1,380 research outputs found
Fragments and frame classes:Towards a uniform proof theory for modal fixed point logics
This thesis studies the proof theory of modal fixed point logics. In particular, we construct proof systems for various fragments of the modal mu-calculus, interpreted over various classes of frames. With an emphasis on uniform constructions and general results, we aim to bring the relatively underdeveloped proof theory of modal fixed point logics closer to the well-established proof theory of basic modal logic. We employ two main approaches. First, we seek to generalise existing methods for basic modal logic to accommodate fragments of the modal mu-calculus. We use this approach for obtaining Hilbert-style proof systems. Secondly, we adapt existing proof systems for the modal mu-calculus to various classes of frames. This approach yields proof systems which are non-well-founded, or cyclic.The thesis starts with an introduction and some mathematical preliminaries. In Chapter 3 we give hypersequent calculi for modal logic with the master modality, building on work by Ori Lahav. This is followed by an Intermezzo, where we present an abstract framework for cyclic proofs, in which we give sufficient conditions for establishing the bounded proof property. In Chapter 4 we generalise existing work on Hilbert-style proof systems for PDL to the level of the continuous modal mu-calculus. Chapter 5 contains a novel cyclic proof system for the alternation-free two-way modal mu-calculus. Finally, in Chapter 6, we present a cyclic proof system for Guarded Kleene Algebra with Tests and take a first step towards using it to establish the completeness of an algebraic counterpart
The Infimum Problem as a Generalization of the Inclusion Problem for Automata
This thesis is concerned with automata over infinite trees. They are given a labeled infinite tree and accept or reject this tree based on its labels. A generalization of these automata with binary decisions are weighted automata. They do not just decide 'yes' or 'no', but rather compute an arbitrary value from a given algebraic structure, e.g., a semiring or a lattice. When passing from unweighted to weighted formalisms, many problems can be translated accordingly. The purpose of this work is to determine the feasibility of solving the inclusion problem for automata on infinite trees and its generalization to weighted automata, the infimum aggregation problem
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Advances and Applications of DSmT for Information Fusion. Collected Works, Volume 5
This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered.
First Part of this book presents some theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes.
Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification.
Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well
Holomorphic functions on complex Banach lattices
We introduce and study the algebraic, analytic and lattice properties of
regular homogeneous polynomials and holomorphic functions on complex Banach
lattices. We show that the theory of power series with regular terms is closer
to the theory of functions of several complex variables than the theory of
holomorphic functions on Banach spaces. We extend the concept of the Bohr
radius to Banach lattices and show that it provides us with a lower bound for
the ratio between the radius of regular convergence and the radius of
convergence of a regular holomorphic function. This allows us to show that the
radius of regular convergence coincides with the radius of convergence for
holomorphic functions on finite dimensional spaces and orthogonally additive
holomorphic functions but that these radii can be radically different on
for
Homomesy via Toggleability Statistics
The rowmotion operator acting on the set of order ideals of a finite poset
has been the focus of a significant amount of recent research. One of the major
goals has been to exhibit homomesies: statistics that have the same average
along every orbit of the action. We systematize a technique for proving that
various statistics of interest are homomesic by writing these statistics as
linear combinations of "toggleability statistics" (originally introduced by
Striker) plus a constant. We show that this technique recaptures most of the
known homomesies for the posets on which rowmotion has been most studied. We
also show that the technique continues to work in modified contexts. For
instance, this technique also yields homomesies for the piecewise-linear and
birational extensions of rowmotion; furthermore, we introduce a -analogue of
rowmotion and show that the technique yields homomesies for "-rowmotion" as
well.Comment: 48 pages, 13 figures, 2 tables; forthcoming, Combinatorial Theor
Valuative lattices and spectra
The first part of the present article consists in a survey about the
dynamical constructive method designed using dynamical theories and dynamical
algebraic structures. Dynamical methods uncovers a hidden computational content
for numerous abstract objects of classical mathematics, which seem a priori
inaccessible constructively, e.g., the algebraic closure of a (discrete) field.
When a proof in classical mathematics uses these abstract objects and results
in a concrete outcome, dynamical methods generally make possible to discover an
algorithm for this concrete outcome. The second part of the article applies
this dynamical method to the theory of divisibility. We compare two notions of
valuative spectra present in the literature and we introduce a third notion,
which is implicit in an article devoted to the dynamical theory of
algebraically closed discrete valued fields. The two first notions are
respectively due to Huber \& Knebusch and to Coquand. We prove that the
corresponding valuative lattices are essentially the same. We establish formal
Valuativestellens\"atze corresponding to these theories, and we compare the
various resulting notions of valuative dimensions.Comment: This file contains also a French version of the paper. English
version appears in the Proceedings of Graz Conference on Rings and
Factorizations 2021. Title: Algebraic, Number Theoretic, and Topological
Aspects of Ring Theory. Editors: Jean-Luc Chabert, Marco Fontana, Sophie
Frisch, Sarah Glaz, Keith Johnson. Springer 2023 ISBN 978-3-031-28846-3 DOI
10.1007/978-3-031-28847-
Erasure in dependently typed programming
It is important to reduce the cost of correctness in programming. Dependent types
and related techniques, such as type-driven programming, offer ways to do so.
Some parts of dependently typed programs constitute evidence of their typecorrectness
and, once checked, are unnecessary for execution. These parts can easily
become asymptotically larger than the remaining runtime-useful computation, which
can cause linear-time algorithms run in exponential time, or worse. It would be
unnacceptable, and contradict our goal of reducing the cost of correctness, to make
programs run slower by only describing them more precisely.
Current systems cannot erase such computation satisfactorily. By modelling
erasure indirectly through type universes or irrelevance, they impose the limitations
of these means to erasure. Some useless computation then cannot be erased and
idiomatic programs remain asymptotically sub-optimal.
This dissertation explains why we need erasure, that it is different from other
concepts like irrelevance, and proposes two ways of erasing non-computational data.
One is an untyped flow-based useless variable elimination, adapted for dependently
typed languages, currently implemented in the Idris 1 compiler.
The other is the main contribution of the dissertation: a dependently typed core
calculus with erasure annotations, full dependent pattern matching, and an algorithm
that infers erasure annotations from unannotated (or partially annotated) programs.
I show that erasure in well-typed programs is sound in that it commutes with
single-step reduction. Assuming the Church-Rosser property of reduction, I show
that properties such as Subject Reduction hold, which extends the soundness result
to multi-step reduction. I also show that the presented erasure inference is sound
and complete with respect to the typing rules; that this approach can be extended
with various forms of erasure polymorphism; that it works well with monadic I/O
and foreign functions; and that it is effective in that it not only removes the runtime
overhead caused by dependent typing in the presented examples, but can also shorten
compilation times."This work was supported by the University of St Andrews (School of Computer
Science)." -- Acknowledgement
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