Limitations
Although first-order logic is sufficient for formalizing much of mathematics, and is commonly used in computer science and other fields, it has certain limitations. These include limitations on its expressiveness and limitations of the fragments of natural languages that it can describe.
For instance, first-order logic is undecidable, meaning a sound, complete and terminating decision algorithm is impossible. This has led to the study of interesting decidable fragments such as C2, first-order logic with two variables and the counting quantifiers and (these quantifiers are, respectively, "there exists at least n" and "there exists at most n") (Horrocks 2010).
Read more about this topic: First-order Logic
Famous quotes containing the word limitations:
“The motion picture made in Hollywood, if it is to create art at all, must do so within such strangling limitations of subject and treatment that it is a blind wonder it ever achieves any distinction beyond the purely mechanical slickness of a glass and chromium bathroom.”
—Raymond Chandler (1888–1959)
“... art transcends its limitations only by staying within them.”
—Flannery O’Connor (1925–1964)
“The only rules comedy can tolerate are those of taste, and the only limitations those of libel.”
—James Thurber (1894–1961)