Abstract
In this paper, we propose a ternary knowing how operator to express that the agent knows how to achieve \(\varphi \) given \(\psi \) while maintaining \(\chi \) in-between. It generalizes the logic of goal-directed knowing how proposed by Wang in [10]. We give a sound and complete axiomatization of this logic.
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Notes
- 1.
See [12] for a survey.
- 2.
- 3.
This ternary modality is first proposed and discussed briefly in the full version of [10], which is under submission.
- 4.
We can obtain the corresponding axioms by taking the intermediate constraint as \(\top \). Note that in [10], we use the name WKKh for \(\mathtt {UKh}\).
- 5.
In [10], the canonical models are much simpler: we just need MCSs and the canonical relations are simply labeled by \(\langle \psi , \varphi \rangle \) for \(\mathcal {K}h{(\psi ,\varphi )}\in \varGamma \).
- 6.
However, the announcement operator \([\varphi ]\) is not reducible in \(\mathbf {L_{Khm}}\) as discussed in the full version of [10] which is under submission.
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Li, Y., Wang, Y. (2017). Achieving While Maintaining:. In: Ghosh, S., Prasad, S. (eds) Logic and Its Applications. ICLA 2017. Lecture Notes in Computer Science(), vol 10119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54069-5_12
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DOI: https://doi.org/10.1007/978-3-662-54069-5_12
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