and I like your 
description above. I'm also aware of challenges to compositionality such 
as context, sequencing, embedding and beliefs.    (015)

So, given the challenges to compositionality and if you agree that
patterns or idioms exist in applied semantics can we expect more than 
just patterns or idioms for a theory of meaning?    (016)

>> Take for example Scott Soames' recent "The Unity of the Proposition."
>>
>> http://www-rcf.usc.edu/~soames/forthcoming_papers/Unity.pdf
> 
> This is a very interesting paper (typically so for Soames, who is an 
> excellent philosopher), but I'm afraid it does not have the relevance to 
> the issue at hand that you think it does.  The paper is in fact, for the 
> most part, a discussion of a well-known historical question concerning 
> the metaphysics of propositions in the work of Frege and Russell.  Only 
> in the last few pages does he offer a "sketch" of a general notion of 
> proposition that might be useful in a modern theory of meaning  an 
> issue that has been at the heart of much discussion in linguistics and 
> the philosophy of language for many years.  In any case, the general 
> philosophical issues Soames broaches are entirely orthogonal to the 
> nature of model theoretic semantics. 
> 
>> Given that model theory implies satisfying an interpretation based 
>> on structures which preserve truth
> 
> Sentences are simply true or false in a given structure (relative to a 
> given interpretation); structures do not in any clear sense "preserve 
> truth".  Truth preservation is typically a property applied to inference 
> rules in a logic.  Specifically, a rule: "From sentences of the form S1, 
> ..., Sn, infer a sentence of the form S*" is said to be truth preserving 
> if, under any interpretation in which sentences of the forms S1, ..., Sn 
> are true, the relevant sentence of the form S* is true as well.  Truth 
> is preserved from the premises of a rule to the sentence inferred by 
> means of the rule.    (017)

But doesn't Tarski say the equivalence of the form T for any sentence 
provides only a partial definition of the truth, then go on to require 
the logical conjunction of all the partial definitions? And wouldn't the 
conjunction of the objects and classes in the interpretation define the 
structure?    (018)

>> implied by the assumption of material adequacy 
> 
> I guess you are alluding to Tarski here.  Material adequacy is a 
> condition on a theory of truth, and a rather simple one, roughly, that 
> all and only those sentences /declared/ by the theory to be true are, in 
> fact, true; a little more rigorously (but still roughly), a materially 
> adequate theory should be able to prove all instances of what Tarski 
> called "Convention T", viz,:
> 
>   "S" is true (under interpretation M) if and only if (under M) S.
> 
> Tarski's famous example is:
> 
>   "Snow is white" is true if and only if snow is white.
> 
> Looking at the paper you pointed us to, I see that you are under a 
> rather serious misimpression about what material adequacy actually is in 
> Tarski's theory.    (019)

I've thought about this a bit and I could be wrong, but what I
understand Tarksi to say in the Semantic Conception of Truth is 1) that 
the sentences declared by the theory to be true are objects; and 2) if 
the representation of those sentences is true and completely describes 
the object, then there's an equivalence relation between the object and 
its representation.    (020)

>> and signatures which lack enough symbols to represent meaning, 
> 
> A signature is simply a declaration of the non-logical lexicon in a 
> language.  I don't know what you mean by a signature "which lacks enough 
> symbols to represent meaning".     (021)

Tarski's criterion for material adequacy references material supposition 
(Supposito Materialis). The literature on material supposition 
differentiates supposition from signification. And I'm sure you'll agree 
that meaning is not the equivalent of naming.    (022)

So would you agree that an applied semantics that would include a 
signature that differentiates supposition from signification, or 
denotation from interpretation as well?    (023)

>> I'm surprised that someone hasn't already proposed revising 
>> the definition of interpretation to include structures where 
>> *fully interpreted* requires meaning, 
> 
> I don't know what you mean by "requiring meaning".  As noted, a model 
> theoretic semantics assigns robust meanings to its logical connectives 
> and gives only general semantical directions with regard to the 
> assignment of meanings non-logical lexical items and complex expressions.    (024)

I'm just drawing the distinction between denotation and interpretation.    (025)

>> not truth (or satisfaction) and complex enough signatures to include 
>> symbols that are interpretants, signs and objects.
> 
> You lost me.    (026)

Here's a diagram with labeled nodes and edges.    (027)

http://www.rickmurphy.org/images/interpretant-triangle.png    (028)

>> Here's a piece I've been working on for a while that speaks to 
>> this issue and has a useful diagram that extends the Triangle of Meaning.
>>
>> It's called Linked Data: Interpretants and Interpretation.
>>
>> Of course there's more than a life time of work to be done to 
>> properly develop what I've proposed, but silence on these important 
>> questions won't last forever !
> 
> I appreciate your efforts, but 150 years of intensive work  in 
> philosophy, linguistics, psychology, sociology, artificial intelligence, 
> and cognitive science   on the many aspects of the problem of meaning 
> has been anything but silent on the questions you raise.    (029)

Agreed and thank you again for your comments.    (030)

> That those 
> questions might not be answered in model theoretic semantics  a rather 
> small aspect of an enormous body of research  is a reflection only of 
> the fact that it was not /designed/ to answer them.
> 
> Chris Menzel
> 
> 
> ------------------------------------------------------------------------
> 
>  
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>      (031)

-- 
Rick    (032)

cell: 703-201-9129
web:  http://www.rickmurphy.org
blog: http://phaneron.rickmurphy.org    (033)


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