相关论文: Hilbert's epsilon as an Operator of Indefinite Com…
A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…
Let $\mathbb{P}$ be the complete metric space consisting of positive invertible operators on an infinite-dimensional Hilbert space with the Thompson metric. We introduce the notion of operator means of probability measures on $\mathbb{P}$,…
This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to…
Computational research on error detection in second language speakers has mainly addressed clear grammatical anomalies typical to learners at the beginner-to-intermediate level. We focus instead on acquisition of subtle semantic nuances of…
Parameter--elliptic pseudodifferential operators given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev…
Aristotle considered particular quantified sentences in his study of syllogisms and in his famous square of opposition. Of course, the logical formulas in Aristotle work were not modern formulas of mathematical logic, but ordinary sentences…
Recent research in extensions of Answer Set Programming has included a renewed interest in the language of Epistemic Specifications, which adds modal operators K ("known") and M ("may be true") to provide for more powerful introspective…
Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…
The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the…
We introduce an approach to high-level conditional planning we call epsilon-safe planning. This probabilistic approach commits us to planning to meet some specified goal with a probability of success of at least 1-epsilon for some…
We study infinite weighted graphs with view to \textquotedblleft limits at infinity,\textquotedblright or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means \textquotedblleft…
In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ($\mathcal{L}_{\lvert\cdot\rvert}$) to a decision procedure for $\mathcal{L}_{\lvert\cdot\rvert}$ extended with set terms…
We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable…
We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…
Lifted probabilistic inference algorithms exploit regularities in the structure of graphical models to perform inference more efficiently. More specifically, they identify groups of interchangeable variables and perform inference once per…
We study two classes of extension problems, and their interconnections: (i) Extension of positive definite (p.d.) continuous functions defined on subsets in locally compact groups $G$; (ii) In case of Lie groups, representations of the…
Stop words, which are considered non-predictive, are often eliminated in natural language processing tasks. However, the definition of uninformative vocabulary is vague, so most algorithms use general knowledge-based stop lists to remove…
We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…
Unbounded (and bounded) Toeplitz operators (TO) with rational symbols are analysed in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains,…
In this paper, we show several bounds for the numerical radius of a Hilbert space operator in terms of the Euclidean operator norm. The obtained forms will enable us to find interesting refinements of celebrated results in the literature.…