Modal Logic for Reasoning About Uncertainty and Confusion

We consider a modal logic that can formalise statements about uncertainty and beliefs such as I think that my wallet is in the drawer rather than elsewhere or I am confused whether my appointment is on Monday or Tuesday.To do that, we expand Gdel modal logic KG with the involutive negation defined as v( , w) = 1v( , w).We provide semantics with the finite model property for our new logic that we call KG inv and show its equivalence to the standard semantics over [0, 1]-valued Kripke models.Namely, we show that is valid in the standard semantics of KG inv iff it is valid in the new semantics.Using this new semantics, we construct a constraint tableaux calculus for KG inv that allows for an explicit extraction of countermodels from complete open branches and then employ the tableaux calculus to obtain the PSPACE-completeness of the validity in KG inv .