Theories of Entailment

Edwin Mares

One traditional role of a logic of a logic of entailment is as a set of closure principles for theories. Looking at logics in this way, and as theories themselves, can be very interesting. A logic determines a closure operator (in Tarski’s sense) on sets of formulas. The theories generated by a closure operator themselves (sometimes) determine closure operators. Looking at the space of theories generated by a “master theory”, and the interaction of the closure operators that they determine, I motivate a variety of different logical systems.