Por Ana Borges (University of Barcelona).
Abstract: We present the logic QRC1, which is a strictly positive fragment of quantified modal logic. The intended reading of the diamond modality is that of consistency of a formal theory. Predicate symbols are interpreted as parametrized axiomatizations. QRC1 is sound with respect to this arithmetical interpretation. Quantified provability logic is known to be undecidable. However, the undecidability proof cannot be performed in our signature and arithmetical reading. We conjecture the logic QRC1 to be arithmetically complete. We takes the first steps towards arithmetical completeness by providing relational semantics for QRC1 with a corresponding completeness proof. We further show the finite model property with respect to domains and number of worlds, which implies decidability.