It is supposed the alternative to Quantum Mechanics Axiomatic. Fluctu-ational Theory save the Mathematics of Quantum Mechanic without change, naming this Mathematics as Method of Indirect Computation. Fluctuational Theory is delete the axiomatic of Quantum Mechanics and replaces it by the assumption of Gravitational Noise. This assumption is connects the Method of Indirect Computation to the Cl...

The birth, raise, development and fortunes of a fundamental theory in thermodynamics, the axiomatic thermodynamics, a creation of Constantin Carathéodory, is thoroughly presented together with a summary of Carathéodory’s biography. Axiomatic thermodynamics is centered around some interesting properties of Pfaffian differential equations, which are here introduced and used for some well-known ca...

In this paper, axiomatic testing of software metrics will be described, The testing is based on representation axiomsjfom the measurement theory. In a case study, the axioms are given for the formal relational structure and the empirical relational structure. 'livo approaches of axiomatic testing are elaborated: deterministic and probabilistic testing.

In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in prover9 (a first-order automated reasoning system which is the successor to otter). After reviewing the second-ord...

In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in prover9 (a first-order automated reasoning system which is the successor to otter). After reviewing the second-ord...

It is well known that Zermelo-Fraenkel Set Theory (ZF), despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to infinitely many axioms, and countable model the Löwenheim–Skolem theorem. This paper presents axioms one accept get rid of these features. For matter, some twenty are formulated in non-classical first-orde...

Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms Group Theory; but some much deeper, Complete Ordered Fields with which Real Analysis starts. Groups abound in sciences, while by Dedekind's theorem there exists only one complete ordered field, up to isomorphism. Cayley's Abstract Alge...

We describe an axiomatic theory for the concept of one-place, partial function, where function is taken in its extensional sense. The theory is rather general, i.e., concepts like natural numbers and sets are definable, and topics as non-strictness and self application can be handled. It contains a model of the (extensional) lambda calculus, and commonly applied mechanisms (like currying, induc...

We discuss the theory of gerrymandering-proof voting rules. Our approach is axiomatic. We show that, for votes over a binary set of alternatives, any rule that is unanimous, anonymous, and gerrymandering-proof must decide a social outcome as a function of the proportions of agents voting for each alternative, and must either be independent of this proportion, or be in one-to-one correspondence ...

The notion of regularity in a Banach algebra was introduced and studied in [KM] and [MM]. A non-empty subset R of a unital Banach algebra A is called a regularity if it satisfies the following two conditions: (i) if a ∈ A and n ∈ N, then a ∈ R ⇔ a ∈ R, (ii) if a, b, c, d are mutually commuting elements of A satisfying ac + bd = 1A then ab ∈ R ⇔ a, b ∈ R. The axioms of regularities are weak enou...