Nondeterministic Phase Semantics and the Undecidability of Boolean BI

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 the core of separation and spatial logics. For this, we define a complete phase semantics suitable 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 the elementary fragment of ILL, which is both undecidable and complete for trivial phase semantics. Thus, we obtain the undecidability of BBI.

Mots clés: Model theory; Boolean BI; Minsky machines encoding; Decidability

Domaines: Logique en informatique [cs.LO]

Dominique Larchey-Wendling, Didier Galmiche. Nondeterministic Phase Semantics and the Undecidability of Boolean BI. ACM Transactions on Computational Logic, 2013, 14 (1), pp.6. ⟨10.1145/2422085.2422091⟩. ⟨hal-01256956⟩