Neighborhood semantics for logic of knowing how

In this paper, we give an alternative semantics to the non-normal logic of knowing how proposed by Fervari et al. (Proc IJCAI 2017:1031-1038, 2017), based on a class of Kripke neighborhood models with both the epistemic relations and neighborhood structures. This alternative semantics is inspired by the same quantifier alternation pattern of there exists for all in the semantics of the know-how modality and the (monotonic) neighborhood semantics for the standard modality. We show that this new semantics is equivalent to the original Kripke semantics in terms of the validities. A key result is a representation theorem showing that the more abstract Kripke neighborhood models can be represented by the concrete Kripke models with action transitions modulo the valid formulas. We prove the completeness of the logic for the neighborhood semantics. The neighborhood semantics can be adapted to other variants of logics of knowing how. It provides us a powerful technical tool to study these logics while preserving the basic semantic intuition.

Automated summary

This paper introduces an alternative semantics for the non-normal logic of knowing how, showing its equivalence to the original Kripke semantics and proving the completeness of the logic. The neighborhood semantics can be a powerful technical tool for studying similar logics while preserving basic semantic intuition.