We propose an axiomatization of Sergeyev’s theory of Grossone, trying to comply with his methodological principles. We find that a simplified form of his Divisibility axiom is sufficient. We use for easier readability a second order language and a predicative second order logic. Our theory is not finitely axiomatizable and is a conservative extension of Peano’s arithmetic.

Under Martin’s Axiom a c.c.c. nonseparable compact space is constructed which maps continuously into [0, 1] with linear fibers. Such a space can not, for instance, map onto [0, 1]א1 .

We show that several logics of common belief and common knowledge are not only complete, but also strongly complete, hence compact. These logics involve a weakened monotonicity axiom, and no other restriction on individual belief. The semantics is of the ordinary fixed-point type.

The theory of finitary biframes as order-theoretical duals bitopological spaces is explored. category a coreflective subcategory that biframes. Some the advantages adopting pointfree notion bispaces are studied. In particular, it shown for every biframe there which plays role analogue to assembly in frames: L A(L) with universal property analogous frame; and such its main component isomorphic o...

A recent debate has focused on different methodological principles underlying the practice of axiom choice in mathematics (cf. Feferman et al., 2000; Maddy, 1997; Easwaran, 2008). The general aim of these contributions can be described as twofold: first to clarify the spectrum of informal justification strategies retraceable in the history of mathematical axiomatics. Second, to evaluate and to ...

One of the major problems of axiom pinpointing for incoherent terminologies is the precise positioning within the conflict axioms. In this paper we present a formal notion for the entailment-based axiom pinpointing of incoherent terminologies, where the parts of an axiom is defined by atomic entailment. Based on these concepts, we prove the one-to-many relationship between existing axiom pinpoi...

Role-based access control is a standard mechanism in information systems. Based on the role a user has, certain information is kept from the user even if requested. For ontologies representing knowledge, deciding what can be told to a user without revealing secrets is more difficult as the user might be able to infer secret knowledge using logical reasoning. In this paper, we present two approa...

This paper de1nes the new concept of completely Hausdor& axiom of an L-topological space by means of L-continuous mappings from an L-topological space to the re1ned Hutton’s unit L-interval by Wang. Some characterizations of the completely Hausdor& axiom, de1ned in this paper, are given, and many nice properties of this kind of completely Hausdor& axiom are proved. For example, it is hereditary...

In this paper a new method for dimensionality reduction in machine learning is proposed and called as Lie group Machine Learning (LML). The theory framework of LML is given, including the conception of one-parameter subgroup, Lie algebra and LML; the geometric properties of LML; the generalization hypothesis axiom, the partition independence hypothesis axiom, the duality hypothesis axiom, the l...

The deflection measurements made using Falling Weight Deflectometers (FWDs) are widely used in the back-calculation of pavement layer moduli. Pavement structural characteristics, changes temperature, and other related factors exert a significant effect on measurements. Therefore, three machine learning methods—Classification Regression Tree (CART), Random Forest (RF), Gradient Boosting Decision...