Bilattice logic properly displayed

Giuseppe Greco, Fei Liang*, Alessandra Palmigiano, Umberto Rivieccio

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


We introduce a proper multi-type display calculus for bilattice logic (with conflation) for which we prove soundness, completeness, conservativity, standard subformula property and cut elimination. Our proposal builds on the product representation of bilattices and applies the guidelines of the multi-type methodology in the design of display calculi.

Original languageEnglish
Pages (from-to)138-155
Number of pages18
JournalFuzzy Sets and Systems
Publication statusPublished - 15 May 2019
Externally publishedYes


This research is supported by the NWO Vidi grant 016.138.314, the NWO Aspasia grant 015.008.054, and the Delft Technology Fellowship awarded to the third author in 2013.

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek015.008.054, 016.138.314


    • Algebraic proof theory
    • Bilattice logic
    • Cut elimination
    • Display calculi
    • Many-valued logics
    • Multi-type calculi
    • Non-classical logics
    • Sequent calculi
    • Substructural logics


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