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Security breaches often arise as a result of users' failure to comply with security policies. Such failures to comply may simply be innocent mistakes. However, there is evidence that, in some circumstances, users choose not to comply because they perceive that the security benefit of compliance is outweighed by the cost that is the impact of compliance on their abilities to complete their operational tasks. That is, they perceive security compliance as hindering their work. The 'compliance budget' is a concept in information security that describes how the users of an organization's systems determine the extent to which they comply with the specified security policy. The purpose of this paper is to initiate a qualitative logical analysis of, and so provide reasoning tools for, this important concept in security economics for which quantitative analysis is difficult to establish. We set up a simple temporal logic of preferences, with a semantics given in terms of histories and sets of preferences, and explain how to use it to model and reason about the compliance budget. The key ingredients are preference update, to account for behavioural change in response to policy change, and an ability to handle uncertainty, to account for the lack of quantitative measures.

We introduce a substructural modal logic of utility that can be used to reason aboutoptimality with respect to properties of states. Our notion of state is quite general, and is able to represent resource allocation problems in distributed systems. The underlying logic is a variant of the modal logic of bunched implications, and based on resource semantics, which is closely related to concurrent separation logic. We consider a labelled transition semantics and establish conditions under which Hennessy—Milner soundness and completeness hold. By considering notions of cost, strategy and utility, we are able to formulate characterizations of Pareto optimality, best responses, and Nash equilibrium within resource semantics. We also show that our logic is able to serve as a logic for a fully featured process algebra and explain the interaction between utility and the structure of processes.