[1] : The Free On-line Dictionary of Computing (27 SEP 03)

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
         pt1,..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 of m.
     
        "the realm of first-order logic", jon barwise, handbook of
        mathematical logic barwise, ed., north holland, nyc, 1977.
     
        1995-05-02
     
     
see also:
formula quantifier scope atomic proposition 

Boolean Logic >> B Words
Boolean Logic, definition of term: Boolean Logic
boolean+logic_pag1.html