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Full Lambek Calculus with Contraction is Undecidable

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    0442807 - ÚI 2017 RIV US eng J - Journal Article
    Chvalovský, Karel - Horčík, Rostislav
    Full Lambek Calculus with Contraction is Undecidable.
    Journal of Symbolic Logic. Roč. 81, č. 2 (2016), s. 524-540. ISSN 0022-4812. E-ISSN 1943-5886
    R&D Projects: GA ČR GAP202/11/1632
    Institutional support: RVO:67985807
    Keywords : substructural logic * full Lambek calculus * contraction rule * square-increasing residuated lattice * equational theory * decidability
    Subject RIV: BA - General Mathematics
    Impact factor: 0.511, year: 2016

    We prove that the set of formulae provable in the full Lambek calculus with the structural rule of contraction is undecidable. In fact, we show that the positive fragment of this logic is undecidable.
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