Comments on the KIF, CG, SUMM report

sowa <>
Date: Wed, 3 Mar 93 11:59:49 EST
From: sowa <>
Message-id: <>
Subject: Comments on the KIF, CG, SUMM report
Cc:, interlingua@ISI.EDU,

Thanks for your comments.  There are many complex issues involved that
will have to be addressed by various research communities.  But in order 
to avoid still unresolved research questions, we decided to adopt the KIF
style of semantics for the proposed ANSI standards.  However, that does
not mean that we intend to stop doing research.

In the report, I distinguished two different versions of conceptual graphs.
I'll call one version IRDS-CG, which is the version of CGs that will adopt
the KIF semantic base and with no extensions that are not syntactically
definable on that base.  I'll call the other version NL-CG, which is not a
single language, but a family od languages with a common core built around
the theory and notation presented in my _Conceptual Structures_ book.
But since that book came out ten years ago, many people have been
extending, modifying, and building upon the basic core.

As I've said in many notes to these mailing lists, I do not believe
that a Tarskian-style of model theory and any of the currently popular
versions of set theory are adequate for natural language semantics.
Nor do I believe that they are convenient for many of the knowledge 
representation problems in AI.  Situation semantics and mereology are 
two examples of approaches that I believe are more suitable than 
conventional model theory and set theory.  Those are approaches that 
I am pursuing for NL-CG.  But for IRDS-CG, I have settled for a more 
conventional approach, primarily as a compromise to get something 
settled so that we can present a united front for a logic-based 
approach, rather than some SQL-like abomination.

Following are some comments on your comments:

>> 2. Describe both the KIF and CG languages using the SUMM ontology as
>>    defined in KIF.
>> 3. Define the syntactic mappings between KIF and CGs so that anything
>>    expressed in either one can be automatically translated into the
>>    other while preserving the native semantics of both.

> This is possible only if the model theories of KIF and CGs are identical (or 
> completely interdefinable, in the way that, e.g., finite sets can be defined 
> as numbers (via some coding scheme) and numbers as finite sets (e.g., a la 
> von Neumann).  It is not obvious to me that this is the case.

As I said above, IRDS-CG and KIF will by fiat have an identical semantic
base.  NL-CG and IRDS-CG will have a very large overlap where two graphs
that look the same will have the same truth values in all standard models.
But in the farther outposts of semantic theory, there will be versions of
NL-CG that cannot be mapped directly into KIF or IRDS-CG.

>> c) SUMM uses modal logic to represent constraints and mandatory
>>    associations.  Conceptual graphs also have monadic relations such
>>    as PSBL (possible) and NECS (necessary) that apply to contexts.
>>    Although KIF semantics is purely first-order, it appears to be
>>    possible to define such modal operators at the metalevel, using
>>    the metalanguage capabilities of KIF.  At the metalevel, it would
>>    be possible to designate certain propositions as "laws"; then any
>>    proposition entailed by the laws would be defined as "necessary",
>>    and any proposition consistent with the laws would be "possible".
>>    At the object level, however, the laws would be syntactically
>>    indistinguishable from any other propositions.
> I don't think I fully understand the idea here, but it seems to me almost 
> surely inadequate since it appears only to provide an analysis for simple de 
> dicto modaliies, i.e., sentences of the form \Diamond A and \Box A where A 
> is nonmodal.  But suppose I wanted to say, e.g., "I might have had a third 
> child who wasn't a violinist but might have been", or more formally,  
> \Diamond\exists x (ThirdChild(x,me) & ~Violinist(x) & \Diamond 
> (Violinist(x))).  This sentence is essentially de re; there is no way to 
> avoid quantifying into the modal context, which means there is no way to 
> pull the modal operators to the outside.  Surely in a general account of 
> modality we're going to want to make statements like this about the modal 
> properties of actual and (as in the example) possible individuals.

Yes.  I'm not certain how far we will be able to go in handling iterated
modalities by this approach.  But there's an interesting paper by 
Michael Dunn from 1973 (see the ref. in my _CS_ book), where he showed
that a semantics based on laws and facts can be defined that is equivalent
to a Kripke-style semantics even for the iterated modalities.  That approach
hasn't received the attention that it deserves, largely because logicians
have been fascinated by all those infinities of possible worlds.  But as
I have said many times, I don't believe in possible worlds, uncountable
sets, and a whole host of similar encrustations that I hope to dispense
with in NL-CG (even though I am allowing them in IRDS-CGs in order to
avoid arguments with mathematicians who spent their lives working in
such fantasy lands).
In any case, for most, if not all, of the applications that we have been
considering in the ANSI IRDS group, statements with a single modal operator 
seem to be sufficient (they are at least far more complete than anything 
that the IRDS or SQL people have been using so far).  But for the NL-CGs, 
people have been exploring all kinds of extensions. and I'm sure that they 
will continue to do so.

>> d) An ongoing issue has been the representation of types or sorts in KIF.
>>  [...]
>>    This syntactic approach treats types as a notational variant of
>>    monadic predicates.  However, it cannot directly handle generalized
>>    quantifiers such as "most", whose semantics depends on the type.  >    
>>    For the sentence "Most cats are on a mat", the corresponding
>>    conceptual graph 
>>    translated to a KIF paraphrase about the cardinality of the set of
>>    cats compared to the cardinality of cats on mats.  This compromise
>>    should be adequate for the ANSI standards, and it does not preclude
>>    future extensions to support types and generalized quantifiers
>>    semantically.

> I think it's worth pointing out explicitly, though, that since the KIF 
> already includes VNBG set theory, it has all the semantic power needed to 
> represent generalized quantifiers.  So to add generalized quantifiers to KIF 
> would only require adding some higher-order syntactic apparatus to the 
> grammar (since GQs express relations between properties) along with clauses 
> that make the appropriate semantic connections.  That way, "Most men love 
> some woman," say, could be expressed in KIF-like notation as something like 
> (most men (kappa ?x (some woman (kappa ?y (loves ?x ?y))))), and would be 
> evaluated in terms of the extensions of the properties so referred to.  Of 
> course, this move needs to be made pretty carefully, since it engenders 
> quite a different approach to quantification generally.

Yes, that's how we would handle such constructions in IRDS-CG.  But as
I have said many times, I do not believe in any version of set theory
that permits uncountable sets.  For that matter, I don't like what
Goodman and Quine call the "Platonistic stance" even of finite set theory.  
I prefer mereology, which collapses {John}, {{John}}, {{{John}}}... to 
just the single individual John.  But I consider that an issue that I 
would discuss in the realm of NL-CG, not IRDS-CG.

>>	[FULTON NOTE:  I am now convinced that for the purposes of 
>>	semantic unification, sorted or typed quantifiers are essential.  
>>	The reason is that different models typically have different 
>>	domains of discourse.  Thus whenever a quantified statement is 
>>	communicated to another model (regardless of the language), 
>>	it must be relativized to its own domain of discourse by inserting
>>	an explicit predicate whose extension is that domain.  Syntactically, 
>>	this relativization could be accomplished by placing that 
>>	predicate in the antecedent position of universals and in 
>>	conjunctive position of existentials, but I believe that user-
>>	friendliness dictates a more uniform process, such as that offered 
>>	by sorted quantifiers.]
> If the issue is user friendliess, then your argument here sounds more like a 
> justification for why sorted quantifiers are useful or convenient, but not 
> for why they are *essential*, as you suggest.

Jim Fulton may have been a bit too enthusiastic in using the term
"essential", since for the versions of KIF, IRDS-CG, and SUMM that 
we have agreed upon, types will be defined by purely syntactic
extensions to an untyped semantic base.  That is quite sufficient for
user friendliness, and it preserves the syntactic appearance of current 
CG systems.  However, I do believe that there are strong philosophical 
and linguistic reasons for going to a typed semantics for NL-CG.