The Undecidability of Boolean BI through Phase Semantics

Dominique Larchey-Wendling (1) , Didier Galmiche (1)

1 TYPES - Logic, proof Theory and Programming

We solve the open problem of the decidability of Boolean BI logic (BBI), which can be considered as the core of separation and spatial logics. For this, we define a complete phase semantics for BBI and characterize it as trivial phase semantics. We deduce an embedding between trivial phase semantics for intuitionistic linear logic (ILL) and Kripke semantics for BBI. We single out a fragment of ILL which is both undecidable and complete for trivial phase semantics. Therefore, we obtain the undecidability of BBI.

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

Dominique Larchey-Wendling, Didier Galmiche. The Undecidability of Boolean BI through Phase Semantics. 25th Annual IEEE Symposium on Logic in Computer Science - LICS 2010, Jul 2010, Edinburgh, United Kingdom. pp.140-149, ⟨10.1109/LICS.2010.18⟩. ⟨hal-00577919⟩