Development of
Semantic Theory
It is instructive, though not
historically accurate, to see the development of contemporary semantic theories
as motivated by the deficiencies that are uncovered when one tries to take the
FOPC example further as a model for how to do natural language semantics. For example, the technique of associating set theoretic
denotations directly with syntactic units is clear and
straightforward for the artificial FOPC example. But when a similar programme
is attempted for a natural language like English, whose syntax is vastly more
complicated, the statement of the interpretation clauses becomes in practice
extremely baroque and unwieldy, especially so when sentences that are
semantically but not syntactically ambiguous are considered [Coo83].
For this reason, in most semantic theories, and in all computer
implementations, the interpretation of sentences is given
indirectly. A syntactically disambiguated sentence is first translated into an
expression of some artificial logical language, where this expression in its
turn is given an interpretation by rules analogous to the interpretation rules
of FOPC. This process factors out the two sources of complexity whose product
makes direct interpretation cumbersome: reducing syntactic variation to a set of common semantic constructs; and building the
appropriate set-theoretical objects to serve as interpretations.
The first large scale semantic
description of this type was developed by]. Montague made a further departure
from the model provided by FOPC in using a more powerful logic (intensional
logic) as an intermediate representation language. All later
approaches to semantics follow Montague in using more powerful logical
languages: while FOPC captures an important range of inferences (involving,
among others, words like every, and some as in the example above), the range of
valid inference patterns in natural languages is far wider. Some of the
constructs that motivate the use of richer logics are sentences involving
concepts like necessity or possibility and
propositional attitude verbs like believe or
know, as well as the inference patterns
associated with other English quantifying expressions like most or more than
half, which cannot be fully captured within FOPC .
For Montague, and others
working in frameworks descended from that tradition (among others, Partee,
e.g., [Par86],
Krifka, e.g., [Kri89],
and Groenendijk and Stokhof, e.g., [GS84,GS91a])
the intermediate logical language was merely a matter of convenience which
could in principle always be dispensed with provided the principle of
compositionality was observed. (I.e., The meaning of a sentence
is a function of the meanings of its constituents, attributed to Frege, [Fre92]).
For other approaches, (e.g., Discourse Representation Theory, [Kam81])
an intermediate level of representation is a necessary component of the theory,
justified on psychological grounds, or in terms of the necessity for explicit
reference to representations in order to capture the meanings of, for example,
pronouns or other referentially dependent items,
elliptical sentences or sentences ascribing mental states
(beliefs, hopes, intentions).
In the case of computational implementations, of course, the issue of the
dispensability of representations does not arise: for practical purposes, some
kind of meaning representation is a sine qua non for any kind of computing.
Discourse Representation Theory (DRT) [Kam81,KR93],
as the name implies, has taken the notion of an intermediate representation as
an indispensable theoretical construct, and, as also implied, sees the main
unit of description as being a discourse rather than sentences in isolation.
One of the things that makes a sequence of sentences constitute a discourse is
their connectivity with each other, as expressed through the
use of pronouns and ellipsis or similar
devices. This connectivity is mediated through the intermediate representation,
however, and cannot be expressed without it.
Dynamic semantics takes the view that the standard truth-conditional view of
sentence meaning deriving from the paradigm of FOPC does not do sufficient
justice to the fact that uttering a sentence changes the context it was uttered
in. Deriving inspiration in part from work on the semantics of programming
languages, dynamic semantic theories have developed several variations on the
idea that the meaning of a sentence is to be equated with the changes it makes
to a context.
Update semantics (e.g., [Vel85,vEdV92])
approaches have been developed to model the effect of asserting a sequence of
sentences in a particular context. In general, the order of such a sequence has
its own significance. A sequence like:
Someone's at the door. Perhaps it's John.
It's Mary!
is coherent, but not all permutations of it
would be:
Someone's at the door. It's Mary. Perhaps
it's John.
Recent strands of this work make connections
with the artificial intelligence literature on truth maintenance
and belief revision .
Dynamic predicate logic [GS91a,GS90]
extends the interpretation clauses for FOPC (or richer logics) by allowing
assignments of denotations to subexpressions to carry over from one sentence to
its successors in a sequence. This means that dependencies that are difficult
to capture in FOPC or other non-dynamic logics, such as that
between someone and it in:
Someone's at the door. It's Mary.
can be correctly modeled, without sacrificing any of the other
advantages that traditional logics offer.
One of the assumptions of
most semantic theories descended from Montague is that information is total, in
the sense that in every situation, a proposition is either true or it is not.
This enables propositions to be identified with the set of situations (or
possible worlds) in which they are true. This has many
technical conveniences, but is descriptively incorrect, for it means that any
proposition conjoined with a tautology (a logical truth) will remain the same
proposition according to the technical definition. But this is clearly wrong:
all cats are cats is a tautology, but The computer crashed, and
The computer crashed and all cats are cats are clearly different propositions
(reporting the first is not the same as reporting the second, for example).
Situation theory [BP83 has attempted to rework the whole logical
foundation underlying the more traditional semantic theories in order to arrive
at a satisfactory formulation of the notion of a partial state of the world or situation, and in turn, a more satisfactory notion of
proposition. This reformulation has
also attempted to generalize the logical underpinnings away from previously
accepted restrictions (for example, restrictions prohibiting sets containing
themselves, and other apparently paradoxical notions) in order to be able to
explore the ability of language to refer to itself in ways that have previously
resisted a coherent formal description
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