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...

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...

in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived

The Axiom of Blackwell Determinacy is a set-theoretic axiom motivated by games used in statistics. It is known that the Axiom of Determinacy implies the Axiom of Blackwell Determinacy. Tony Martin has conjectured that the two axioms are equivalent. We develop the “simulation technique” which allows us to simulate boundedness proofs under the assumption of Blackwell Determinacy and deduce strong...

The Pasch axiom is a strong geometric property which was noted and discussed even from the period of Euclid. Modern geometers followed the study of the Pasch axiom and in the context of axiomatic convexity this axiom was widely studied by pioneers in convexity theory. The connected graphs G for which the geodesic interval function I satisfies the Pasch axiom were characterized by Chepoi in 1994...

In this article we discuss some elementary concepts in axiomatics, which is the study of axioms. The axiomatic system we use is that of a metric space, which will be familiar to many readers. Metric spaces were introduced by the French mathematician Maurice Fréchet in 1906 as a generalization of the real numbers and the “distance function” f (x , y) = |x − y|. The aim is to construct limits, co...

Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL interactive proof assistant, and this formalization utilizes a semantically correct embedding of free logic in classical higher-order logic. The modeling and fo...

Both the Continuum Hypothesis and Martin's Axiom allow induc-tive constructions to continue in circumstances where the inductive hypothesis might otherwise fail. The search for useful related axioms procedes naturally in two directions: towards "Super Martin's Axioms ," which extend MA to broader classes of orders; and towards "Anti-Martin's Axioms" (AMA's) which are strictly weaker than CH, bu...

This research used MiChat and SayHi as materials for forensic investigations using three different tools, namely MOBILedit, Magnet Axiom, Belkasoft. These tools will show each performance in the process. We also added a rooting process an option if data cannot be extracted optimally even when these applications. The result of this study shows that cases studied with processes without root acces...