106,564 research outputs found
A Complete and Recursive Feature Theory
Various feature descriptions are being employed in logic programming
languages and constrained-based grammar formalisms. The common notational
primitive of these descriptions are functional attributes called features. The
descriptions considered in this paper are the possibly quantified first-order
formulae obtained from a signature of binary and unary predicates called
features and sorts, respectively. We establish a first-order theory FT by means
of three axiom schemes, show its completeness, and construct three elementarily
equivalent models. One of the models consists of so-called feature graphs, a
data structure common in computational linguistics. The other two models
consist of so-called feature trees, a record-like data structure generalizing
the trees corresponding to first-order terms. Our completeness proof exhibits a
terminating simplification system deciding validity and satisfiability of
possibly quantified feature descriptions.Comment: Short version appeared in the 1992 Annual Meeting of the Association
for Computational Linguistic
Transmutations and spectral parameter power series in eigenvalue problems
We give an overview of recent developments in Sturm-Liouville theory
concerning operators of transmutation (transformation) and spectral parameter
power series (SPPS). The possibility to write down the dispersion
(characteristic) equations corresponding to a variety of spectral problems
related to Sturm-Liouville equations in an analytic form is an attractive
feature of the SPPS method. It is based on a computation of certain systems of
recursive integrals. Considered as families of functions these systems are
complete in the -space and result to be the images of the nonnegative
integer powers of the independent variable under the action of a corresponding
transmutation operator. This recently revealed property of the Delsarte
transmutations opens the way to apply the transmutation operator even when its
integral kernel is unknown and gives the possibility to obtain further
interesting properties concerning the Darboux transformed Schr\"{o}dinger
operators.
We introduce the systems of recursive integrals and the SPPS approach,
explain some of its applications to spectral problems with numerical
illustrations, give the definition and basic properties of transmutation
operators, introduce a parametrized family of transmutation operators, study
their mapping properties and construct the transmutation operators for Darboux
transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1111.444
A Neural Theory of Visual Search: Recursive Attention to Segmentations and Surfaces
A neural theory is proposed in which visual search is accomplished by perceptual grouping and segregation, which occurs simultaneous across the visual field, and object recognition, which is restricted to a selected region of the field. The theory offers an alternative hypothesis to recently developed variations on Feature Integration Theory (Treisman, and Sato, 1991) and Guided Search Model (Wolfe, Cave, and Franzel, 1989). A neural architecture and search algorithm is specified that quantitatively explains a wide range of psychophysical search data (Wolfe, Cave, and Franzel, 1989; Cohen, and lvry, 1991; Mordkoff, Yantis, and Egeth, 1990; Treisman, and Sato, 1991).Air Force Office of Scientific Research (90-0175); Defense Advanced Research Projects Agency (AFOSR 90-0083, ONR N00014-92-J-4015); Office of Naval Research (N00014-91-J-4100); British Petroleum (89-A-1204); National Science Foundation (IRI-90-00530
The Computable Universe Hypothesis
When can a model of a physical system be regarded as computable? We provide
the definition of a computable physical model to answer this question. The
connection between our definition and Kreisel's notion of a mechanistic theory
is discussed, and several examples of computable physical models are given,
including models which feature discrete motion, a model which features
non-discrete continuous motion, and probabilistic models such as radioactive
decay. We show how computable physical models on effective topological spaces
can be formulated using the theory of type-two effectivity (TTE). Various
common operations on computable physical models are described, such as the
operation of coarse-graining and the formation of statistical ensembles. The
definition of a computable physical model also allows for a precise
formalization of the computable universe hypothesis--the claim that all the
laws of physics are computable.Comment: 33 pages, 0 figures; minor change
Typing after syntax. An argument from quotation and ellipsis
The paper, assuming the general framework of Chomsky’s (2013a, 2015b) current version of the Minimalist syntax, investigates the syntax of quotation in light of ellipsis. I show that certain unexpected effects arising for quotational ellipsis are problematic for the standard feature valuation system and, especially, for the theory of phases. I discuss some effects of two possible interpretations of such ellipsis, as well as a constraint following from deviant antecedents, to show that the standard view on the internal syntax of quotational expressions should be reconsidered. The paper offers a new view on feature valuation, as well as the connection between the Narrow Syntax and the C-I interface, defined in terms of recursive typing taking place at the interface
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