Argument
Well-formed formula
Overview
In mathematical logic, propositional logic, and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet, constructed following the defined grammar of a formal language.
The abbreviation wff is pronounced "woof", or sometimes "wiff", "weff", or "whiff".
A formal language can be identified with the set of formulas in the language. A formula is a syntactic object that can be given a semantic meaning by means of an interpretation. Two key uses of formulas are in propositional logic and predicate logic.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what Well-formed formula is.
Thus there arises a classification of modes of formation, or in the language commonly used by mathematicians, a classification of Functions. Any number, considered as formed from any other number, is called a function of it; and there are as many kinds of functions as there are modes of formation. The simple functions are by no means numerous, most functions being formed by the combination of several of the…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
States what Well-formed formula is.
When a formula of this kind is discovered, it is no longer called an empirical formula, but a law of Nature; and is sooner or later made the basis of an hypothesis which is to explain it. These simple formulæ are not usually, if ever, exactly true, but they are none the less important for that; and the great triumph of the hypothesis comes when it explains not only the formula, but also the deviations from the…
Charles S. Peirce, Chance, Love, and Logic
States what Well-formed formula is.
Related ideas
- Formal language
- First-order logic
- Effective method
- Type–token distinction
- Propositional variable
- Formal grammar
- Logical connective
- Propositional logic
- Mathematical logic
- Domain of discourse
- Symbol (formal)
- Peano axioms
- Polish notation
- University of Michigan
- Yale University
- Quantifier (logic)
- Atomic formula
- Yale Law School
- Alonzo Church
- Higher-order logic
- Backus–Naur form
- Wilhelm Ackermann
- David Hilbert
- Existential quantification
Place in the tradition
Part of First-order logic.