Nature Research Intelligence Topics Topic summaries Mathematical Sciences Pure Mathematics Mathematical Logic, Set Theory, Lattices and Universal Algebra Mathematical logic, set theory ...

and also some ‘conceptual’ set theory of philosophical interest in its treatment of infinite sets, cardinals and ordinals. From classical logic, it deals with propositional and first-order inference ...

Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...

244) of the text the semantics of propositional logic is usually defined in English, or with truth tables, e.g. S ^ T is true when S is true and T is true, and false otherwise e.g. True, False, ~True, ...