It is possible to synthesise tableau deduction calculi from the specifications of logics. In this course we give an introduction to a powerful method for synthesising sound, complete and terminating tableau calculi for description logics, modal logics and related fragments of first-order logic. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules which can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding an unrestricted blocking mechanism yields a terminating tableau calculus. The method provides a general approach to developing tableau decision procedures for expressive logics. We illustrate the method on several examples from non-classical logic.
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