Abstract
This paper describes a proof search system for a modal substructural (concatenation) logic based on Gabbay's Labelled Deductive System (LDS) as a case study. The logic combines resource (linear or Lambek Calculus) with modal features, and has applications in AI and natural language processing. We present axiomatic and LDS style proof theories and semantics for the logic, with soundness and completeness results. For non-classical logic theorem proving, we show that LDS is flexible and generic, and can be mechanised directly. This partially verifies Gabbay's open claims that LDS is suitable to study combinations of logics. We believe our approach can be extended to any variant which combines substructurality and modality.
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