Actuality in Propositional Modal Logic

作者：Hazen Allen P^*; Rin Benjamin G; Wehmeier Kai F

来源：Studia Logica, 2013, 101(3): 487-503.

DOI：10.1007/s11225-012-9395-x

• Modal logic
• Actuality
• Eliminability
• Redundancy
• KRIPKE models
• Neighborhood models

We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula in the propositional modal language with A, there is a formula not containing A such that and are materially equivalent at the actual world in every Kripke model (respectively, neighborhood model). Inspection of the proofs leads to corresponding proof-theoretic results concerning the eliminability of the actuality operator in the actuality extension of any normal propositional modal logic and of any "classical" modal logic. As an application, we provide an alternative proof of a result of Williamson's to the effect that the compound operator Aa- behaves, in any normal logic between T and S5, like the simple necessity operator a- in S5.

• 出版日期2013-6