Abstract
AbstractWe present a substructural epistemic logic, based on Boolean BI, in which the epistemic modalities are parametrized on agents’ local resources. The new modalities can be seen as generalizations of the usual epistemic modalities. The logic combines Boolean BI’s resource semantics—we introduce BI and its resource semantics at some length—with epistemic agency. We illustrate the use of the logic in systems modelling by discussing some examples about access control, including semaphores, using resource tokens. We also give a labelled tableaux calculus and establish soundness and completeness with respect to the resource semantics.
Highlights
The concept of resource is important in many fields including, among others, computer science, economics and security
We show that ERL is a conservative extension of Boolean BI (BBI) and Epistemic Logic (EL) and that, in the presence of additional properties of the partial resource monoid (Definition 1), there are some noteworthy relationships between modalities
In the case of the labelled calculus for ESL [14], which is an epistemic extension of BBI, we deal with constraints that are parametrized by agents but do not handle the presence of resources in the scope of the modal operators
Summary
The concept of resource is important in many fields including, among others, computer science, economics and security. An LSM model is a 4-tuple (W , R, R, V), where W is a set of worlds, R is a partial monoid of ‘resources’ (Res, , e), R ⊆ (W × Res) × (W × Res) is a ref lexive and transitive relation and V is an interpretation of propositional letters in ℘ (W × Res) Using the both dimensions of ‘worlds’ to handle, respectively, both classical modality and resource parametrization, we have w, r | ♦sφ iff there exist w ∈ W and r ∈ R such that r s ↓,. The idea of introducing agents, together with their knowledge, into the resource semantics has led to an Epistemic Separation Logic, called ESL, in which epistemic possible worlds are considered as resources [14] This logic corresponds to an extension of BBI with a knowledge modality, Ka, such that Kaφ means that the agent a knows that φ holds. The work presented here builds upon and strongly develops early ideas presented in [20]
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