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A Multidimensional Modal Translation for a Formal System Motivated by Situation Semantics

The content of this paper is as follows: first a multidimensional quantified modal logic is presented, and soundness, completeness, and com-pactness are proven for it. Then we propose a translation of the sentences of the language L presented in J. Barba's "Two formal systems for situation semantics" (to appear in Notre Dame Journal of Formal Logic) and prove that it is a suitable translation. Finally, we propose a notion of persistence for the sentences of L (inspired in the concept of persistence defined in Situation Semantics) and find its modal counterpart in our multidimensional system.