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between neighborhood semantics for contingency logic on augmented frames and
Kripke semantics for that logic.
For further research we leave the question whether the axiomatization
CL
is
strongly complete with respect to the class of augmented neighbourhood frames
(see Section 5 for soundness). We further wish to investigate the suitable notion
of bisimulation on neighborhood models for CL , and to characterize CL as
a fragment within modal logic and within first-order logic, where [1, 7] may
help. Finally, we wish to advance the investigation of dynamics on neighborhood
models and in substructural logics, as initiated in studies like [9,15].
Acknowledgements. Jie Fan thanks support of the Major Project 12&ZD119
of National Social Science Foundation of China. Hans van Ditmarsch is also
aliated to IMSc, Chennai, as research associate. He acknowledges support from
ERC project EPS 313360. We thank Yanjing Wang for useful discussions and
the ICLA reviewers for their encouraging enthusiasm about our work.
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