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If a proposition P is true for all B, this is written P forall B. forall is one of the two so-called quantifiers, and translates the universal quantifier forall . The Wolfram ...

An early name for calculus of variations. The term is also sometimes used in place of predicate calculus.

The set of all ground atoms that can be formed from predicate symbols from a clause in Skolemized form S and terms from the Herbrand universe H of S.

The rule (F,F=>G)/G, where => means "implies," which is the sole rule of inference in propositional calculus. This rule states that if each of F and F=>G is either an axiom ...

A symbol employed in a formal propositional calculus.

A quantified system of real algebraic equations and inequalities in variables {x_1,...,x_n} is an expression QS=Q_1(y_1)Q_2(y_2)...Q_m(y_m)S(x_1,...,x_n;y_1,...,y_m), where Q ...

The logical axiom R(x,y)=!(!(x v y) v !(x v !y))=x, where !x denotes NOT and x v y denotes OR, that, when taken together with associativity and commutativity, is equivalent ...

A relation < is a strict order on a set S if it is 1. Irreflexive: a<a does not hold for any a in S. 2. Asymmetric: if a<b, then b<a does not hold. 3. Transitive: a<b and b<c ...

For every proposition involving logical addition and multiplication ("or" and "and"), there is a corresponding proposition in which the words "addition" and "multiplication" ...

A statement is in disjunctive normal form if it is a disjunction (sequence of ORs) consisting of one or more disjuncts, each of which is a conjunction (AND) of one or more ...