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L ogic The systematic presentation of the valid patterns (forms) of inference and certain implications which hold among propositions , relying heavily on the meaning of structural words such as “all,” “some,” “if,” “not,” “and,” and “or.” It is divided into standard (or classical) logic, non-standard logic, and inductive logic. Standard logic includes traditional logic (Aristotelian syllogism) and modern classical logic, which is an expansion of traditional logic and is composed mainly of the propositional calculus and predicate calculus . Non-standard logics include the extensions of classical logic, sometimes called extended logic, and deviations from classical logic, sometimes called deviant logic . Extended logic includes logics such as modal logic, tense logic, deontic logic , epistemic logic, preference logic, and imperative logic. Deviant logic includes logics such as many-valued logic, intuitionist logic , and quantum logic. We can gain additional insight into the form of some systems of logic by seeing that they can be mapped onto one another. Systems of formal logic can be developed by proof from axioms or through natural deduction , which gives rules of inference from given assumptions. Formal logic contrasts with informal logic, which deals with the relations of implication arising from context-related words. Logical systems seek to attain consistency and ... log in or subscribe to read full text