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A sentential variable, also called a propositional variable, that can be substituted for in arbitrary sentential formulas (Carnap 1958, p. 24).

An expression built up from statements letters by appropriate application of connectives (Mendelson 1997, p. 13).

A syllogism, also known as a rule of inference, is a formal logical scheme used to draw a conclusion from a set of premises. An example of a syllogism is modus ponens.

A theory is a set of sentences which is closed under logical implication. That is, given any subset of sentences {s_1,s_2,...} in the theory, if sentence r is a logical ...

A property of individuals which is shared by every individual.

The quantifier "for all" ( forall ), sometimes also known as the "general quantifier."

Inference of the truth of an unknown result obtained by noting its similarity to a result already known to be true. In the hands of a skilled mathematician, analogy can be a ...

The connective in A<=>B (also denoted A=B) that returns a true result iff A and B are either both true or both false. The biconditional is also called an equivalence.

A clause is a disjunction of literals.

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.