Approximations of modal logics: K and beyond

Inspired by recent work on approximations of classical logic, we present a method that approximates several modal logics in a modular way. Our starting point is the limitation of the n-degree of introspection that is allowed, thus generating modal n-logics. Semantics for n-logics is presented, in which formulas are evaluated with respect to paths, and not possible worlds. A tableau-based proof system is presented, n-SST, and soundness and completeness is shown for the approximation of modal logics K, T, D, S4 and S5. Key words: Modal Logic, Approximated Inference, Single Step Tableaux

• Type: Journal
• Year: 2008
• Where: APAL
• Authors: Guilherme de Souza Rabello, Marcelo Finger
• Keywords: APAL 2008, Logic, Modal Logic, Modal N-logics