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Journal of Logic and Computation 2006 16(1):27-59; doi:10.1093/logcom/exi071
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Vol. 16 No. 1, © The Author, 2006. Published by Oxford University Press. All rights reserved.

Original Articles

A Hybrid Intuitionistic Logic: Semantics and Decidability

Rohit Chadha1, Damiano Macedonio2 and Vladimiro Sassone3

1 Center for Logic and Computation, IST, Lisboa 1049-001, Portugal. Email: rchadha{at}math.ist.utl.pt, 2 Dipartimento di Informatica Universitá Ca' Foscari 30172 Venezia, Italy. Email: mace{at}dsi.unive.it, 3 ECS, University of Southampton. Email: vs{at}ecs.soton.ac.uk

We study a hybrid intuitionistic modal logic suitable for reasoning about distribution of resources. The modalities of the logic allow validation of properties in a particular place, in some place and in all places. We provide a sound and complete Kripke semantics. We also define a sound and complete birelational semantics, and show that it enjoys the finite model property: if a judgement is not valid in the logic, then there is a finite birelational counter-model. Hence, we prove that the logic is decidable.

Keywords: Spatial distribution of resources, spatial modalities, Kripke and birelational semantics, soundness and completeness, finite-model property

Received 15 January 2005.


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