59,714 research outputs found
An interpretation of the Sigma-2 fragment of classical Analysis in System T
We show that it is possible to define a realizability interpretation for the
-fragment of classical Analysis using G\"odel's System T only. This
supplements a previous result of Schwichtenberg regarding bar recursion at
types 0 and 1 by showing how to avoid using bar recursion altogether. Our
result is proved via a conservative extension of System T with an operator for
composable continuations from the theory of programming languages due to Danvy
and Filinski. The fragment of Analysis is therefore essentially constructive,
even in presence of the full Axiom of Choice schema: Weak Church's Rule holds
of it in spite of the fact that it is strong enough to refute the formal
arithmetical version of Church's Thesis
Perspectives for proof unwinding by programming languages techniques
In this chapter, we propose some future directions of work, potentially
beneficial to Mathematics and its foundations, based on the recent import of
methodology from the theory of programming languages into proof theory. This
scientific essay, written for the audience of proof theorists as well as the
working mathematician, is not a survey of the field, but rather a personal view
of the author who hopes that it may inspire future and fellow researchers
Robust Tuning Datasets for Statistical Machine Translation
We explore the idea of automatically crafting a tuning dataset for
Statistical Machine Translation (SMT) that makes the hyper-parameters of the
SMT system more robust with respect to some specific deficiencies of the
parameter tuning algorithms. This is an under-explored research direction,
which can allow better parameter tuning. In this paper, we achieve this goal by
selecting a subset of the available sentence pairs, which are more suitable for
specific combinations of optimizers, objective functions, and evaluation
measures. We demonstrate the potential of the idea with the pairwise ranking
optimization (PRO) optimizer, which is known to yield too short translations.
We show that the learning problem can be alleviated by tuning on a subset of
the development set, selected based on sentence length. In particular, using
the longest 50% of the tuning sentences, we achieve two-fold tuning speedup,
and improvements in BLEU score that rival those of alternatives, which fix
BLEU+1's smoothing instead.Comment: RANLP-201
Classical logic, continuation semantics and abstract machines
One of the goals of this paper is to demonstrate that denotational semantics is useful for operational issues like implementation of functional languages by abstract machines. This is exemplified in a tutorial way by studying the case of extensional untyped call-by-name λ-calculus with Felleisen's control operator 𝒞. We derive the transition rules for an abstract machine from a continuation semantics which appears as a generalization of the ¬¬-translation known from logic. The resulting abstract machine appears as an extension of Krivine's machine implementing head reduction. Though the result, namely Krivine's machine, is well known our method of deriving it from continuation semantics is new and applicable to other languages (as e.g. call-by-value variants). Further new results are that Scott's D∞-models are all instances of continuation models. Moreover, we extend our continuation semantics to Parigot's λμ-calculus from which we derive an extension of Krivine's machine for λμ-calculus. The relation between continuation semantics and the abstract machines is made precise by proving computational adequacy results employing an elegant method introduced by Pitts
D-Bees: A Novel Method Inspired by Bee Colony Optimization for Solving Word Sense Disambiguation
Word sense disambiguation (WSD) is a problem in the field of computational
linguistics given as finding the intended sense of a word (or a set of words)
when it is activated within a certain context. WSD was recently addressed as a
combinatorial optimization problem in which the goal is to find a sequence of
senses that maximize the semantic relatedness among the target words. In this
article, a novel algorithm for solving the WSD problem called D-Bees is
proposed which is inspired by bee colony optimization (BCO)where artificial bee
agents collaborate to solve the problem. The D-Bees algorithm is evaluated on a
standard dataset (SemEval 2007 coarse-grained English all-words task corpus)and
is compared to simulated annealing, genetic algorithms, and two ant colony
optimization techniques (ACO). It will be observed that the BCO and ACO
approaches are on par
An Analysis of Source-Side Grammatical Errors in NMT
The quality of Neural Machine Translation (NMT) has been shown to
significantly degrade when confronted with source-side noise. We present the
first large-scale study of state-of-the-art English-to-German NMT on real
grammatical noise, by evaluating on several Grammar Correction corpora. We
present methods for evaluating NMT robustness without true references, and we
use them for extensive analysis of the effects that different grammatical
errors have on the NMT output. We also introduce a technique for visualizing
the divergence distribution caused by a source-side error, which allows for
additional insights.Comment: Accepted and to be presented at BlackboxNLP 201
A Formalization of Polytime Functions
We present a deep embedding of Bellantoni and Cook's syntactic
characterization of polytime functions. We prove formally that it is correct
and complete with respect to the original characterization by Cobham that
required a bound to be proved manually. Compared to the paper proof by
Bellantoni and Cook, we have been careful in making our proof fully contructive
so that we obtain more precise bounding polynomials and more efficient
translations between the two characterizations. Another difference is that we
consider functions on bitstrings instead of functions on positive integers.
This latter change is motivated by the application of our formalization in the
context of formal security proofs in cryptography. Based on our core
formalization, we have started developing a library of polytime functions that
can be reused to build more complex ones.Comment: 13 page
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