Sentence examples for foundational systems from inspiring English sources

Because of this, the existing results in which these notions appeared could not be reconstructed in the accepted foundational systems.

It should be mentioned that other foundational systems for Bishop-style constructive mathematics were introduced in the early 1970's.

Recent advances in 'omics' technologies and computational systems biology have brought the foundational systems approach of metabolic engineering into focus.

In particular, there were no definitions of these notions in terms of concepts accepted in the foundational systems designed for the reconstruction of classical mathematics (for example, Russell and Whitehead's theory of types or Zermelo's set theory).

Proof-theoretic interpretations have also been employed to compare constructive and intuitionistic ZF set theories among each others, as well as with their classical counterparts, and also with other foundational systems for constructive mathematics, such as constructive type theory and explicit mathematics (see e.g. Griffor and Rathjen 1994, Tupailo 2003).

Tarski's aim in a series of works on semantical notions was precisely to propose mathematically acceptable definitions of those notions, and in particular acceptable in some one of the chief foundational systems (the system chosen by Tarski will change with time; see below).

Conducting proofs in such a "painstakingly foundational system" (Harrison 2006) has some significant benefits.

Collectively, this simple peptide-based material provides an ideal foundational system for a variety of bioregenerative approaches.

This refusal has led to the criticism that his approach lacks the precision that a logician would normally expect of a foundational system.

These foundational systems-level analyses should help inform community studies of incidence/prevalence and mental health risk factors to determine priority conditions and targeted expansion of mental healthcare systems in low-and middle-income countries (LMICs).

Unfortunately, this effort does not translate into strengthening the foundational system of relevant child-specific data generation, collation, and use for purposes of study and policy design.