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A Hybrid Intuitionistic Logic: Semantics and Decidability

A Hybrid Intuitionistic Logic: Semantics and Decidability
A Hybrid Intuitionistic Logic: Semantics and Decidability
An intuitionistic, hybrid modal logic suitable for reasoning about distribution of resources was introduced by Jia and Walker. The modalities of the logic allow validation of properties in a particular place, in some place and in all places. We give a sound and complete Kripke semantics for the logic extended with disjunctive connectives. The extended logic can be seen as an instance of Hybrid IS5. We also give 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.
spatial distribution of resources, spatial modalities, Kripke and birelational semantics, soundness and completeness, finite-model property
27-59
Chadha, R.
3b2e898a-478e-418a-9423-19952e596acf
Macedonio, D.
fd742c8a-820c-4ad2-a72a-94c44171917f
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7
Chadha, R.
3b2e898a-478e-418a-9423-19952e596acf
Macedonio, D.
fd742c8a-820c-4ad2-a72a-94c44171917f
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7

Chadha, R., Macedonio, D. and Sassone, V. (2006) A Hybrid Intuitionistic Logic: Semantics and Decidability. Journal of Logic and Computation, 16 (1), 27-59.

Record type: Article

Abstract

An intuitionistic, hybrid modal logic suitable for reasoning about distribution of resources was introduced by Jia and Walker. The modalities of the logic allow validation of properties in a particular place, in some place and in all places. We give a sound and complete Kripke semantics for the logic extended with disjunctive connectives. The extended logic can be seen as an instance of Hybrid IS5. We also give 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.

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More information

Published date: 2006
Additional Information: To appear
Keywords: spatial distribution of resources, spatial modalities, Kripke and birelational semantics, soundness and completeness, finite-model property
Organisations: Web & Internet Science

Identifiers

Local EPrints ID: 261850
URI: http://eprints.soton.ac.uk/id/eprint/261850
PURE UUID: 9a48c249-eefa-4a12-94b5-1165d0b22d28

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Date deposited: 27 Jan 2006
Last modified: 14 Mar 2024 06:59

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Contributors

Author: R. Chadha
Author: D. Macedonio
Author: V. Sassone

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