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

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

The language of Stratified Sets is confluent and strongly normalising

We study the properties of the language of Stratified Sets (first-order logic with $\in$ and a stratification condition) as used in TST, TZT, and (with stratifiability instead of stratification) in Quine's NF. We find that the syntax forms a nominal algebra for substitution and that stratification and stratifiability imply confluence and strong normalisation under rewrites corresponding naturally to $\beta$-conversion.Comment: arXiv admin note: text overlap with arXiv:1406.406

A Theory of Explicit Substitutions with Safe and Full Composition

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the first part of this paper. Then, very simple technology in named variable-style notation is used to establish a theory of explicit substitutions for the lambda-calculus which enjoys a whole set of useful properties such as full composition, simulation of one-step beta-reduction, preservation of beta-strong normalisation, strong normalisation of typed terms and confluence on metaterms. Normalisation of related calculi is also discussed.Comment: 29 pages Special Issue: Selected Papers of the Conference "International Colloquium on Automata, Languages and Programming 2008" edited by Giuseppe Castagna and Igor Walukiewic

Fighting Authorship Linkability with Crowdsourcing

Massive amounts of contributed content -- including traditional literature, blogs, music, videos, reviews and tweets -- are available on the Internet today, with authors numbering in many millions. Textual information, such as product or service reviews, is an important and increasingly popular type of content that is being used as a foundation of many trendy community-based reviewing sites, such as TripAdvisor and Yelp. Some recent results have shown that, due partly to their specialized/topical nature, sets of reviews authored by the same person are readily linkable based on simple stylometric features. In practice, this means that individuals who author more than a few reviews under different accounts (whether within one site or across multiple sites) can be linked, which represents a significant loss of privacy. In this paper, we start by showing that the problem is actually worse than previously believed. We then explore ways to mitigate authorship linkability in community-based reviewing. We first attempt to harness the global power of crowdsourcing by engaging random strangers into the process of re-writing reviews. As our empirical results (obtained from Amazon Mechanical Turk) clearly demonstrate, crowdsourcing yields impressively sensible reviews that reflect sufficiently different stylometric characteristics such that prior stylometric linkability techniques become largely ineffective. We also consider using machine translation to automatically re-write reviews. Contrary to what was previously believed, our results show that translation decreases authorship linkability as the number of intermediate languages grows. Finally, we explore the combination of crowdsourcing and machine translation and report on the results

From nominal sets binding to functions and lambda-abstraction: connecting the logic of permutation models with the logic of functions

Permissive-Nominal Logic (PNL) extends first-order predicate logic with term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets. In PNL, the forall-quantifier or lambda-binder are just term-formers satisfying axioms, and their denotation is functions on nominal atoms-abstraction. Then we have higher-order logic (HOL) and its models in ordinary (i.e. Zermelo-Fraenkel) sets; the denotation of forall or lambda is functions on full or partial function spaces. This raises the following question: how are these two models of binding connected? What translation is possible between PNL and HOL, and between nominal sets and functions? We exhibit a translation of PNL into HOL, and from models of PNL to certain models of HOL. It is natural, but also partial: we translate a restricted subsystem of full PNL to HOL. The extra part which does not translate is the symmetry properties of nominal sets with respect to permutations. To use a little nominal jargon: we can translate names and binding, but not their nominal equivariance properties. This seems reasonable since HOL---and ordinary sets---are not equivariant. Thus viewed through this translation, PNL and HOL and their models do different things, but they enjoy non-trivial and rich subsystems which are isomorphic

Introducing a Calculus of Effects and Handlers for Natural Language Semantics

In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the same pattern: they are instances of a monad. In this paper, we present an extension of the simply-typed lambda calculus that exploits this uniformity using the recently discovered technique of effect handlers. We prove that our calculus exhibits some of the key formal properties of the lambda calculus and we use it to construct a modular semantics for a small fragment that involves multiple distinct semantic phenomena

Data-driven online temperature compensation for robust field-oriented torque-controlled induction machines

Squirrel-cage induction machines (IMs) with indirect field-oriented control are widely used in industry and are frequently chosen for their accurate and dynamic torque control. During operation, however, temperature rises leading to changes in machine parameters. The rotor resistance, in particular, alters, affecting the accuracy of the torque control. The authors investigated the effect of a rotor resistance parameter mismatch in the control algorithm on the angular rotor flux misalignment and the subsequent deviation of stator currents and motor torque from their setpoints. Hence, an online, data-driven torque compensation to eliminate the temperature effect is proposed to enable robust torque-controlled IMs. A model-based analysis and experimental mapping of the temperature effect on motor torque is presented. A temperature-torque lookup-table is subsequently implemented within the control algorithm demonstrating the ability to reduce the detrimental effect of temperature on torque control. Experimental results on a 5.5 kW squirrel-cage induction motor show that the proposed data-driven online temperature compensation method is able to reduce torque mismatch when compared to having no temperature compensation. Up to 17% torque mismatch is reduced at nominal torque and even up to 23% at torque setpoints that are lower than 20% of the nominal torque. A limited torque error of <1% remains in a broad operating range