214 research outputs found
Proof Nets and the Complexity of Processing Center-Embedded Constructions
This paper shows how proof nets can be used to formalize the notion of
``incomplete dependency'' used in psycholinguistic theories of the
unacceptability of center-embedded constructions. Such theories of human
language processing can usually be restated in terms of geometrical constraints
on proof nets. The paper ends with a discussion of the relationship between
these constraints and incremental semantic interpretation.Comment: To appear in Proceedings of LACL 95; uses epic.sty, eepic.sty,
rotate.st
A Polynomial-Time Algorithm for the Lambek Calculus with Brackets of Bounded Order
Lambek calculus is a logical foundation of categorial grammar, a linguistic paradigm of grammar as logic and parsing as deduction. Pentus (2010) gave a polynomial-time algorithm for determining provability of bounded depth formulas in L*, the Lambek calculus with empty antecedents allowed. Pentus\u27 algorithm is based on tabularisation of proof nets. Lambek calculus with brackets is a conservative extension of Lambek calculus with bracket modalities, suitable for the modeling of syntactical domains. In this paper we give an algorithm for provability in Lb*, the Lambek calculus with brackets allowing empty antecedents. Our algorithm runs in polynomial time when both the formula depth and the bracket nesting depth are bounded. It combines a Pentus-style tabularisation of proof nets with an automata-theoretic treatment of bracketing
Partial Orders, Residuation, and First-Order Linear Logic
We will investigate proof-theoretic and linguistic aspects of first-order
linear logic. We will show that adding partial order constraints in such a way
that each sequent defines a unique linear order on the antecedent formulas of a
sequent allows us to define many useful logical operators. In addition, the
partial order constraints improve the efficiency of proof search.Comment: 33 page
Experimenting with Transitive Verbs in a DisCoCat
Formal and distributional semantic models offer complementary benefits in
modeling meaning. The categorical compositional distributional (DisCoCat) model
of meaning of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) combines aspected of
both to provide a general framework in which meanings of words, obtained
distributionally, are composed using methods from the logical setting to form
sentence meaning. Concrete consequences of this general abstract setting and
applications to empirical data are under active study (Grefenstette et al.,
arxiv:1101.0309; Grefenstette and Sadrzadeh, arXiv:1106.4058v1 [cs.CL]). . In
this paper, we extend this study by examining transitive verbs, represented as
matrices in a DisCoCat. We discuss three ways of constructing such matrices,
and evaluate each method in a disambiguation task developed by Grefenstette and
Sadrzadeh (arXiv:1106.4058v1 [cs.CL]).Comment: 5 pages, to be presented at GEMS 2011, as part of EMNLP'11 workshop
Experimental Support for a Categorical Compositional Distributional Model of Meaning
Modelling compositional meaning for sentences using empirical distributional
methods has been a challenge for computational linguists. We implement the
abstract categorical model of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) using
data from the BNC and evaluate it. The implementation is based on unsupervised
learning of matrices for relational words and applying them to the vectors of
their arguments. The evaluation is based on the word disambiguation task
developed by Mitchell and Lapata (2008) for intransitive sentences, and on a
similar new experiment designed for transitive sentences. Our model matches the
results of its competitors in the first experiment, and betters them in the
second. The general improvement in results with increase in syntactic
complexity showcases the compositional power of our model.Comment: 11 pages, to be presented at EMNLP 2011, to be published in
Proceedings of the 2011 Conference on Empirical Methods in Natural Language
Processin
Monoid automata for displacement context-free languages
In 2007 Kambites presented an algebraic interpretation of
Chomsky-Schutzenberger theorem for context-free languages. We give an
interpretation of the corresponding theorem for the class of displacement
context-free languages which are equivalent to well-nested multiple
context-free languages. We also obtain a characterization of k-displacement
context-free languages in terms of monoid automata and show how such automata
can be simulated on two stacks. We introduce the simultaneous two-stack
automata and compare different variants of its definition. All the definitions
considered are shown to be equivalent basing on the geometric interpretation of
memory operations of these automata.Comment: Revised version for ESSLLI Student Session 2013 selected paper
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