Studia Logica

, Volume 87, Issue 2–3, pp 145–169 | Cite as

Type Logics and Pregroups



We discuss the logic of pregroups, introduced by Lambek [34], and its connections with other type logics and formal grammars. The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whose universe is an arbitrary monoid.


bilinear algebra pregroup Lambek calculus substructural logics 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Research Group on Mathematical LinguisticsRovira i Virgili University in TarragonaTarragonaSpain
  2. 2.Faculty of Mathematics and Computer ScienceAdam Mickiewicz University in PoznańPoznanPoland
  3. 3.Faculty of Mathematics and Computer ScienceUniversity of Warmia and Mazury in OlsztynOlsztynPoland

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