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Communication Dans Un Congrès Année : 2020

Indexed Frames and Hybrid Logics

Résumé

We define and study the notion of 'indexed frames', i.e., tuples (W1, W2, R1, R2) where each Ri is a binary relation on W1 × W2 such that Ri(w1, w2)(v1, v2) implies wi = vi. They generalise, among other things, products of Kripke frames. We show that the logic of indexed frames is the fusion logic K ⊕ K. We show the relation between indexed frames and relativised products and we obtain the different logics of indexed frames when we impose certain constraints on the relations R1 and R2. Indexed frames were seemingly first used in [8], whithin a proposal for a broader multi-modal framework called Epistemic Logic of Friendship, allowing for both an epistemic accessibility relation and a ‘friendship’ relation. The set of agents is encoded in the semantics, and these agents are named using nominal variables (a notion borrowed from hybrid logic) with the novelty that these nominals only refer to the elements of one of the sets. [7] provided an axiomatisation for a fragment of the language. We give a simplified proof of this result and we axiomatise an extension of this fragment
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Dates et versions

hal-02936432 , version 1 (11-09-2020)

Identifiants

  • HAL Id : hal-02936432 , version 1

Citer

Philippe Balbiani, Saúl Fernández González. Indexed Frames and Hybrid Logics. International Conference on Advances in Modal Logic (AiML 2020), University of Helsinki, Finland, Aug 2020, Helsinki, Finland. pp.56-72. ⟨hal-02936432⟩
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