Logics with probabilistic team semantics and the Boolean negation
Miika Hannula, Minna Hirvonen, Juha Kontinen, Yasir Mahmood, Arne Meier, Jonni Virtema · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · 2023
We study the expressivity and the complexity of various logics in probabilistic team semantics with the Boolean negation. In particular, we study the extension of probabilistic independence logic with the Boolean negation, and a recently introduced logic FOPT. We give a comprehensive picture of the relative expressivity of these logics together with the most studied logics in probabilistic team semantics setting, as well as relating their expressivity to a numerical variant of second-order logic. In addition, we introduce novel entropy atoms and show that the extension of first-order logic by entropy atoms subsumes probabilistic independence logic. Finally, we obtain some results on the complexity of model checking, validity, and satisfiability of our logics.