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.

%G eng %0 Journal Article %J Synthese %D In Press %T A Logic for the Discovery of Deterministic Causal Regularities %A Mathieu Beirlaen %A Bert Leuridan %A Frederik Van De Putte %B Synthese %P 1–33 %G eng %0 Journal Article %J Erkenntnis %D 2017 %T That will do: Logics of Deontic Necessity and Sufficiency %A Frederik Van De Putte %X 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.

%B Rew. Symb. Logic %V 9 %P 370-379 %G eng