An axiomatic basis for plane geometry

Axiomatic Systems for Geometry∗

An axiomatic system contains a set of primitives and axioms. The primitives are Adaptation to the current course is in the margins. object names, but the objects they name are left undefined. This is why the primitives are also called undefined terms. The axioms are sentences that make assertions about the primitives. Such assertions are not provided with any justification, they are neither tru...

An axiomatic study of infinite basis

We present a new technique for studying the w-axiomatizability of the semantics in the ltbt-spectrum. Although Fokkink et al. have recently solved most of the problems still open, our main goal is to shed light on them, and to simply and unify their proofs. Besides, we will focus on preorders (and make a fundamental use of the axiom for ready simulation semantics) instead of equivalences, since...

Notes on Axiomatic Geometry

An Axiomatic Basis for Reasoning about Trust in PKIs

Trust is essential to a communication channel. The trust relationships, which play an important role in Public Key Infrastructures (PKIs), need to be formalized for providing a reliable modelling methodology to support secure digital communications. In this paper, we present a typed modal logic used for specifying and reasoning about trust in PKIs. In order to study trust relationships within P...

The Fundamental Theorems of Elementary Geometry. an Axiomatic Analysis

Introduction. The present investigation is concerned with an axiomatic analysis of the four fundamental theorems of Euclidean geometry which assert that each of the following triplets of lines connected with a triangle is copunctual: the medians, the altitudes, the perpendicular bisectors, and the bisectors of the angles. The general framework for our discussion will be provided by an affine pl...