37,760 research outputs found
Existential witness extraction in classical realizability and via a negative translation
We show how to extract existential witnesses from classical proofs using
Krivine's classical realizability---where classical proofs are interpreted as
lambda-terms with the call/cc control operator. We first recall the basic
framework of classical realizability (in classical second-order arithmetic) and
show how to extend it with primitive numerals for faster computations. Then we
show how to perform witness extraction in this framework, by discussing several
techniques depending on the shape of the existential formula. In particular, we
show that in the Sigma01-case, Krivine's witness extraction method reduces to
Friedman's through a well-suited negative translation to intuitionistic
second-order arithmetic. Finally we discuss the advantages of using call/cc
rather than a negative translation, especially from the point of view of an
implementation.Comment: 52 pages. Accepted in Logical Methods for Computer Science (LMCS),
201
Quantified CTL: Expressiveness and Complexity
While it was defined long ago, the extension of CTL with quantification over
atomic propositions has never been studied extensively. Considering two
different semantics (depending whether propositional quantification refers to
the Kripke structure or to its unwinding tree), we study its expressiveness
(showing in particular that QCTL coincides with Monadic Second-Order Logic for
both semantics) and characterise the complexity of its model-checking and
satisfiability problems, depending on the number of nested propositional
quantifiers (showing that the structure semantics populates the polynomial
hierarchy while the tree semantics populates the exponential hierarchy)
Semantic Tagging with Deep Residual Networks
We propose a novel semantic tagging task, sem-tagging, tailored for the
purpose of multilingual semantic parsing, and present the first tagger using
deep residual networks (ResNets). Our tagger uses both word and character
representations and includes a novel residual bypass architecture. We evaluate
the tagset both intrinsically on the new task of semantic tagging, as well as
on Part-of-Speech (POS) tagging. Our system, consisting of a ResNet and an
auxiliary loss function predicting our semantic tags, significantly outperforms
prior results on English Universal Dependencies POS tagging (95.71% accuracy on
UD v1.2 and 95.67% accuracy on UD v1.3).Comment: COLING 2016, camera ready versio
Do Neural Nets Learn Statistical Laws behind Natural Language?
The performance of deep learning in natural language processing has been
spectacular, but the reasons for this success remain unclear because of the
inherent complexity of deep learning. This paper provides empirical evidence of
its effectiveness and of a limitation of neural networks for language
engineering. Precisely, we demonstrate that a neural language model based on
long short-term memory (LSTM) effectively reproduces Zipf's law and Heaps' law,
two representative statistical properties underlying natural language. We
discuss the quality of reproducibility and the emergence of Zipf's law and
Heaps' law as training progresses. We also point out that the neural language
model has a limitation in reproducing long-range correlation, another
statistical property of natural language. This understanding could provide a
direction for improving the architectures of neural networks.Comment: 21 pages, 11 figure
Towards an embedding of Graph Transformation in Intuitionistic Linear Logic
Linear logics have been shown to be able to embed both rewriting-based
approaches and process calculi in a single, declarative framework. In this
paper we are exploring the embedding of double-pushout graph transformations
into quantified linear logic, leading to a Curry-Howard style isomorphism
between graphs and transformations on one hand, formulas and proof terms on the
other. With linear implication representing rules and reachability of graphs,
and the tensor modelling parallel composition of graphs and transformations, we
obtain a language able to encode graph transformation systems and their
computations as well as reason about their properties
- …