相关论文: Consistency, non triviality and redundancy in math…

As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…

We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…

While the terms "redundancy" and "consensus" are often used as synonyms in the context of quantum objectivity, we show here that these should be understood as two related but distinct notions, that quantify different features of the…

We study functional and concurrent calculi with non-determinism, along with type systems to control resources based on linearity. The interplay between non-determinism and linearity is delicate: careless handling of branches can discard…

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…

Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates…

Much recent work has shown how cross-linguistic variation is constrained by competing pressures from efficient communication. However, little attention has been paid to the role of the systematicity of forms (regularity), a key property of…

Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…

The fundamental impasses and ruptures in various domains of the canonical, unitary science, or the 'end of science', become the more and more evident. The natural unity of being is recovered within a universal nonperturbative method leading…

Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…

Redundancy matrices provide insights into the load carrying behavior of statically indeterminate structures. This information can be employed for the design and analysis of structures with regard to certain objectives, for example…

Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the…

This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.…

On one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide…

Computer systems can be found everywhere: in space, in our homes, in our cars, in our pockets, and sometimes even in our own bodies. For concerns of safety, economy, and convenience, it is important that such systems work correctly.…

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…

Nonmonotonic reasoning is a pattern of reasoning that allows an agent to make and retract (tentative) conclusions from inconclusive evidence. This paper gives a possible-worlds interpretation of the nonmonotonic reasoning problem based on…

A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for when two distinct formal derivations can be taken as denoting the same logical argument. In the literature one finds criteria which are…

Recently there has been much interest and progress in extending the definition of contextuality to systems with disturbance. We prove that such an endeavor cannot simultaneously satisfy the following principles: (1) any deterministic system…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…