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Neighbourhood Structures: Bisimilarity and Basic Model Theory

Helle Hvid Hansen ; Clemens Kupke ; Eric Pacuit.

Neighbourhood structures are the standard semantic tool used to reason about non-normal modal logics. The logic of all neighbourhood models is called classical modal logic. In coalgebraic terms, a neighbourhood frame is a coalgebra for the contravariant powerset functor composed with itself, denoted&nbsp;[&hellip;]

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Coinductive Foundations of Infinitary Rewriting and Infinitary Equational Logic

Jörg Endrullis ; Helle Hvid Hansen ; Dimitri Hendriks ; Andrew Polonsky ; Alexandra Silva.

We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has neither the need for ordinals nor for metric convergence.&nbsp;[&hellip;]

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