Interpolation in fragments of classical linear logic
Journal of Symbolic Logic
Displaying modal logic
Formalised Cut Admissibility for Display Logic
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
State of the union: type inference via Craig interpolation
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Quantified invariant generation using an interpolating saturation prover
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
A Unified Display Proof Theory for Bunched Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Applications of craig interpolants in model checking
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
MERIT: an interpolating model-checker
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
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We give a general proof-theoretic method for proving Craig interpolation for displayable logics, based on an analysis of the individual proof rules of their display calculi. Using this uniform method, we prove interpolation for a spectrum of display calculi differing in their structural rules, including those for multiplicative linear logic, multiplicative additive linear logic and ordinary classical logic. Our analysis of proof rules also provides new insights into why interpolation fails, or seems likely to fail, in many substructural logics. Specifically, contraction appears particularly problematic for interpolation except in special circumstances.