Abstract
We propose a separation logic where resources are histories (sequences) of epistemic actions so that resource update means concatenation of histories and resource decomposition means splitting of histories. This separation logic, called AMHSL, allows us to reason about the past: does what is true now depend on what was true in the past, before certain actions were executed? We show that the multiplicative connectives can be eliminated from a logical language with also epistemic and action model modalities, if the horizon of epistemic actions is bounded.
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Notes
- 1.
The \(*\) of multiplicative conjunction \(\varphi *\psi \) is as the \(*\) in \(*\)-valid, but the latter is motivated by the Kleene-\(*\) of arbitrary iteration.
- 2.
They are all even \(*\)-valid in the \(\models \) semantics, on models \(\mathcal {M}\mathcal {E}^\omega \), but not on models \(\mathcal {M}\mathcal {E}^\textbf{max}\) as that would need relativization of each axiom to \(\lnot [h]\bot \rightarrow \). However we will not use (nor claim) that.
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Acknowledgements
We very much wish to thank the reviewers for their comments. A reviewer pointed out an error in the proof of the case \(c([h](\varphi *\psi ))\) of Lemma 5, that needed repair by strengthening the weight of case \(c(\varphi *\psi )\) in Definition 9. Another reviewer mentioned that AMHSL allows to reason about the length of histories. We added an example.
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Ditmarsch, H.v., Galmiche, D., Gawek, M. (2023). A Separation Logic with Histories of Epistemic Actions as Resources. In: Hansen, H.H., Scedrov, A., de Queiroz, R.J. (eds) Logic, Language, Information, and Computation. WoLLIC 2023. Lecture Notes in Computer Science, vol 13923. Springer, Cham. https://doi.org/10.1007/978-3-031-39784-4_10
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