A multidimensional modal translation for a formal system motivated by situation semantics (Q1182697)

The paper defines a system of modal logic \(\mathbb{L} (M)\), which is essentially quantified S4 extended by a family of operators \(\otimes_ i\), for \(i\in\omega\), such that \(\otimes_ i A\) means, intuitively, that \(A\) is true in the \(i\)th of some given sequence of worlds of type \(\omega\). Possible worlds semantics and a sequent calculus are given, and soundness and completeness proved. The paper then defines a translation, \(T\), from the language \(\mathbb{L}\) of the author [``Two formal systems for situation semantics'', Notre Dame J. Formal Logic (to appear)] and shows that a formula, \(A\), is valid in this system iff \(T(A)\) is valid in \(\mathbb{L} (M)\).