Thurs
June 15 |
Ben Keil
UCLA Department of Linguistics
"Generation of Natural Language from Decidable Logics"
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Recent work by Sylvain Pogodalla [1] and Ian Pratt-Hartmann [2] have
explored the use of decidable logics in the generation of natural
language sentences and texts. Pogodalla uses the decidability of
multiplicative linear logic directly (by generating a sentence from a
constructive proof of its grammaticality). Pratt-Hartmann, on the other
hand, aims to find interpreted (fragments of natural) languages with
expressive power equivalent to that of logics known to be decidable.
The motivation being that such equivalences may have advantageous uses
in automated translation tasks and that it provides a means for
automated checking of argument validity.
In its current stage of development, as Pratt-Hartmann's work is---as
he himself writes---"certainly not ... practically useful ... [h]owever,
the techniques developed ... carry over easily to various salient
extensions ...."; I wish to probe this claim.
In this talk, I demonstrate that the technique that Pratt-Hartmann has
developed creates texts that are (to an extreme degree) unnecessarily
verbose, and fail to take advantage of all available information. For
example, taking the interpretation of a natural language sentence and
using it as input to Pratt-Hartmann's technique, one cannot regenerate
the original sentence; moreover the output from his technique will be a
text several sentences long.
I propose an alternative method of generating natural language from
logical structures centered around the fact that the set of
interpretations of the sentences of a language is itself a language.
This means, among other things, that it has a grammar. This grammar can
be used for parsing an input interpretation to check if it coresponds
directly to a natural language sentence, as well as for generation,
where the interpretations generated are then guaranteed to correspond to
a natural language sentence. Then, the output from the grammar can be
transduced to a natural language sentence that includes the desired
interpretation among its possible meanings.
[1] Pogodalla, Sylvain. Generation with Semantic Proof Nets. url:
http://citeseer.ist.psu.edu/459766.html
[2] Pratt-Hartmann, Ian. A Two-Variable Fragment of English. Journal of
Logic, Language and Information, 12(1), 2003, pp. 13--45.
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| 4:00PM
3103c Campbell Hall
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Thurs
June 1 |
Philippe Schlenker
UCLA Department of Linguistics
"Super Liars"
Kripke 1975 provided a trivalent theory of truth in which paradoxes -for
instance (i) below- are neither true nor false and have the value #.
(i) This very sentence is false.
However Kripke's theory buys a solution to the paradoxes by sacrificing the
expressive power of his language. One might well want to state that (i) is
something other than 'true' - which is clearly the case, since (i) has the
value #. But such a sentence cannot be defined in the language. To
express it, we would need a negation not* ('weak negation') which returns
the value 'true' when it applies to a sentence with the value '#'. But if
such a negation could be defined, we could also define a 'super Liar' as in
(ii):
(ii) This very sentence is not* true.
But (ii) can neither be true (for then it would be false), nor false (for
then it would be true), nor # (this would make it true again); if it were
added to Kripke's language, it would immediately make his logic
inconsistent. Kripke has no solution to this problem.
I sketch an alternative solution which builds upon Kripke's theory of truth
but adds many negations and truth values to his logic. The analysis
- I start by observing that the Super Liar is (most) naturally expressed in
natural language as: 'This sentence is something other than true', with
overt quantification over truth values. As is quite generally the case with
natural language quantifiers, 'something' has an implicit domain
restriction, which in the present case is a set of truth values.
- Taking this observation literally, I define a hierarchy of negations
which each has an ordinal as its domain restriction. I do not pre-judge how
many truth values are needed, and I take each truth value to be itself an
ordinal. Writing domain restrictions as a subscript a in the object
language, I define the following semantics (F is any formula, and a and b
are any ordinals):
not_a F has the value:
0 iff F has the value 1
1 iff F has the value b with b=0 or 1 < b < a
b iff F has the value b with b \204 a.
- The result is a logic which:
- unlike Kripke's system, displays a form of expressive completeness
(specifically, each truth function over a finite set of truth values can be
expressed)
- has a variety of fixed points (at least when the language forms a set):
one of them emulates Kripke's 'least fixed point', and assigns only 3
different truth values; one of them assigns to each Liar of the form L_a: not_a True(L_a)
the value a.
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| 4:00PM
3103c Campbell Hall
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Thurs
May 4 |
Edward Keenan
UCLA Department of Linguistics
"A Semantic Classification of Natural Language Quantifiers"
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We characterize the fundamental classes of NL quantifiers exhibiting
various "naturalness" results: the elementary classes -- INT
(intersective = existential Dets) and CO-INT (co-intersective =
universal Dets) are both isomorphic to the superficially simpler class
of generalized quantifiers (GQs). The cardinality Dets over finite E
are characterized as INT intersect PI, the set of permutation
invariant functions of type <1,1>. Similarly CO-CARD = COL-INT
intersect PI. The boolean closure of INT union CO-INT is CONS, the
set of conservative functions. We study the proportionality Dets,
PROP, a proper boolean subalgebra of CONS. Proportionality Dets are
among the least well understood -- They are typically not first order
definable and not sortally reducible (meaning they make essential use
of the domain restricting head noun). We consider some typical
entailment paradigms involving proportionality Dets as they are the
least well understood deductively. We provide a way of counting them,
though our best figure requires determining the prime factors (but not
how many times a given one occurs) of the size of the domain (assumed
finite). In CONS less PROP we find various presuppositional Dets like
THE TEN. We show how they are built from boolean compounds of
intersective and co-intersective Dets.
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| 4:00PM
3103c Campbell Hall
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Thurs
Apr 27 |
Greg Kobele
UCLA Department of Linguistics
"Mild context sensitivity without structure?"
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We usually think of strings as being structured, and of grammatical
operations as being sensitive to this structure. This perspective
gains much intuitive support from the apparent structure-sensitivity
of natural language (consider Chomsky's discussion of the Yes-No
question transformation). This is not the only perspective we could
take however. An alternative views strings as unstructured (or as
having a `flat' structure), and grammatical operations as imposing
structure upon them. Interestingly, both perspectives ennable us to
describe basic patterns of interest to linguists (copying, multiple
and crossed dependencies), while at the same time ruling out other,
linguistically unrealistic, ones (non-semilinear or -polynomially
time recognizable). What then are we to make of the arguments for
structured strings? Are they irreducibly semantic, or can we make
sense of them at the level of strings and definable string sets?
References: Carlos Martin-Vide et al.
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| 4:00PM
3103c Campbell Hall
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Thurs
Apr 20 |
Johan van Benthem
Amsterdam & Stanford
"Semantic Dynamics: a Uniform Logical Approach"
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The 'Dynamic Turn' has put actions at center stage in semantics and
pragmatics of natural language, and far beyond. In this talk, we
discuss how modern dynamic logics of information work, across a range
of phenomena in information update, belief revision, preference
change, and probabilistic update.
References:
One is a lonely number: Logic and communication,
A mini-guide to logic in action, and
papers under 'Research' here
and here.
NOTE THE UNUSUAL TIME, PLACE
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| 5:00PM
2122 Campbell Hall
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Thurs
Mar 9 |
Greg Kobele
UCLA Department of Linguistics
"On the locality of syntactic relations: Long-distance Agree is
Spec-Head with funky spell-out"
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Minimalist Syntacticians have recently distanced themselves
from the proposal that all feature checking is done in local
configurations (usually spec-head), allowing instead an infinity of
structural configurations to permit feature checking (this infinity
is compactly described by reference to c-command). Needless to say,
this move has caused some consternation. But what is the debate
really about? Are there measurable empirical differences between
these two proposals? Or are they (like so much else) just disputes
over notation? Couching discussion in the formal framework of
minimalist grammars, I show that the abstract structure of agree- and
spec-head- based theories of feature checking are identical in every
respect, and that the peculiarities in pronunciation and
interpretation which motivated the agree-theory in the first place
are naturally expressed in a minimalist spec-head theory. I conclude
with considerations of locality conditions peculiar to agree-ment,
and their spec-head reformulations.
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| 4:00PM
3103c Campbell Hall
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Mon
Mar 6 |
Edward Stabler
UCLA Department of Linguistics
"Grammar monads and transformers"
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Generative grammars provided the first characterizations of
the Chomsky hierarchy, and the first real insights into how language
structure reflects the time and memory requirements of the
processor. But most natural descriptions of human languages involve
exceptions, blocking, last resorts, reanalysis, reduplication,
optimality, optionality, economy, and noncompositionality. None of
these are well handled by standard generative mechanisms. Some formal
linguists ignore the tricky parts, thinking we just don't understand
them yet (the 'right' descriptions shouldn't need exceptions or those
other tricky things). Some others resort to surface-y probabilistic
analyses that abandon the insights of standard grammars but at least
allow some of the exceptional and squishy cases. Here a different
route is explored: put the grammar in a monad and obtain the missing
expressive power with monad transformers. Some examples -- 'tricky'
and 'squishy' examples -- are briefly treated. Then, even more
briefly, we describe one approach to mapping out monad transformer
capabilities, showing that they are not as far from standard analyses
as it might have seemed at first.
NOTE THE UNUSUAL DAY, TIME, PLACE
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| 2:00PM
3114 Rolfe Hall
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Thurs
Feb 13 |
Marcus Kracht
UCLA Department of Linguistics
"The Modal Logic of Multidominance"
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In continuation of my previous talk last term I shall present in more
detail how one can use logic to talk about trees and multidominance
structures. There are two rivals: monadic second order logic (MSO) and
modal logic. While for trees there is Rabin's result allows to easily
get decidability of MSO, the algorithmic complexity is very high
(nonelementary). Also the proof is quite complex. Modal logics, on the
other hand, are not only far easier to use and give reasonable
complexity bounds in the known cases, for example the logic of a
CF-tree set and the logic of all multidominance structures. It also
turns out that for all I know they offer enough expressive power for
linguistic purposes. All that linguists need to say can be expressed
in modal logic. However, the project is so far unfinished. There are
some grammar formalisms within generative grammar whose decidability
is still open.
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| 4:00PM
3103c Campbell Hall
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Thurs
Feb 16 |
Greg Kobele
UCLA Department of Linguistics
"Structure Copying Without Copying Structure"
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Mechanisms ensuring that two constituents are identically
constituted abound in the linguistic literature, although nowhere are
their inner machinations spellt-out in any detail (with the notable
exception of multiple-dominance based accounts [see, e.g. Gaertner
(2002)]). As a precursor to a mechanism of structure copying, it
behooves us to get clear on how we are to understand the structure
copied in the first place. It is useful to make a three-way
distinction among interpretations of what the tree-like
representations of syntactic structure `mean.' The received
interpretation of syntactic structure, that it is a first-rate
syntactic object, is not only a computational worst-case scenario, but
also is inconsistent with a theory of syntax which incorporates phases
(cyclic interpretation at the interfaces with concomitant destruction
of interpreted structure). Another natural interpretation of
syntactic structure views it not as an object in its own right, but as
a high-level description of the derivational process which resulted in
the actual syntactic object. According to this interpretation of
structure, `copying structure' is re-interpreted as deriving
independent structures in the same way. I show how to implement the
copy-theory of movement in minimalist grammars, when structure is thus
understood as an epiphenomenon of the derivation, and cannot be
accessed by syntactic operations (like copying). Interestingly, the
final interpretation of syntactic structure, according to which
structure is best understood as a name for a pair of phonological and
semantic objects, and accordingly copying structure just *is* copying
phonological or semantic objects, can, in the context of minimalist
grammars, be shown to result in a theory strongly equivalent to the
derivational interpretation of copying.
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| 4:00PM
3103c Campbell Hall
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Tues
Jan 24 |
Willemijn Vermaat
Universiteit Utrecht UiL-OTS
"The Logic of Variation: A cross-linguistic account of wh-question formation"
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Generative linguists and categorial grammarians aim to develop a
system of Universal Grammar to explain structural variation across
languages while at the same time accounting for uniformity in
interpretation. The generative tradition has provided a broad
empirical perspective on cross-linguistic diversity. The type-logical
tradition provides logical tools to understand this diversity in
deductive terms.
In this talk, I will present the logic of variation as a system of
universal grammar. With this logic, I provide a deductive account of
the cross-linguistic diversity in wh-question formation (questions
starting with `who', `what', etc.). The combination of structural
variation and uniform semantic interpretation in wh-question
formation can be accounted for in terms of three assumptions: (1)
Higher-order type assignment: higher-order type assignment to wh-
elements accounts for the uniformity in the semantic interpretation
of wh-questions; (2) A fixed structural module: variation in the
structural realization is bounded by a restricted set of structural
rules which is claimed to be fixed by Universal Grammar;
consequently, (3) Strong lexicalism: cross-linguistic variation in
wh-question formation must be entirely reducible to differences in
lexical type-assignment, that is, there are no language-specific
structural rules.
I provide empirical support for this view by presenting analyses of
wh-questions in languages that structurally differ in wh-question
formation. The various language phenomena discussed in this talk have
been implemented with Grail, a parser for categorial type logics and
can be analyzed on-line.
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4:00 PM
3103 Campbell Hall
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