Undecidability of Relation-Changing Modal Logics
نویسندگان
چکیده
Relation-changing modal logics are extensions of the basic modal logic that allow to change the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to delete, add and swap edges in the model, both locally and globally. We investigate the satisfiability problem of these logics. We define satisfiability-preserving translations from an undecidable memory logic to relation-changing modal logics. This way we show that their satisfiability problems are undecidable.
منابع مشابه
Undecidability of a Very Simple Modal Logic with Binding
We show undecidability of the satisfiability problem of what is arguably the simplest non-sub-Boolean modal logic with an implicit notion of binding. This work enriches the series of existing results of undecidability of modal logics with binders, which started with Hybrid Logics and continued with Memory Logics. 1 Modal Logics, Names and Binders Modal Logics are languages that are able to desc...
متن کاملRelation-Changing Logics as Fragments of Hybrid Logics
Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to delete, add, and swap edges in the model, both locally and globally. We provide translations from these logics to hybrid logic along with an implementation....
متن کاملUndecidability of Multi-modal Hybrid Logics
This paper establishes undecidability of satisfiability for multi-modal logic equipped with the hybrid binder ↓ , with respect to frame classes over which the same language with only one modality is decidable. This is in contrast to the usual behaviour of many modal and hybrid logics, whose uni-modal and multi-modal versions do not differ in terms of decidability and, quite often, complexity. T...
متن کاملUndecidability of the Logic of Overlap Relation over Discrete Linear Orderings
The validity/satisfiability problem for most propositional interval temporal logics is (highly) undecidable, under very weak assumptions on the class of interval structures in which they are interpreted. That, in particular, holds for most fragments of Halpern and Shoham’s interval modal logic HS. Still, decidability is the rule for the fragments of HS with only one modal operator, based on an ...
متن کامل