Modal Logics of Succession for 2-Dimensional Integral Spacetime

摘要

We consider the problem of axiomatizing various natural “successor” logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages, and prove completeness theorems. We also establish that the irreflexive successor logic in the “standard” modal language (i.e. the language containing □ and ⋄) is not finitely axiomatizable.