Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
1,065
result(s) for
"Conditionals (Logic)"
Sort by:
A Philosophical Guide to Conditionals
Conditionals are of two basic kinds, often called ‘indicative’ and ‘subjunctive’. This book expounds and evaluates the main literature about each kind. It eventually defends the view of Adams and Edgington that indicatives are devices for expressing subjective probabilities, and the view of Stalnaker and Lewis that subjunctives are statements about close possible worlds. But it also discusses other views, e.g. that indicatives are really material conditionals, and Goodman's approach to subjunctives.
eBook
Uniform Consistency for Functional Conditional IU/I-Statistics Using Delta-Sequences
U-statistics are a fundamental class of statistics derived from modeling quantities of interest characterized by responses from multiple subjects. U-statistics make generalizations the empirical mean of a random variable X to the sum of all k-tuples of X observations. This paper examines a setting for nonparametric statistical curve estimation based on an infinite-dimensional covariate, including Stute’s estimator as a special case. In this functional context, the class of “delta sequence estimators” is defined and discussed. The orthogonal series method and the histogram method are both included in this class. We achieve almost complete uniform convergence with the rates of these estimators under certain broad conditions. Moreover, in the same context, we show the uniform almost-complete convergence for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship, which is of its own interest. Among the potential applications are discrimination problems, metric learning and the time series prediction from the continuous set of past values.
Journal Article
CONDITIONAL REASONING AND THE SHADOWS IT CASTS ONTO THE FIRST-ORDER LOGIC: THE NELSONIAN CASE
We define a natural notion of standard translation for the formulas of conditional logic which is analogous to the standard translation of modal formulas into the first-order logic. We briefly show that this translation works (modulo a lightweight first-order encoding of the conditional models) for the minimal classical conditional logic$\\mathsf {CK}$introduced by Brian Chellas in [3]; however, the main result of the article is that a classically equivalent reformulation of these notions (i.e., of standard translation plus theory of conditional models) also faithfully embeds the basic Nelsonian conditional logic$\\mathsf {N4CK}$, introduced in [11] into$\\mathsf {QN4}$, the paraconsistent variant of Nelson’s first-order logic of strong negation. Thus$\\mathsf {N4CK}$is the logic induced by the Nelsonian reading of the classical Chellas semantics of conditionals and can, therefore, be considered a faithful analogue of$\\mathsf {CK}$on the non-classical basis provided by the propositional fragment of$\\mathsf {QN4}$. Moreover, the methods used to prove our main result can be easily adapted to the case of modal logic, which makes it possible to improve an older result [10, Proposition 7] by S. Odintsov and H. Wansing about the standard translation embedding of the Nelsonian modal logic$\\mathsf {FSK}^d$into$\\mathsf {QN4}$.
Journal Article
Possible Worlds Semantics for Indicative and Counterfactual Conditionals?
Conditional structures lie at the heart of the sciences, humanities, and everyday reasoning. This is why conditional logics – logics specifically designed to account for natural language conditionals – are an active, interdisciplinary area. Discussing a wide range of topics, this book gives a formal and a philosophical account of indicative and counterfactual conditionals in terms of Chellas-Segerberg semantics.
eBook
A Martingale-Free Introduction to Conditional Gaussian Nonlinear Systems
The conditional Gaussian nonlinear system (CGNS) is a broad class of nonlinear stochastic dynamical systems. Given the trajectories for a subset of state variables, the remaining follow a Gaussian distribution. Despite the conditionally linear structure, the CGNS exhibits strong nonlinearity, thus capturing many non-Gaussian characteristics observed in nature through its joint and marginal distributions. Desirably, it enjoys closed analytic formulae for the time evolution of its conditional Gaussian statistics, which facilitate the study of data assimilation and other related topics. In this paper, we develop a martingale-free approach to improve the understanding of CGNSs. This methodology provides a tractable approach to proving the time evolution of the conditional statistics by deriving results through time discretization schemes, with the continuous-time regime obtained via a formal limiting process as the discretization time-step vanishes. This discretized approach further allows for developing analytic formulae for optimal posterior sampling of unobserved state variables with correlated noise. These tools are particularly valuable for studying extreme events and intermittency and apply to high-dimensional systems. Moreover, the approach improves the understanding of different sampling methods in characterizing uncertainty. The effectiveness of the framework is demonstrated through a physics-constrained, triad-interaction climate model with cubic nonlinearity and state-dependent cross-interacting noise.
Journal Article
An Intuitionistically Complete System of Basic Intuitionistic Conditional Logic
We introduce a basic intuitionistic conditional logic
IntCK
that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that
IntCK
stands in a very natural relation to other similar logics, like the basic classical conditional logic
CK
and the basic intuitionistic modal logic
IK
. As for the basic intuitionistic conditional logic
ICK
proposed in Weiss (
Journal of Philosophical Logic
,
48
, 447–469,
2019
),
IntCK
extends its language with a diamond-like conditional modality
◊
→
, but its (
◊
→
)-free fragment is also a proper extension of
ICK
. We briefly discuss the resulting gap between the two candidate systems of basic intuitionistic conditional logic and the possible pros and cons of both candidates.
Journal Article
Conditional Quantization for Some Discrete Distributions
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the finite support are preselected, then the quantization is called a conditional quantization. In this paper, we have determined the conditional quantization, first for two different finite discrete distributions with a same conditional set, and for a finite discrete distribution with two different conditional sets. Next, we have determined the conditional and unconditional quantization for an infinite discrete distribution with support 12n:n∈N. We have also investigated the conditional quantization for an infinite discrete distribution with support 1n:n∈N. At the end of the paper, we have given a conjecture and discussed about some open problems based on the conjecture.
Journal Article