Sahlqvist Correspondence Theory for Sabotage Modal Logic

Sabotage modal logic (SML) is a kind of dynamic logics. It extends static modal logic with a dynamic modality which is interpreted as "after deleting an arrow in the frame, the formula is true". In the present paper, we are aiming at solving an open problem, namely giving a Sahlqvist-type correspondence theorem for sabotage modal logic. We use the standard minimal-valuation techniques to show that the Sahlqvist fragment of sabotage modal logic has first-order correspondents. We also give an algorithm ALBA to compute the first-order correspondents of sabotage Sahlqvist formulas. We give some remarks and future directions at the end of the paper.