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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 ...

If the property of being an object is expressed by a basic predicate of the system, then such a predicate (if it exists) is called a universal predicate, or universal ...

A property of individuals which is shared by every individual.

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

A universal sentence is a sentence (i.e., formula of the predicate calculus without free variables) whose variables are universally quantified.

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.