Re: SUO: Program Semantics
Chris,
We usually agree on technical issues, but we often get into fights
over which innovators deserve the most (or in this case, at least some)
credit for subsequent developments.
JS> I agree that Montague's system has had more influence among
> professional linguists, but that is primarily because linguists feel
> that a logician is more prestigious and worthy of a citation than
> a mere computer programmer.
CM> Let's not be silly here, John. Woods' work may be just dandy, but
> it was hardly a bias against programmers, and awe for logicians, that
> caused Montague's work to get all the attention among linguists.
> It was because of Montague's great sensitivity to a wide range of
> grammatical phenomena in natural language that had been entirely
> overlooked by philosophers and logicians to that point, as well as his
> wide knowledge of syntactic theory.
I agree about the "wide range of grammatical phenomena... that had
been entirely overlooked by philosophers and logicians." But that
observation merely confirms my point about how little attention most
philosophers and logicians pay to anything not written by their buddies.
In the 1960s, computational linguists had already implemented parsers
for a much wider range of syntactic phenomena than those "philosophers
and logicians" had ever dreamed of.
And don't give Montague credit for his "wide knowledge of syntactic
theory". The version of syntax he used was categorial grammar,
which was certainly an elegant proposal in the 1930s when Ajdukiewicz
introduced it. But by the 1960s, it was very long in the tooth and
hardly a suitable foundation for NL parsers (or semantic interpreters).
Even Barbara Partee, who has been Montague's most devoted publicist
among linguists, admitted that categorial grammar should be replaced
by a more flexible syntactic foundation.
CM> And, of course, the paradigm itself was extraordinarily fruitful.
When I first came across Montague's writings in the 1970s, I was
impressed by his synthesis of many previously independent lines of
thought -- syntax, semantics, lambda calculus, functionals, possible
worlds, quantification, and modal logic. It was certainly a major
achievement for which he deserves a lot of credit. But as a foundation
for the future, it has proved to be a dead end -- despite the many
attempts by logicians to rescue it from its rebarbative notation.
JS> But much as I like lambda calculus, I believe that Montague's
> formalism was a disaster that has done more to hinder widespread
> use of logic than it has done to promote it.
CM> Rubbish.
On the contrary, the only thing worse than Montague's notation for
syntax was his notation for semantics. It was Carnap (1947) who
suggested that the intension of a sentence be defined as a function
from possible worlds to truth values. I admit that Montague was
astonishingly brilliant in devising a method for carrying out that
suggestion to its ultimate conclusion: to each grammar rule, he
assigned a lambda expression for a function that defined the
intension of the corresponding syntactic constituent.
The upshot of that construction (i.e., the _reductio_) was Montague's
definition of the intension of the word _the_ as a function from
a function from possible worlds to sets of individuals to a function
from possible words to individuals. That was a construction that
even Ajdukiewicz couldn't have imagined, since he first published his
grammar in a language that had no definite article.
But the fact that languages as diverse as Polish, Latin, Chinese, and
Japanese get along quite well without definite (or indefinite) articles
indicates that there is something decidedly wrong about a theory that
attaches such a heavy-handed construction to them.
For a well balanced view of Montague's achievement in comparison to
some of his contemporaries, such as Roger Schank and Noam Chomsky,
I recommend the following excerpt.
John
_______________________________________________________________________
1.3 Metaphysical Baggage and Observable Results
Linguistic theories are usually packaged in metaphysical terms that
go far beyond the available evidence. Chomsky's metaphysics may be
summarized in a single sentence from _Syntactic Structures_: "Grammar
is best formulated as a self-contained study independent of semantics."
For Montague, the title and opening sentence of "English as a Formal
Language" express his point of view: "I reject the contention that
an important theoretical difference exists between formal and natural
languages." Schank's outlook is summarized in the following sentence
from _Conceptual Information Processing_: "Conceptual Dependency
Theory was always intended to be a theory of how humans process
natural language that was explicit enough to allow for programming
it on a computer." These characteristic sentences provide a key to
understanding their authors' motivation. Yet their achievements are
easier to understand when the metaphysics is ignored. Look at what
they do, not at what they say.
In their attitudes and metaphysics, Schank and Montague are
irreconcilable. Montague is the epitome of the kind of logician
that Schank has always denounced as misguided or at best irrelevant.
Montague stated every detail of his theory in a precise formalism, while
Schank made sweeping generalizations and left the detailed programming
to his students. For Montague, the meaning of a sentence is a function
from possible worlds to truth values; for Schank, it is a diagram
that represents human conceptualizations. On the surface, their only
point of agreement is their implacable opposition to Chomsky and "the
developments emanating from the Massachusetts Institute of Technology"
(Montague 1970). Yet in their reaction against Chomsky, both Montague
and Schank evolved positions that are remarkably similar, although their
terminology hides the resemblance. What Chomsky called a noun, Schank
called a picture producer, and Montague called a function from entities
to truth values. But those terms are irrelevant to anything that they
ever did: Schank never produced a single picture or even stated a
plausible hypothesis about how one might be produced from his diagrams;
Montague never applied any of his functions to the real world, let alone
the infinity of possible worlds he so freely assumed.
In neutral terms, what Montague and Schank did could be described
in a way that makes the logicist and AI points of view nearly
indistinguishable:
1. Semantics, not syntax, is the key to understanding language.
The traditional grammatical categories are surface manifestations
of the more fundamental semantic categories.
2. Associated with each word is a characteristic semantic structure
that determines how it combines with other words in a sentence.
3. The grammar of a language can be reduced to relatively simple rules
that show what categories of words may occur on the right or the
left of a given word (the Schankian expectations or the cancellation
rules of categorial grammar). The variety of sentence patterns is
not the result of a complex grammar, but of the complex interactions
between a simple grammar and the underlying semantic structures.
4. The meaning of a sentence is derived by combining the semantic
structures for each of the words it contains. The combining
operations are primarily semantic, although they are guided by
word order and inflections.
5. The denotation of a sentence in a possible world is computed by
evaluating its meaning representation in terms of a model of that
world. Although Schank never used logical terms like _denotation_,
his question-answering systems embodied effective procedures for
computing denotations, while Montague's infinities were
computationally intractable.
Terms like _picture producer_ or _function from entities to truth
values_ engender heated arguments, but they have no effect on the
application of the theory to language, to the world, or to a computer
implementation. Without the metaphysical baggage, both theories
incorporate a semantics-based approach that is widely accepted in AI
and computational linguistics.
At the level of data structures and operations, there are significant
differences between Montague and Schank. Montague's representations
were lambda expressions, which have the associated operations of
function application, lambda expansion, and lambda contraction. His
metaphysics gave him a rigorous methodology for assigning each word
to one of his categories of functions (even though he never actually
applied those functions to any world, real or possible). And his
concerns about logic led him to a careful treatment of quantifiers,
modalities, and their scope. Schank's representations are graphs on
paper and LISP structures of various kinds in his students' programs.
The permissible operations include any manipulations of those structures
that could be performed in LISP. Schank's lack of a precise formalism
gave his students the freedom and flexibility to invent novel
solutions to problems such as the use of world knowledge in language
understanding, which Montague's followers never attempted to address.
Yet that lack of formalism led to _ad hoc_ accretions in the programs
that made them unmaintainable. Many of Schank's students found it
easier to start from scratch and write a new parser than to modify one
that was written by an earlier generation of students. Montague and
Schank have complementary strengths: rigor vs. flexibility; logical
precision vs. open-ended access to background knowledge; exhaustive
analysis of a tiny fragment of English vs. a broad-brush sketch of
a wide range of language use.
Montague and Schank represent two extremes on the semantics-based
spectrum, which is broad enough to encompass most AI work on language.
Since the extremes are more complementary than conflicting, it is
possible to formulate approaches that combine the strengths of both:
a precise formalism, the expressive power of intensional logic, and
the ability to use background knowledge in language understanding.
To allow greater flexibility, some of Montague's rigid constraints
must be relaxed: his requirement of a strict one-to-one mapping
between syntactic rules and semantic rules; his use of lambda
expressions as the primary meaning representation; and his inability
to handle ellipsis, metaphor, metonymy, anaphora, and anything
requiring background knowledge. With a more appropriate formalism,
such limitations could be overcome within a rigorous theoretical
framework.
Source: http://www.jfsowa.com/ontology/lex1.htm