What is LFG? in LFG FAQ

[Tara W Mohanan]

The answer to the question "What is Lexical Functional Grammar?"
in the FAQ (Frequently Asked Questions) of the LFG list makes
us a little uncomfortable. This is because we feel that the
description is one-sided; it does not reflect what many linguists
(including us) may find what is valuable in LFG. There are many
dimensions to a question like "What is LFG?"  We think it is
important that each of us articulate for ourselves and others
what these different threads are, so that it would accommodate
and appeal to linguists of different persuations and temperaments.
In what follows, we make an attempt to articulate our perception.

In order to do this, we need to use terms like theory, framework
and model. However, these terms have different meanings for
different linguists, and hence we will define our own meanings
in painful detail and with some illustration. We apologise for
what could be plodding through the obvious, but our experience
has been that the use of these terms is a potential source of
miscommunication.

1.  A GENERAL SCHEME FOR UNPACKING

It is useful to begin by acknowledging at least five different
dimensions of theoretical research, namely:
        A.      Theoretical laws;
        B.      Conceptual frameworks;
        C.      Formal frameworks;
        D.      Theoretical models; and
        E.      Research programmes.

1.1. Laws

By "laws" we mean general statements that express regularities.
Examples of laws in natural sciences include laws of gravitation /
electromagnetism / genetics. The counterparts of laws in linguistics
are variously called rules, constraints, templates, conventions,
conditions, etc. Laws of language structure can be either at the
crosslinguistic level (universal laws) or at the language particular
level. Examples of laws at the level of universal grammar include
binding conditions, linking rules, islands/subjacency,
subject condition, lexical integrity, structure preservation
constraint, association conventions, percolation conventions,
and so on. Examples of laws at the level of English grammar
include statements such as "An onset cannot have more than
three segments." and "The possessive and plural affixes cannot
be attached to the same noun." PS rules state the laws governing
the well formedness of phrase structure. X-bar theory is a
collection of crosslinguistic laws that hold on phrase structure.

As far as we can tell, the first appearance of crosslinguistic
laws in linguistics was in the A-over-A condition that developed
into islands and subjacency. The next was the laws of X-bar theory.
This was followed by the laws of relational grammar, which got
incorporated into various frameworks in different ways.

1.2. Conceptual framework

By "conceptual framework" we mean a set of related general concepts
that enter into the formulation of laws and representations. The laws
of gravitation are formulated in terms of the conceptual framework
of gravity, acceleration, momentum, velocity, mass, distance, and
so on.  Representations of molecular structure are formulated in
terms of the framework of electrons, bonds, double bonds,  and so on.
In linguistics, concepts like noun, verb, adjective are part of the
conceptual framework of grammatical categories in terms of which
syntactic   representations, universal and language particular laws
are formulated. Concepts like voicing, nasality, labiality, and
backness are part ot the conceptual framework of phonological
categories in terms of which phonological representations, rules
and constraints are formulated. "Should the notions of subject
and primary object be expressed as spec of agr-s and spec-of agr-o, or
as [-r, -o] and [-r, +o]?"  belong to the domain of conceptual
frameworks.

It might be useful here to distinguish between the *concepts* of
a conceptual framework, and the *vocabulary* of the conceptual
framework. For instance, the vocabulary {subject, object} and
{spec-of-agr-s and spec-of-agr-o} express the same concepts.
The difference between the two frameworks is in the vocabulary,
not concepts. If we agree on this, it is easy to see that the
idea that the GB framework does not employ grammatical functions
is correct only with respect to its vocabulary, not its concepts.
This is not to say that the vocabulary is trivial or unimportant.
In fact, vocabularies often embody metaphors that are tied up
with particular world views, and guide the direction of
further research.

1.3. Formal framework

By "formal framework" we mean the formal algebra (i.e., the formal
language cum system of calculations) that allows us to express
linguistic laws and linguistic representations, and calculate
their consequences. Newton's theory of gravitation is formulated
within the formal frameworks of differential calculus and Euclidian
geometry. Einstein's theory of gravitation calls for Reimannian
geometry. In linguistics,  issues of rules vs. constraints,
monotonicity, structure building rules vs. structure changing
rules, binary vs. multivalent features, etc., distinguish one
formal framework from another. Questions such as "Should the
relation between the wh gap and its filler be expressed in terms
of movement with traces, base generated empty categories, or as
a relation between two types of functions?" are questions about
the choice of formal frameworks.

1.4. Model

By "model" we mean a set of assumptions on the skeletal structure
of an object, as in the model of atom or the model of the solar
system. In linguistics, issues of the organisation of grammar,
typically involving (i) levels of representation, (ii) modules
of the grammar, and (iii) their relationships are associated with
differences among models. Thus, the Aspects model of grammar differs
from the Syntactic Structures model in both the levels of representation
they contain, and their relationship. The Aspects model differs from
the model of EST mainly in the interaction between levels: the latter,
not the former, permits a direct interaction between semantic
representation and surface structure representation.

1.5. Research programme

By "research programme" we mean a set of assumptions and values
governing the object of inquiry, what counts as relevant evidence,
the criteria of success, failure, and degrees of success in the
evaluation of laws, frameworks, and models, what counts as a
good argument, and so on. The research programme of science prior
to Galileo assumed that a good explanation should be consistent
with scriptures. Galileo changed the rules of the game, saying
that all that mattered was consistency with experiment (which
can be expanded to cover non-experimental observations as well.).
The object of inquiry in Chomsky's linguistics is language as a
mental system, that of sociolinguistics is that of language as a
social system. The GPSG research programme denies the fruitfulness
of pursuing the mental linguistic system. [We have never understood
what the GPSG object of inquiry is.] (Saying that language is a
"formal object" does not make sense, because "formal object"
refers to the model that we construct. If language is a formal
object, then gravity is also a formal object.). In Kiparsky's
research programme, corpus evidence (as realised in the entries
in the dictionary of a language) has high priority, while
experimental evidence from the behaviour of a language user
(as in play languages, speech errors, judgements on the acceptability
of coinages, etc) has lower priority. In Halle's research program
both have equal priority. In our own research programme, we find,
corpus evidence has lower priority.

When the research programme of an individual researcher or a
conceptual framework of a particular theory comes to be shared by
a research community, it becomes part of what Thomas Kuhn called a
paradigm. A paradigm in addition contains features such as templates
of prestigious analyses and arguments, favored modes of thinking,
conventions of discourse, and so on.

Thus, when someone says "GB", (s)he may be talking about GB theoretical
laws, GB conceptual framework (concepts, vocabulary), GB formal framework,
GB model, or the GB paradigm.  A GB analysis is situated in the context of
the GB laws, which in turn is situated in the context of the GB framework
and model, and these in turn are situated in the context of the GB paradigm.

To illustrate how we can unpack the different threads of theoretical
research using the above world view, we may say that the so called
Aspects "theory" and SPE "theory" had no theoretical laws at the
crosslinguistic level. All that they offered were a model, conceptual
framework, and formal framework.

2. CHARACTERISING LFG / GB VS. LFG

2.1. Laws

Laws of language structure could be at least of two types:
those that express the regularities internal to a given type
of information (such as regularities internal to c-structure
or internal to f-structure), and those that express the regularities
in the pairing between two types of information (such as the
regularities in the relation between c-structure and f-structure).
We will refer to the former as well formedness laws and the
latter as correspondence laws (=linking laws).

Function argument biuniqueness, subject condition, consistency,
and so on, state regularities internal to f-structure. The laws
of X-bar theory state the regularities internal to c-structure.
These are both universal well-formedness laws.

Annotations on PS rules express regularities in the language
internal pairings between c-structure and f-structure. Linking
rules in the Lexical Mapping Theory express the crosslinguistic
regularities governing the relation between argument structure
and grammatical function structure. These are examples of correspondence
laws. LFG is now in the process of developing cross linguistic
correspodence laws to express the regularities in the pairing
of c-structure f-structure.

Another avenue that we think we must explore in LFG will be the
correspondence laws governing the relationship between semantic
structure on the one hand, and  c-structure, f-structure, and
phonological structure on the other.

2.2. Conceptual frameworks

As for differences at the level of conceptual frameworks, it is easy
to see that LFG and GB have very different vocabularies, and therefore
different metaphors and world views. However, we doubt very much if
they employ different concepts.

2.3. Formal frameworks

The most striking difference between LFG and GB lies in their
respective formal frameworks. The formal framework for the expression
of laws in GB employs the mechanism of transformations. Early LFG
used the device of transformations in relating pairs of lexical
entries. Thus, rules such as the passive and dative in early LFG
are essentially lexical transformations stated in terms of grammatical
functions. (We hope that this remark does not need to be defended
in detail.) Subsequent work in LFG abandoned this device. We won't
say much about the uniqueness of LFG along the dimension of formal
frameworks, since this is well known. The Kaplan & Bresnan article
"Lexical Functional Grammar: A Formal System for Grammatical Representation"
(in The Mental Representation of Grammatical Relations) is essentially
the articulation of the LFG formal framework for the statement of laws
(ps rules, annotation, ..) and representations (c-str, f-str).

2.4. Models

The issue of models is somewhat tricky, because the substance of the
GB family of models is not easy to unpack. Here is what we think.

First, the GB surface structure that Chomsky makes occasional remarks
on is equivalent to LFG c-structure. (GB surface structure is located
inside the PF module.) This level contains information about overt words,
the classification of words, the grouping of words into phrases, the
classification of phrases, and overt word order. This means there are
no null elements in surface structure.  If c-structure contains empty
categories, therefore, the equivalence is not exact.

The d-structure in GB captures approximately the same information
as argument structure in LFG. S-structure carries information about
grammatical functions like subject and object. It also carries
information about functions like topic and focus. All this information
is copied into LF by means of traces. Ignoring the effects of
"restructuring" (whose status is unclear in GB research) we may say
that LF carries information about argument structure, clausal
grammatical functions, "sentential" grammatical functions (topic,
focus), and grammatically significant semantic information (scope,
antecedentship, ..). The information carried by d-structure and
s-structure are reduntant, since all this is present in LF anyway,
which is why these levels of representation were abandoned in the
minimalist model of the GB family of models.  Thus, LF representations
in GB are the equivalent of f-structure representions in LFG (assuming
that representations of argument structure in LFG are still internal to
rather than outside f-structure).

Ignoring differences in detail, the substance of the levels of
representation in GB and LFG is roughly the same. (This is not to
say that the differences in detail are empirically unimportant.)
However, they are radically different in their interaction. For
instance, GB does not permit direct interaction between phonological
information and semantic information. Hence scope related intontational
effects need to be expressed in terms of syntactic diacritics.
The non-sequential parallel architecture of LFG does not prevent
direct interaction between meaning and pronunciation.

2.5. Research Program

The LFG research programme takes off from the GB research programme
of investigating language as a mental system, and takes it to its
logical conclusion. In this sense, LFG is more Chomskian than Chomsky.
An articulation of this view is given in Bresnan & Kaplan's article
"Introduction: Grammas as Mental Representations of Language" (in
The Mental Representation of Grammatical Relations). As far as this
aspect is concerned, GPSG and LFG are very distinct entities.
We are not sure where HPSG stands.

3.  What we find attractive about LFG

What is it that we (KPM and TM) resonate to in LFG? First, the
research program, with is commitment to the strong competence
hypothesis. Second, the model, with its parallel architecture,
the possibility of a number of copresent dimensions and subdimensions
of linguistic structure linked to one another through correspondence
laws. Third, the conceptual framework that makes a clean separation
between information about the classification of words and phrases
(grammatical categories) and what these words and phrases do in a
structure (grammatical functions). Another aspect of the LFG model
that we respond to is the distinction between lexical and non-lexical
modules, though recent work suggests that the details of this broad
distinction need to be scrutinised carefully.

By and large, although we think that formalism is important for
ensuring rigour and precision in the articulation and evaluation
of a theory, we are unexcited by issues of formalism.


KP Mohanan and Tara Mohanan

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Tara W Mohanan, Dept of English & Literature, NUS