Abstract
We propose an epistemic strategy logic with future and past time operators, called \(\text {SLKP}\), for Strategy Logic with Knowledge of the Past. With \(\text {SLKP}\) we can model mutually observed moves/actions in strategic contexts. In a semantic game, agents may completely or partially observe other agents’ moves, their moves may depend on their knowledge of other players’ strategies, and their knowledge may depend on the history of their own or other’s moves. The logic \(\text {SLKP}\) also allows us to describe temporal properties involving past, future, and composed tenses such as future perfect or counterfactual assertions. We illustrate SLKP by formalising the quantum cryptography protocol BB84, with the purpose to initiate an integrated epistemic and strategic treatment of agent interactions in quantum systems.
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Notes
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Configurations are commonly referred to as states. In this paper we use the word configuration instead, to avoid ambiguities since state is also used in its physical sense, to designate the state of a photon in
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Acknowledgement
We thank the reviewers for their helpful comments. We acknowledge financial support from ERC project EPS 313360. Hans van Ditmarsch is also affiliated to IMSc, Chennai, India.
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Chareton, C., van Ditmarsch, H. (2017). Strategic Knowledge of the Past in Quantum Cryptography. In: Baltag, A., Seligman, J., Yamada, T. (eds) Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science(), vol 10455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55665-8_24
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