Related papers: Arbitrarily Close
This article explores the connection between boolean-valued class models of set theory and the theory of arbitrary objects in roughly Kit Fine's sense of the word. In particular, it explores the hypothesis that the set theoretic universe as…
Terms of Church's $\lambda$-calculus can be considered equivalent along many different definitions, but context equivalence is certainly the most direct and universally accepted one. If the underlying calculus becomes probabilistic,…
Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of…
The notion of analyticity is studied in the context of hypercomplex numbers. A critical review of the problems arising from the conventional approach is given. We describe a local analyticity condition which yields the desired type of…
Given a compact basic semi-algebraic set we provide a numerical scheme to approximate as closely as desired, any finite number of moments of the Hausdorff measure on the boundary of this set. This also allows one to approximate interesting…
Surprisal theory links human processing effort to the predictability of an upcoming linguistic unit, but empirical work often leaves the notion of a unit underspecified. In practice, experimental stimuli are segmented into linguistically…
In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of 'relative ability of subsets of approximation…
Classical black holes and event horizons are highly non-local objects, defined in relation to the causal past of future null infinity. Alternative, quasilocal characterizations of black holes are often used in mathematical, quantum, and…
Generalized noncontextuality is a well-studied notion of classicality that is applicable to a single system, as opposed to Bell locality. It relies on representing operationally indistinguishable procedures identically in an ontological…
The intractability of any problem and the randomness of its solutions have an obvious intuitive connection. However, the challenge till now has been that there is no practical way to firmly establish if the solution to a problem is actually…
The semantics of assignment and mutual exclusion in concurrent and multi-core/multi-processor systems is presented with attention to low level architectural features in an attempt to make the presentation realistic. Recursive functions on…
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
The problem of defining a statistical ensemble of random graphs with an arbitrary connectivity distribution is discussed. Introducing such an ensemble is a step towards uderstanding the geometry of wide classes of graphs independently of…
We obtain a criterion for an analytic subset of a Euclidean space to contain points of differentiability of a typical Lipschitz function, namely, that it cannot be covered by countably many sets, each of which is closed and purely…
In this paper, we present the concept of Approximate grammar and how it can be used to extract information from a documemt. As the structure of informational strings cannot be defined well in a document, we cannot use the conventional…
A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds which were proposed in the last decades. Such an operation is indispensable in order to perform…
Limit can be defined by two axioms: 1. Strict inequality between limits implies, ultimately, strict inequality between functions. 2. For constant functions limit is trivial. How can basic results on convergence be derived from these axioms?…
As is well known the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit. We identified one reason for this long ago: insufficient decay of the probability density either near infinity or near poles of…
The concept of an angle is one that often causes difficulties in metrology. These are partly caused by a confusing mixture of several mathematical terms, partly by real mathematical difficulties and finally by imprecise terminology. The…
When conducting inference on partially identified parameters, confidence regions may cover the whole identified set with a prescribed probability, to which we will refer as set coverage, or they may cover each of its point with a prescribed…