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The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

Deduction is the process of drawing conclusions from premises and syllogisms.

A class of processes which attempt to round off a domain and simplify its theory by adjoining elements.

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 ...