Sentence examples for statement is formalized from inspiring English sources

In "Relational analysis approach", the problem statement is formalized.

which is formalized below with a theorem.

"Research is formalized curiosity.

This is formalized in the following definition.

Firstly, the biological knowledge is formalized.

Functional similarity is formalized using GO (gene ontology) annotations.

This basic evolutionary insight is formalized in constraint-based modeling.

This intuition is formalized by the ABBA-BABA test.

Using familiar techniques from the arithmetization of syntax, it is not difficult to see that this statement can be formalized in the language of first-order arithmetic as a \ \Pi^0_2\ -statement – i.e. a statement \ \Pi^0_2\ -statementm \(\forall x \exists y \psi(x,y)\) where \(\psi(x,y)\) contains only bounded numerical quantifiers.e

However, (34) and (35) do not assert that being obligatory is equivalent with being the case, for the latter statement should be formalized as A ↔ !A.

Any mathematical statement can be formalized into the language of set theory, and any mathematical theorem can be derived, using the calculus of first-order logic, from the axioms of ZFC, or from some extension of ZFC.