Tarski's relevance logic; Version 2 [article]

Roger D. Maddux
2019 arXiv   pre-print
Tarski's relevance logic is defined and shown to contain many formulas and derived rules of inference. The definition arises from Tarski's work on first-order logic restricted to finitely many variables. It is a relevance logic because it contains the Basic Logic of Routley-Plumwood-Meyer-Brady, has Belnap's variable-sharing property, and avoids the paradoxes of implication. It does not include several formulas used as axioms in the Anderson-Belnap system R. For example, the Axiom of
more » ... ion is not in Tarski's relevance logic. On the other hand, the Rules of Contraposition and Disjunctive Syllogism are derived rules of inference in Tarski's relevance logic. It also contains a formula (not previously known or considered as an axiom for any relevance logic) that provides a counterexample to a completeness theorem of T. Kowalski (that the system R is complete with respect to the class of dense commutative relation algebras).
arXiv:1901.06567v2 fatcat:wdbky3c7vrcfncj3ktgddr34re