Sentence examples for axiomatic form from inspiring English sources
It calls for a formalization of all of mathematics in axiomatic form, together with a proof that this axiomatization of mathematics is consistent.
The intuitionistic calculus aims at presenting in axiomatic form those and only those principles of propositional logic that are accepted as sound in intuitionist mathematics.
According to his theory of proofs, everything was to be put into an axiomatic form, allowing the rules of inference to be only those of elementary logic, and only those conclusions that could be reached from this finite set of axioms and rules of inference were to be admitted.
For Proclus the axiomatic form mirrors the metaphysical structure of emanation.
However, examples of the semantic approach focusing on mathematical structures and satisfaction of set-theoretic relations have focused on syntactic features including the axiomatic form of a theory in the discussion of reduction (Sarkar 1998, da Costa and French 2003).
The axiomatic form in Euclid is more complex, relying not just on first principles (communis animi conceptio), the only type of principle used by Boethius and Alan, but also on definitions, petitiones, theorems, etc. Euclid is the model for Nicolas of Amiens's Ars Catholicae Fidei.
It should be stressed that from a constructive point of view this plurality of options (and thus systems), rather than causing uneasiness, is a highly desirable situation, as it constitutes a form of "axiomatic freedom".
The axiomatic approach to neuroeconomics forms part of a wider agenda for the incorporation of nonstandard data into economics.
The ideal had the form of an axiomatic system.
According to Bolzano, a mathematical theory should be presented in the form of an axiomatic theory, whose propositions are deduced from previous propositions according to their objective dependence and eventually from the axioms.
Moreover, let (mathfrak{M}_{E}) be the family of all nonempty compact subsets of E. We use the following definition of the measure of noncompactness, which is in the form of an axiomatic way.
