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...

Lemma 1. Let 4ABC be a triangle with acute angles ∠A and ∠C. Drop a perpendicular from B to the base line ←→ AC, and let F be the foot. Then A ∗ F ∗ C. Proof. Observe that F 6= A since ∠BAC is not a right angle. Likewise F 6= C. So by Axiom B-3, one of A,F,C is between the other two. If F ∗A ∗C then ∠BAC is external to ∠BFA, so ∠BAC > ∠BFA which contradicts the assumption that ∠A is acute. Like...

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

As the first illustration of a potential satisfier for the ‘platitudes for truth’ in the appendix to his engaging recent discussion of the concept of truth (Wright 1999), Crispin Wright has proposed a notion of ‘truth conceived as coherence’ for arithmetic. This paper attempts to clarify certain aspects of Wright’s proposal. Take the standard first-order language of arithmetic L. Let B be some ...

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...

First-order languages have been introduced to describe beliefs formally and the concept of revision is defined for model as well as proof. A logical inference system named R-calculus is defined to derive all maximal contractions of a base of belief set for its given refutations. The R-calculus consists of the structural rules, an axiom, a cut rule and the rules for logical connectives and quant...