first-order logic
The language describing the truth of
mathematical formulas. Formulas describe properties of
terms and have a truth value. The following are atomic
formulas:
True
False
p(t1,..tn) where t1,..,tn are terms and p is a predicate.
If F1, F2 and F3 are formulas and v is a variable then the
following are compound formulas:
F1 ^ F2 conjunction - true if both F1 and F2 are true,
F1 V F2 disjunction - true if either or both are true,
F1 => F2 implication - true if F1 is false or F2 is
true, F1 is the antecedent, F2 is the
consequent (sometimes written with a thin
arrow),
F1 <= F2 true if F1 is true or F2 is false,
F1 == F2 true if F1 and F2 are both true or both false
(normally written with a three line
equivalence symbol)
~F1 negation - true if f1 is false (normally
written as a dash '-' with a shorter vertical
line hanging from its right hand end).
For all v . F universal quantification - true if F is true
for all values of v (normally written with an
inverted A).
Exists v . F existential quantification - true if there
exists some value of v for which F is true.
(Normally written with a reversed E).
The operators ^ V => <= == ~ are called connectives. "For
all" and "Exists" are quantifiers whose scope is F. A
term is a mathematical expression involving numbers,
operators, functions and variables.
The "order" of a logic specifies what entities "For all" and
"Exists" may quantify over. First-order logic can only
quantify over sets of atomic propositions. (E.g. For all p
. p => p). Second-order logic can quantify over functions on
propositions, and higher-order logic can quantify over any
type of entity. The sets over which quantifiers operate are
usually implicit but can be deduced from well-formedness
constraints.
In first-order logic quantifiers always range over ALL the
elements of the domain of discourse. By contrast,
second-order logic allows one to quantify over subsets.
["The Realm of First-Order Logic", Jon Barwise, Handbook of
Mathematical Logic (Barwise, ed., North Holland, NYC, 1977)].
(2005-12-27)
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first-prder logic first-oprder logic first-porder logic first-krder logic first-okrder logic first-korder logic first-lrder logic first-olrder logic first-lorder logic first-arder logic first-erder logic first-urder logic first-o4der logic first-or4der logic first-o4rder logic first-o$der logic first-or$der logic first-o$rder logic first-o5der logic first-or5der logic first-o5rder logic first-oeder logic first-oreder logic first-oerder logic first-otder logic first-ortder logic first-otrder logic first-odder logic first-ordder logic first-odrder logic first-ofder logic first-orfder logic first-ofrder logic first-ogder logic first-orgder logic first-ogrder logic first-orwer logic first-ordwer logic first-orwder logic first-oreer logic first-ordeer logic first-oreder logic first-orrer logic first-ordrer logic first-orrder logic first-orser logic first-ordser logic first-orsder logic first-orfer logic first-ordfer logic first-orfder logic first-orxer logic first-ordxer logic first-orxder logic first-orcer logic first-ordcer logic first-orcder logic first-orver logic first-ordver logic first-orvder logic first-or er logic first-ord er logic first-or der logic first-ord3r logic first-orde3r logic first-ord3er logic first-ord#r logic first-orde#r logic first-ord#er logic first-ord4r logic first-orde4r logic first-ord4er logic first-ordwr logic first-ordewr logic first-ordwer logic first-ordrr logic first-orderr logic first-ordrer logic first-ordsr logic first-ordesr logic first-ordser logic first-orddr logic first-ordedr logic first-ordder logic first-ordfr logic first-ordefr logic first-ordfer logic first-ordar logic first-ordir logic first-ordor logic first-ordur logic first-orde4 logic first-order4 logic first-orde4r logic first-orde$ logic first-order$ logic first-orde$r logic first-orde5 logic first-order5 logic first-orde5r logic first-ordee logic first-ordere logic first-ordeer logic first-ordet logic first-ordert logic first-ordetr logic first-orded logic first-orderd logic first-ordedr logic first-ordef logic first-orderf logic first-ordefr logic first-ordeg logic first-orderg logic first-ordegr logic first-order iogic first-order liogic first-order ilogic first-order oogic first-order loogic first-order ologic first-order pogic first-order lpogic first-order plogic first-order kogic first-order lkogic first-order klogic first-order ,ogic first-order l,ogic first-order ,logic first-order .ogic first-order l.ogic first-order .logic first-order l9gic first-order lo9gic first-order l9ogic first-order l(gic first-order lo(gic first-order l(ogic first-order l0gic first-order lo0gic first-order l0ogic first-order ligic first-order loigic first-order liogic first-order lpgic first-order lopgic first-order lpogic first-order lkgic first-order lokgic first-order lkogic first-order llgic first-order lolgic first-order llogic first-order lagic first-order legic first-order lugic first-order loric first-order logric first-order lorgic first-order 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Definition commonly spelled as: Defanition or Defenition, Synonym as: Synonim, Sinonym or Sinonim, Thesaurus as: Thesorus or Thesauris, Dictionary as: Dictionery or Dictionry and Define is usually not misspelled. What does mispell meen? It Meens...
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