Sentence examples for axiomatic structure from inspiring English sources

Bourbaki is the collective pseudonym for the authorship of 36 volumes of comprehensive texts, started in 1939 by an elite group of French mathematicians, designed to present mathematics in a contemporary and original way, and to illustrate its axiomatic structure.

Rather than attempt to define things so that problems could not arise, they suggested that it was possible to dispense with definitions and cast all of mathematics in an axiomatic structure using the ideas of set theory.

The ideal would be a formal axiomatic structure that would allow a deduction of the empirical generalizations which, combined with statements of initial conditions, permit a deduction of particular empirical facts (thus explaining their truth).

As we shall see in the next section, it is also important when it comes to the axiomatic structure of mereology, including the axiomatics of the most classical theories.

By contrast, while sharing a model of geometric axiomatic structure of knowledge, Newton's project of natural philosophy was meant to be autonomous from a system of philosophy and, in the new context, still endorsed for its model of organization and its empirical reasoning values of formal synthesis and ontological simplicity (see the entry on Newton and Janiak 2008).

Ever since, "set theory" has generally been identified with the branch of mathematical logic that studies transfinite sets, originating in Cantor's result that R has a greater cardinality than N. But, as the foregoing discussion shows, set theory was both effect and cause of the rise of modern mathematics: the traces of this origin are indelibly stamped on its axiomatic structure.

Even so, this work did much to convince later scholars, including many of the Pragmatic View, of certain weaknesses in understanding theories as deductive axiomatic structures.

Questions related to assessing uncertainty and considering multiple objectives are tackled within the axiomatic structures of MAUT (Multi-attribute Utility Theory).

There are also general prescriptions for functional schemas that facilitate discussions for the presence of consciousness in computational systems and axiomatic structures that define necessary architectural features without which it would be difficult to represent sensations.

In short order, McCrea, Walker and Robertson succumbed to Milne's methodological recommendations: first, to carry out an operationalist paring of non-observational concepts, then, secondly, to embed the resulting minimalist concept set in an axiomatic hypothetical-deductive structure.

The following year, Dedekind published a paper in which he provided an axiomatic analysis of the structure of the set R of real numbers.