Canonical Models and the Complexity of Modal Team Logic
نویسنده
چکیده
We study modal team logic MTL and the dependence-free fragment FO2[∼] of two-variable team logic, which extend modal logic ML and two-variable logic FO2 with team semantics by a Boolean negation ∼. We settle the open question of the complexity of their respective satisfiability problems, and prove that both are complete for a non-elementary complexity class. We also prove that the model checking problem is PSPACE-complete for several fragments of MTL and FO[∼]. Based on the well-known standard translation from ML to FO2, we propose an team-semantical translation from MTL into FO2[∼].
منابع مشابه
Strong Completeness of Coalgebraic Modal Logics
Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics often present subtle difficulties – up to the point that canonical models may fail to exist, as is the case e.g. in most probabilistic logics. Here, we present a...
متن کاملThe expressive power of modal logic with inclusion atoms
Modal inclusion logic is the extension of basic modal logic with inclusion atoms, and its semantics is defined on Kripke models with teams. A team of a Kripke model is just a subset of its domain. In this paper we give a complete characterisation for the expressive power of modal inclusion logic: a class of Kripke models with teams is definable in modal inclusion logic if and only if it is clos...
متن کاملSuhrawardi's Modal Syllogisms
Suhrawardi’s logic of the Hikmat al-Ishraq is basically modal. So to understand his modal logic one first has to know the non-modal part upon which his modal logic is built. In my previous paper ‘Suhrawardi on Syllogisms’(3) I discussed the former in detail. The present paper is an exposition of his treatment of modal syllogisms. On the basis of some reasonable existential presuppositi...
متن کاملInternal Models for Coalgebraic Modal Logics
We present ongoing work into the systematic study of the use of dual adjunctions in coalgebraic modal logic. We introduce a category of internal models for a modal logic. These are constructed from syntax, and yield a generalised notion of canonical model. Further, expressivity of a modal logic is shown to be characterised by factorisation of its models via internal models and the existence of ...
متن کاملPartiality and Adjointness in Modal Logic
Following a proposal of Humberstone, this paper studies a semantics for modal logic based on partial “possibilities” rather than total “worlds.” There are a number of reasons, philosophical and mathematical, to find this alternative semantics attractive. Here we focus on the construction of possibility models with a finitary flavor. Our main completeness result shows that for a number of standa...
متن کامل