Semirings of Evidence

2021 ◽  
Author(s):  
Michael Baur ◽  
Thomas Studer
Keyword(s):  
Fixed Point ◽  
Algebraic Structure ◽  
Polynomial Functions ◽  
Justification Logic ◽  
Semantic Approach ◽  
Syntactic Form

Abstract In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models evidence by a semiring. Hence justification terms can be interpreted as polynomial functions on that semiring. This provides an adequate semantics for evidence terms and clarifies the role of variables in justification logic. Moreover, the algebraic structure makes it possible to compute with evidence. Depending on the chosen semiring this can be used to model trust, probabilities, cost, etc. Last but not least the semiring approach seems promising for obtaining a realization procedure for modal fixed point logics.

scholarly journals Stochastic Flips on Dimer Tilings

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Thomas Fernique ◽  
Damien Regnault
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Upper Bound ◽  
Numerical Experiments ◽  
Triangular Grid ◽  
Expected Number ◽  
Worst Case ◽  
Average Case ◽  
International Audience

International audience This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

scholarly journals Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 59
Author(s):  
Ahmed Salem ◽  
Mohammad Alnegga
Keyword(s):  
Fixed Point ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of A Solution ◽  
New Class ◽  
Research Article ◽  
Analysis Technique ◽  
Modern Analysis

In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo’s fixed point theorem. A numerical example is presented to clarify our outcomes.

Later Wittgenstein's Anti-Philosophical Therapy

Philosophy ◽  
2014 ◽  
Vol 89 (2) ◽  
pp. 251-272 ◽  
Author(s):  
Dale Jacquette
Keyword(s):  
Conceptual Framework ◽  
Language Game ◽  
Semantic Approach ◽  
Philosophical Investigations ◽  
Philosophical Grammar

AbstractThe object of this essay is to discuss Ludwig Wittgenstein's remarks inPhilosophical Investigationsand elsewhere in the posthumously published writings concerning the role of therapy in relation to philosophy. Wittgenstein's reflections seem to suggest that there is a kind of philosophy or mode of investigation targeting the philosophical grammar of language uses that gratuitously give rise to philosophical problems, and produce in many thinkers philosophical anxieties for which the proper therapy is intended to offer relief. Two possible objectives of later Wittgensteinian therapy are proposed, for subjectivepsychologicalversus objectivesemanticsymptoms of ailments that a therapy might address for the sake of relieving philosophical anxieties. The psychological in its most plausible form is rejected, leaving only the semantic. Semantic therapy in the sense defined and developed is more general and long-lasting, and more in the spirit of Wittgenstein's project on a variety of levels. A semantic approach treats language rather than the thinking, language-using subject as the patient needing therapy, and directs its attention to the treatment of problems in language and the conceptual framework a language game use expresses in its philosophical grammar, rather than to soothing unhappy or socially ill-adjusted individual psychologies.

scholarly journals Properties of RG interfaces for 2D boundary flows

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Anatoly Konechny
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Variational Method ◽  
Boundary Conditions ◽  
The Other ◽  
Two Dimensional ◽  
Conformal Boundary ◽  
First Approximation ◽  
Local Operators

Abstract We consider RG interfaces for boundary RG flows in two-dimensional QFTs. Such interfaces are particular boundary condition changing operators linking the UV and IR conformal boundary conditions. We refer to them as RG operators. In this paper we study their general properties putting forward a number of conjectures. We conjecture that an RG operator is always a conformal primary such that the OPE of this operator with its conjugate must contain the perturbing UV operator when taken in one order and the leading irrelevant operator (when it exists) along which the flow enters the IR fixed point, when taken in the other order. We support our conjectures by perturbative calculations for flows between nearby fixed points, by a non-perturbative variational method inspired by the variational method proposed by J. Cardy for massive RG flows, and by numerical results obtained using boundary TCSA. The variational method has a merit of its own as it can be used as a first approximation in charting the global structure of the space of boundary RG flows. We also discuss the role of the RG operators in the transport of states and local operators. Some of our considerations can be generalised to two-dimensional bulk flows, clarifying some conceptual issues related to the RG interface put forward by D. Gaiotto for bulk 𝜙1,3 flows.

A HOLISTIC SEMANTIC FRAMEWORK FOR THE PROVISION OF SERVICES IN THE DOMAIN OF eGOVERNMENT

2009 ◽  
Vol 19 (07) ◽  
pp. 961-993 ◽  
Author(s):  
LUIS ÁLVAREZ SABUCEDO ◽  
LUIS ANIDO RIFÓN ◽  
RUBÉN MÍGUEZ PÉREZ ◽  
JUAN SANTOS GAGO
Keyword(s):  
Software Architecture ◽  
High Speed ◽  
Research Institutions ◽  
Software Platform ◽  
Semantic Approach ◽  
Semantic Framework ◽  
Provision Of Services ◽  
Domain Semantics ◽  
Accessibility Issues

Providing support for eGovernment services is currently a high-speed race for public administrations and research institutions. In this process towards a fully transactional platform, several projects have made their contribution. Regretfully, current solutions unveils some drawbacks regarding interoperability and accessibility issues. In this context, this paper proposes a semantic approach to fulfill holistic services in the domain. Semantics is called to play a role of first importance as a tool for interoperability. LifeEvents and AdministrativeServices are artifacts defined within this technology. Using these, an entire software architecture is derived and, eventually implemented by means of a software platform also described in this paper. Finally, some conclusions are presented.

scholarly journals Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Aníbal Areia ◽  
Francisco Carvalho ◽  
João T. Mexia
Keyword(s):  
Jordan Algebra ◽  
Algebraic Structure ◽  
Minimum Variance ◽  
Jordan Algebras ◽  
Symmetric Matrices ◽  
Sufficient Statistics ◽  
Unbiased Estimators

AbstractWe will discuss orthogonal models and error orthogonal models and their algebraic structure, using as background, commutative Jordan algebras. The role of perfect families of symmetric matrices will be emphasized, since they will play an important part in the construction of the estimators for the relevant parameters. Perfect families of symmetric matrices form a basis for the commutative Jordan algebra they generate. When normality is assumed, these perfect families of symmetric matrices will ensure that the models have complete and sufficient statistics. This will lead to uniformly minimum variance unbiased estimators for the relevant parameters.

Variants of Determinacy in Parallel Program Schemata

1987 ◽  
Vol 10 (3) ◽  
pp. 225-246
Author(s):  
Udo Kelter
Keyword(s):  
Equivalence Relation ◽  
Response Times ◽  
Parallel Systems ◽  
Parallel Program ◽  
Formal Models ◽  
Syntactic Form ◽  
Speed Up ◽  
Universal Definition ◽  
Definition Of

Systems which use parallel processing to speed up response times are normally required to be determinate. Parallel program schemata are formal models of parallel systems which serve to exactly define determinacy. Three variants of determinacy have frequently been used in the literature: Two “semantic” ones, which refer to the final contents of variables and to the sequences of contents, and a “syntactic” one, which is based upon the notion of conflict. Variants of determinacy can be derived with a universal definition of determinacy (as presented in [K73]) which uses a parameter, namely an equivalence relation on computations. Each of the above variants corresponds to a certain equivalence relation. The main aim of this paper is to investigate the role of “read-only”-operations, e.g. pure tests. Results of tests do not matter for both semantic forms of determinacy, whereas they are relevant for the syntactic form. We will snow that different variants of semantic and syntactic determinacy can be obtained by judging read-only operations as relevant or not.

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