TY - UNPB T1 - Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Applications Y1 - Submitted A1 - Van De Putte, Frederik A1 - Klein, Dominik ER - TY - UNPB T1 - Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Applications Y1 - Submitted A1 - Frederik Van De Putte ED - Klein, Dominik KW - classical modal logics KW - coalition logic KW - distributed belief KW - multi-agent systems KW - pointwise intersection KW - pooling modalities AB -

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 - Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability JF - Studia Logica Y1 - 2020 A1 - Van De Putte, Frederik A1 - Klein, Dominik AB -

We establish completeness and the finite model property for logics featuring the pooling modalities that were introduced in Van De Putte and Klein (Pooling modalities and pointwise intersection: semantics, expressivity, and applications). The definition of our canonical models combines standard techniques with a so-called “puzzle piece construction”, which we first illustrate informally. After that, we apply it to the weakest classical logics with pooling modalities and investigate the technique’s potential for the axiomatization of stronger logics, obtained by imposing well-known frame conditions on the models.

VL - online first ER - TY - UNPB T1 - Pointwise intersection in neighbourhood modal logic Y1 - 2018 A1 - Van De Putte, Frederik A1 - Klein, Dominik ER -