The phrase "axiomatic structures" is correct and usable in written English.
It can be used in contexts related to mathematics, logic, or philosophy, where foundational principles or systems are being discussed.
Example: "In the study of geometry, axiomatic structures provide the necessary framework for proving theorems."
Alternatives: "fundamental frameworks" or "basic systems".
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.
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.
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 axiomatic structure of the statement 'I rebel, therefore we exist,' demands the present be equal to the future.
In that regard, guilt is measured by whether the rebel abides by the structure of her rebellion―the same axiomatic structure we saw in Badiou.
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.
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).
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.
