Related papers: KF, PKF, and Reinhardt's Program
The work presents the brief exposition of the proof (in ZF) of inaccessible cardinals nonexistence. To this end in view there is used the apparatus of subinaccessible cardinals and its basic tools -- reduced formula spectra and matrices and…
We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$-positivity for maps between matrix algebras. Starting from a compact family of $\alpha$-admissible unit…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
Questions concerning the proof-theoretic strength of classical versus non-classical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of…
Inspired by some new advances on normal factor graphs (NFGs), we introduce NFGs as a simple and intuitive diagrammatic approach towards encoding some concepts from linear algebra. We illustrate with examples the workings of such an approach…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
The paper proposes and studies new classical, type-free theories of truth and determinateness with unprecedented features. The theories are fully compositional, strongly classical (namely, their internal and external logics are both…
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…
We provide a wide-ranging study of the scenario where a subset of the relations in a relational vocabulary are visible to a user --- that is, their complete contents are known --- while the remaining relations are invisible. We also have a…
A new $\theta$ function primitive is proposed that almost achieves the combined efficiency of the addition, multiplication and successor growth operations. This $\theta$ function symbol enables the constructing of an "IQFS(PA+)" axiom…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…
Let HN denote the problem of determining whether a system of multivariate polynomials with integer coefficients has a complex root. It has long been known that HN in P implies P=NP and, thanks to recent work of Koiran, it is now known that…
Relational verification encompasses research directions such as reasoning about data abstraction, reasoning about security and privacy, secure compilation, and functional specificaton of tensor programs, among others. Several relational…
Kalman Filters are one of the most influential models of time-varying phenomena. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption in a variety of disciplines. Motivated by…
We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the and Clifford algebras. This last algebra gives proof of the von Neumann basic…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. Several classical probabilistic inference tasks (such as MAP and computing marginals) have not yet received a lot of attention for…
In this article we reconstruct the Frauchiger and Renner argument, taking into account that the assertions of the argument are made at different times. To do this, we use a formalism of quantum histories, namely the Theory of Consistent…
In 1991 H\'ebrard introduced a factorization of words that turned out to be a powerful tool for the investigation of a word's scattered factors (also known as (scattered) subwords or subsequences). Based on this, first Karandikar and…
We introduce a framework for representing a variety of interesting problems as inference over the execution of probabilistic model programs. We represent a "solution" to such a problem as a guide program which runs alongside the model…