Labelled Tableaux for Linear Time Bunched Implication Logic

In this paper, we define the logic of Linear Temporal Bunched Implications ( LTBI ), a temporal extension of the Bunched Implications logic BI that deals with resource evolution over time, by combining the BI separation connectives and the LTL temporal connectives. We first present the syntax and semantics of LTBI and illustrate its expressiveness with a significant example. Then we introduce a tableau calculus with labels and constraints, called T LTBI , and prove its soundness w.r.t. the Kripke-style semantics of LTBI . Finally we discuss and analyze the issues that make the completeness of the calculus not trivial in the general case of unbounded timelines and explain how to solve the issues in the more restricted case of bounded timelines.