Swap logic

Abstract

We investigate dynamic modal operators that can changethe model during evaluation. We define the logicSLby extending thebasic modal language with the♦modality, which is a diamond operatorthat in addition has the ability to invert pairs of related elements in thedomain while traversing an edge of the accessibility relation.SLis very expressive: it fails to have the finite and the tree model prop-erty. We show thatSLis equivalent to a fragment of first-order logic byproviding a satisfiability preserving translation. In addition, we providean equivalence preserving translation fromSLto the hybrid logicH(:,↓).We also define a suitable notion of bisimulation forSLand investigate itsexpressive power, showing that it lies strictly between the basic modallogic andH(:,↓). We finally show that its model checking problem isPSpace-complete and its satisfiability problem is undecidable.