23,809 research outputs found
Modalities, Cohesion, and Information Flow
It is informally understood that the purpose of modal type constructors in
programming calculi is to control the flow of information between types. In
order to lend rigorous support to this idea, we study the category of
classified sets, a variant of a denotational semantics for information flow
proposed by Abadi et al. We use classified sets to prove multiple
noninterference theorems for modalities of a monadic and comonadic flavour. The
common machinery behind our theorems stems from the the fact that classified
sets are a (weak) model of Lawvere's theory of axiomatic cohesion. In the
process, we show how cohesion can be used for reasoning about multi-modal
settings. This leads to the conclusion that cohesion is a particularly useful
setting for the study of both information flow, but also modalities in type
theory and programming languages at large
A Labelled Analytic Theorem Proving Environment for Categorial Grammar
We present a system for the investigation of computational properties of
categorial grammar parsing based on a labelled analytic tableaux theorem
prover. This proof method allows us to take a modular approach, in which the
basic grammar can be kept constant, while a range of categorial calculi can be
captured by assigning different properties to the labelling algebra. The
theorem proving strategy is particularly well suited to the treatment of
categorial grammar, because it allows us to distribute the computational cost
between the algorithm which deals with the grammatical types and the algebraic
checker which constrains the derivation.Comment: 11 pages, LaTeX2e, uses examples.sty and a4wide.st
Indexing the Event Calculus with Kd-trees to Monitor Diabetes
Personal Health Systems (PHS) are mobile solutions tailored to monitoring
patients affected by chronic non communicable diseases. A patient affected by a
chronic disease can generate large amounts of events. Type 1 Diabetic patients
generate several glucose events per day, ranging from at least 6 events per day
(under normal monitoring) to 288 per day when wearing a continuous glucose
monitor (CGM) that samples the blood every 5 minutes for several days. This is
a large number of events to monitor for medical doctors, in particular when
considering that they may have to take decisions concerning adjusting the
treatment, which may impact the life of the patients for a long time. Given the
need to analyse such a large stream of data, doctors need a simple approach
towards physiological time series that allows them to promptly transfer their
knowledge into queries to identify interesting patterns in the data. Achieving
this with current technology is not an easy task, as on one hand it cannot be
expected that medical doctors have the technical knowledge to query databases
and on the other hand these time series include thousands of events, which
requires to re-think the way data is indexed. In order to tackle the knowledge
representation and efficiency problem, this contribution presents the kd-tree
cached event calculus (\ceckd) an event calculus extension for knowledge
engineering of temporal rules capable to handle many thousands events produced
by a diabetic patient. \ceckd\ is built as a support to a graphical interface
to represent monitoring rules for diabetes type 1. In addition, the paper
evaluates the \ceckd\ with respect to the cached event calculus (CEC) to show
how indexing events using kd-trees improves scalability with respect to the
current state of the art.Comment: 24 pages, preliminary results calculated on an implementation of
CECKD, precursor to Journal paper being submitted in 2017, with further
indexing and results possibilities, put here for reference and chronological
purposes to remember how the idea evolve
Nominal Abstraction
Recursive relational specifications are commonly used to describe the
computational structure of formal systems. Recent research in proof theory has
identified two features that facilitate direct, logic-based reasoning about
such descriptions: the interpretation of atomic judgments through recursive
definitions and an encoding of binding constructs via generic judgments.
However, logics encompassing these two features do not currently allow for the
definition of relations that embody dynamic aspects related to binding, a
capability needed in many reasoning tasks. We propose a new relation between
terms called nominal abstraction as a means for overcoming this deficiency. We
incorporate nominal abstraction into a rich logic also including definitions,
generic quantification, induction, and co-induction that we then prove to be
consistent. We present examples to show that this logic can provide elegant
treatments of binding contexts that appear in many proofs, such as those
establishing properties of typing calculi and of arbitrarily cascading
substitutions that play a role in reducibility arguments.Comment: To appear in the Journal of Information and Computatio
Multi-level Contextual Type Theory
Contextual type theory distinguishes between bound variables and
meta-variables to write potentially incomplete terms in the presence of
binders. It has found good use as a framework for concise explanations of
higher-order unification, characterize holes in proofs, and in developing a
foundation for programming with higher-order abstract syntax, as embodied by
the programming and reasoning environment Beluga. However, to reason about
these applications, we need to introduce meta^2-variables to characterize the
dependency on meta-variables and bound variables. In other words, we must go
beyond a two-level system granting only bound variables and meta-variables.
In this paper we generalize contextual type theory to n levels for arbitrary
n, so as to obtain a formal system offering bound variables, meta-variables and
so on all the way to meta^n-variables. We obtain a uniform account by
collapsing all these different kinds of variables into a single notion of
variabe indexed by some level k. We give a decidable bi-directional type system
which characterizes beta-eta-normal forms together with a generalized
substitution operation.Comment: In Proceedings LFMTP 2011, arXiv:1110.668
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