Related papers: A Model Theory for the Potential Infinite
We discuss the problems of incompleteness and inexpressibility. We introduce almost self-referential formulas, use them to extend set theory, and relate their expressive power to that of infinitary logic. We discuss the nature of proper…
Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…
The usual nonnegative modulus function is based on addition. A natural different modulus function on the set of positive reals is introduced. Arguments for results for series through the usual modulus function are transformed to arguments…
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
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…
Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of…
We propose the extension of the complex numbers to be the new domain where new concepts, like negative and imaginary probabilities, can be defined. The unit of the new space is defined as the solution of the unsolvable equation in the…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
We describe the non-minimal Standard Model, consisting of minimalistic extensions of the Standard Model, which for all we know is the theory of the universe, able to describe all of the universe from the beginning of time. Extensions…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
A generalization of the definition of a one-dimensional improper integral with an infinite limit is presented. The new definition extends the range of valid integrals to include integrals which were previously considered to not be…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
In this paper the theory of robust output regulation of distributed parameter systems with infinite-dimensional exosystems is extended for plants with unbounded control and observation. As the main result, we present the internal model…
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…
We study a new extension of the weak MSO logic, talking about boundedness. Instead of a previously considered quantifier U, expressing the fact that there exist arbitrarily large finite sets satisfying a given property, we consider a…
In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
An extension of algebras is a homomorphism of algebras preserving identities. We use extensions of algebras to study the finitistic dimension conjecture over Artin algebras. Let $f: B \to A$ be an extension of Artin algebras. We denote by…