FIRST-ORDER LOGIC
\fˈɜːstˈɔːdə lˈɒd͡ʒɪk], \fˈɜːstˈɔːdə lˈɒdʒɪk], \f_ˈɜː_s_t_ˈɔː_d_ə l_ˈɒ_dʒ_ɪ_k]\
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The language describing the truth ofmathematical formulas. Formulas describe properties ofterms and have a truth value. The following are atomicformulas: 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 thefollowing are compound formulas: F1 ^ F2conjunction - true if both F1 and F2 are true, F1 V F2disjunction - true if either or both are true, F1 => F2implication - true if F1 is false or F2 istrue, F1 is the antecedent, F2 is theconsequent (sometimes written with a thinarrow), F1 <= F2true if F1 is true or F2 is false, F1 == F2true if F1 and F2 are both true or both false(normally written with a three lineequivalence symbol) ~F1negation - true if f1 is false (normallywritten as a dash '-' with a shorter verticalline hanging from its right hand end). For all v . Funiversal quantification - true if F is truefor all values of v (normally written with aninverted A). Exists v . Fexistential quantification - true if thereexists some value of v for which F is true. (Normally written with a reversed E).The operators ^ V => <= == ~ are called connectives. "Forall" and "Exists" are quantifiers whose scope is F. Aterm 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 onlyquantify over sets of atomic propositions. (E.g. For all p. p => p). Second-order logic can quantify over functions onpropositions, and higher-order logic can quantify over anytype of entity. The sets over which quantifiers operate areusually implicit but can be deduced from well-formednessconstraints.In first-order logic quantifiers always range over ALL theelements 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 ofMathematical Logic (Barwise, ed., North Holland, NYC, 1977)].
By Denis Howe
Word of the day
Dopamine Acetyltransferase
- An enzyme that catalyzes the of groups from acetyl-CoA to arylamines. They have wide specificity for aromatic amines, particularly serotonin, and can also catalyze acetyl transfer between arylamines without CoA. EC 2.3.1.5.