相关论文: White Hole, Black Whole, and The Book

Logic $L$ was introduced by Lewitzka [7] as a modal system that combines intuitionistic and classical logic: $L$ is a conservative extension of CPC and it contains a copy of IPC via the embedding $\varphi\mapsto\square\varphi$. In this…

This paper concerns a generalization of the Rees algebra of ideals due to Eisenbud, Huneke and Ulrich that works for any finitely generated module over a noetherian ring. Their definition is in terms of maps to free modules. We give an…

As an example of empirical metamathematics, we present a detailed study of the dependency structure of the 465 theorems in Euclid's Elements, finding empirical signatures of concepts such as the power of a theorem. We apply similar methods…

A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework…

In this thesis we shall present two logical systems, MP and MP, for the purpose of reasoning about knowledge and effort. These logical systems will be interpreted in a spatial context and therefore, the abstract concepts of knowledge and…

Locales have been studied as "topologies without points", mainly by tools of category theory. While traditional topology presents a space as a set of points with specified neighborhoods, localic topology presents a space as a lattice of…

Black holes are extreme spacetime deformations where even light is imprisoned. There is an extensive astrophysical evidence for the real and abundant existence of these prisons of matter and light in the Universe. Mathematically, black…

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…

Starting from Bunge's (1977) scientific ontology, we expose a materialistic relational theory of space-time, that carries out the program initiated by Leibniz, and provides a protophysical basis consistent with any rigorous formulation of…

This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…

Space and time are central concepts for understanding our World. They are important ingredients at the core of every scientific theory and subject of intense debate in philosophy. Albert Einstein's Special and General theories of Relativity…

Line bundles of rational degree are defined using Perfectoid spaces, and their co-homology computed via standard \v{C}ech complex along with Kunneth formula. A new concept of `braided dimension' is introduced, which helps convert the curse…

Consider an elliptic curve, defined over the rational numbers, and embedded in projective space. The rational points on the curve are viewed as integer vectors with coprime coordinates. What can be said about a rational point if a bound is…

Physical cosmology tries to understand the Universe at large with its origin and evolution. Observational and experimental situations in cosmology do not allow us to proceed purely based on the empirical means. We examine in which sense our…

Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…

Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…

We give an intrinsic characterization of all subsets of a doubling metric space that can arise as a member of some system of dyadic cubes on the underlying space, as constructed by M. Christ.

S. Chandrasekhar wrote in the prologue to his book on black holes, "The black holes of nature are the most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time."…

The paper investigates an evidence-based semantics for epistemic logics. It is shown that the properties of knowledge obtained from a potentially infinite body of evidence are described by modal logic S5. At the same time, the properties of…

We show how semiclassical black holes can be reinterpreted as an effective geometry, composed of a large ensamble of horizonless naked singularities (eventually smoothed at the Planck scale). We call this new items {\it frizzyballs}, which…