We study classical modal logics with pooling modalities, i.e. unary modal operators that allow one to express properties of sets obtained by the pointwise intersection of neighbourhoods. We discuss salient properties of these modalities, situate the logics in the broader area of modal logics (with a particular focus on relational semantics), establish key properties concerning their expressive power, and discuss their application to epistemic/doxastic logic, the logic of evidence-based belief, deontic logic, and logics of agency and ability.

ER - TY - JOUR T1 - A Logic for the Discovery of Deterministic Causal Regularities JF - Synthese Y1 - In Press A1 - Mathieu Beirlaen A1 - Bert Leuridan A1 - Frederik Van De Putte SP - 1–33 ER - TY - JOUR T1 - That will do: Logics of Deontic Necessity and Sufficiency JF - Erkenntnis Y1 - 2017 A1 - Frederik Van De Putte AB - We study a logic for deontic necessity and sufficiency, as originally proposed in van Benthem :36–41, 1979). Building on earlier work in modal logic, we provide a sound and complete axiomatization for it, consider some standard extensions, and study other important properties. After that, we compare this logic to the logic of “obligation as weakest permission” from Anglberger et al. :807–827, 2015). |

In (Anglberger et al., 2015, Section 4.1), a deontic logic is proposed which explicates the idea that a formula φ is obligatory if and only if it is (semantically speaking) the weakest permission. We give a sound and strongly complete, Hilbert style axiomatization for this logic. As a corollary, it is compact, contradicting earlier claims from Anglberger et al. (2015). In addition, we prove that our axiomatization is equivalent to Anglberger et al.’s infinitary proof system, and show that our results are robust w.r.t. certain changes in the underlying semantics.

VL - 9 SP - 370-379 ER -