Temporal epistemic logic is a well-established framework for expressing agents knowledge and how it evolves over time. Within language-based security these are central issues, for instance in the context of declassification. We propose to bring these two areas together. The paper presents a computational model and an epistemic temporal logic used to reason about knowledge acquired by observing program outputs. This approach is shown to elegantly capture standard notions of noninterference and declassification in the literature as well as information flow properties where sensitive and public data intermingle in delicate ways.
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