different between wff vs axiom

English

Alternative forms

• WFF

Pronunciation

• IPA^(key): /w?f/, /w?f/, /w?f/

Noun

wff (plural wffs)

1. Acronym of well-formed formula.
   • 1964, On the Occurence of Non-deontic WFF's in Argument Forms Having Deontic WFF's as Conclusion

     which are of the form P(S) and hence we know that we can decide its truth value if we can decide the truth Value of all d-wff's of form P(S). But if it is of the form P(S ) then it is equivalent to P(T) where T is the dans of S. But by the principle of […]

   • 2001, James L. Hein, Discrete Structures, Logic, and Computability, Jones & Bartlett Learning (?ISBN), page 350:

     A grammatically correct expression is called a well-formed formula, or wff for short, which can be pronounced "woof." To decide whether an expression is a wff , we need to precisely define the syntax (or grammar) rules for the formation of wffs […]

   • 2002, Fernando C. N. Pereira, Stuart M. Shieber, Prolog and Natural-Language Analysis, Microtome Publishing (?ISBN), page 76:

     The set of well-formed formulas (wffs) is the smallest set satisfying the following conditions: • If p is an n-ary predicate symbol (an element of Pn) and t1 ,. .., tn are terms, p(t1 ,. ..,tn) is a wff. • If p is a wff and x is a variable, (?x)p and (?x)p are […]

References

English

Etymology

From Middle French axiome in the 15th century, from Latin axi?ma (“axiom; principle”), from Ancient Greek ?????? (axí?ma, “that which is thought to fit, a requisite, that which a pupil is required to know beforehand, a self-evident principle”), from ????? (axió?, “to think fit or worthy, to require, to demand”), from ????? (áxios, “fit, worthy”, literally “weighing as much as; of like value”), from ??? (ág?, “I drive”).

Pronunciation

• (Received Pronunciation) IPA^(key): /?aks.?.?m/
• (General American) enPR: ?k's??m, IPA^(key): /?æks.i.?m/
• Hyphenation: ax?i?om

Noun

axiom (plural axioms or axiomata) (the latter is becoming less common and is sometimes considered archaic)

1. (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
2. (logic, mathematics, proof theory) A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).
3. An established principle in some artistic practice or science that is universally received.

Synonyms

• (philosophy, mathematics): axioma (now rare)
• (logic, mathematics): postulate

Hypernyms

• (logic): well-formed formula, wff, WFF

Hyponyms

• (mathematics): axiom of choice, axiom of infinity, axiom of pairing, axiom of power set, axiom of regularity, axiom of union, completeness axiom, parallel axiom

Holonyms

• (logic): formal system

Derived terms

• axiomatic
• axiomatical
• axiomatically
• axiomatise, axiomatize
• axiomatisation, axiomatization

Translations

See also

References

• axiom in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
• axiom in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.

Further reading

• axiom on Wikipedia.Wikipedia

Anagrams

• amoxi

Czech

Noun

axiom m

1. axiom

Derived terms

• axiom výb?ru m

Related terms

• axiomatický
• axiomatizovat
• axiomatizace

Swedish

Noun

axiom n

1. axiom

Declension

Related terms

• axiomatisk