Russell's "Mathematical Logic as Based on the Theory of Types" (1908) is an accessible presentation of these ideas.
It was first developed by Russell in the fundamental memoir Mathematical Logic as based on the theory of types of 1908.
Although first introduced in 1903, the theory of types was further developed by Russell in his 1908 article "Mathematical Logic as Based on the Theory of Types" and in the three-volume work he co-authored with Alfred North Whitehead, Principia Mathematica (1910, 1912, 1913).
This in turn led to type theory's more mature expression five years later in Russell's 1908 article, "Mathematical Logic as Based on the Theory of Types," and in the monumental work he co-authored with Alfred North Whitehead, Principia Mathematica (1910, 1912, 1913).
Quine's set theory New Foundations (abbreviated NF), proposed in 1937 in his paper "New foundations for mathematical logic", is also based on a procedure for identifying the objects in successive types in order to obtain an untyped theory.
Logical frameworks are computer systems which allow a user to formalise mathematics using specially designed languages based upon mathematical logic and Church's theory of types.
The considered problem is how to create the intelligent level of the software, find an adequate knowledge representations and evidences for mobile robots, based on mathematical logic, and suggested IGEC technology.
Ontologies are formal models based on mathematical logic that describe classes of things and their relations and can facilitate the sharing and exchange of accident scenarios and bring with them the support of automated reasoning which facilitates the location of information of past accidents.
Similarly, L. Sprague de Camp and Fletcher Pratt's Harold Shea series, about a modern American who finds himself in the worlds of various mythologies, depicts a system of magic based on mathematical logic.
Qualitative chemometrics is based on discrete mathematics mainly on mathematical logic, graph theory and combinatorial analysis.
