First-order Logic - Limitations

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 limitations of pleasure cannot be overcome by more pleasure.
    Mason Cooley (b. 1927)

    Much of what contrives to create critical moments in parenting stems from a fundamental misunderstanding as to what the child is capable of at any given age. If a parent misjudges a child’s limitations as well as his own abilities, the potential exists for unreasonable expectations, frustration, disappointment and an unrealistic belief that what the child really needs is to be punished.
    Lawrence Balter (20th century)

    To note an artist’s limitations is but to define his talent. A reporter can write equally well about everything that is presented to his view, but a creative writer can do his best only with what lies within the range and character of his deepest sympathies.
    Willa Cather (1876–1947)