11,831 research outputs found
Closed nominal rewriting and efficiently computable nominal algebra equality
We analyse the relationship between nominal algebra and nominal rewriting,
giving a new and concise presentation of equational deduction in nominal
theories. With some new results, we characterise a subclass of equational
theories for which nominal rewriting provides a complete procedure to check
nominal algebra equality. This subclass includes specifications of the
lambda-calculus and first-order logic.Comment: In Proceedings LFMTP 2010, arXiv:1009.218
From nominal to higher-order rewriting and back again
We present a translation function from nominal rewriting systems (NRSs) to
combinatory reduction systems (CRSs), transforming closed nominal rules and
ground nominal terms to CRSs rules and terms, respectively, while preserving
the rewriting relation. We also provide a reduction-preserving translation in
the other direction, from CRSs to NRSs, improving over a previously defined
translation. These tools, together with existing translations between CRSs and
other higher-order rewriting formalisms, open up the path for a transfer of
results between higher-order and nominal rewriting. In particular, techniques
and properties of the rewriting relation, such as termination, can be exported
from one formalism to the other.Comment: 41 pages, journa
Higher-order port-graph rewriting
The biologically inspired framework of port-graphs has been successfully used
to specify complex systems. It is the basis of the PORGY modelling tool. To
facilitate the specification of proof normalisation procedures via graph
rewriting, in this paper we add higher-order features to the original
port-graph syntax, along with a generalised notion of graph morphism. We
provide a matching algorithm which enables to implement higher-order port-graph
rewriting in PORGY, thus one can visually study the dynamics of the systems
modelled. We illustrate the expressive power of higher-order port-graphs with
examples taken from proof-net reduction systems.Comment: In Proceedings LINEARITY 2012, arXiv:1211.348
Nominal Unification from a Higher-Order Perspective
Nominal Logic is a version of first-order logic with equality, name-binding,
renaming via name-swapping and freshness of names. Contrarily to higher-order
logic, bindable names, called atoms, and instantiable variables are considered
as distinct entities. Moreover, atoms are capturable by instantiations,
breaking a fundamental principle of lambda-calculus. Despite these differences,
nominal unification can be seen from a higher-order perspective. From this
view, we show that nominal unification can be reduced to a particular fragment
of higher-order unification problems: Higher-Order Pattern Unification. This
reduction proves that nominal unification can be decided in quadratic
deterministic time, using the linear algorithm for Higher-Order Pattern
Unification. We also prove that the translation preserves most generality of
unifiers
Resource-Bound Quantification for Graph Transformation
Graph transformation has been used to model concurrent systems in software
engineering, as well as in biochemistry and life sciences. The application of a
transformation rule can be characterised algebraically as construction of a
double-pushout (DPO) diagram in the category of graphs. We show how
intuitionistic linear logic can be extended with resource-bound quantification,
allowing for an implicit handling of the DPO conditions, and how resource logic
can be used to reason about graph transformation systems
A Type-coherent, Expressive Representation as an Initial Step to Language Understanding
A growing interest in tasks involving language understanding by the NLP
community has led to the need for effective semantic parsing and inference.
Modern NLP systems use semantic representations that do not quite fulfill the
nuanced needs for language understanding: adequately modeling language
semantics, enabling general inferences, and being accurately recoverable. This
document describes underspecified logical forms (ULF) for Episodic Logic (EL),
which is an initial form for a semantic representation that balances these
needs. ULFs fully resolve the semantic type structure while leaving issues such
as quantifier scope, word sense, and anaphora unresolved; they provide a
starting point for further resolution into EL, and enable certain structural
inferences without further resolution. This document also presents preliminary
results of creating a hand-annotated corpus of ULFs for the purpose of training
a precise ULF parser, showing a three-person pairwise interannotator agreement
of 0.88 on confident annotations. We hypothesize that a divide-and-conquer
approach to semantic parsing starting with derivation of ULFs will lead to
semantic analyses that do justice to subtle aspects of linguistic meaning, and
will enable construction of more accurate semantic parsers.Comment: Accepted for publication at The 13th International Conference on
Computational Semantics (IWCS 2019
Derivation of linearized transfer functions for switching-mode regulations. Phase A: Current step-up and voltage step-up converters
Small-signal models are derived for the power stage of the voltage step-up (boost) and the current step-up (buck) converters. The modeling covers operation in both the continuous-mmf mode and the discontinuous-mmf mode. The power stage in the regulated current step-up converter on board the Dynamics Explorer Satellite is used as an example to illustrate the procedures in obtaining the small-signal functions characterizing a regulated converter
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