Studia Logica

, Volume 89, Issue 1, pp 1–18 | Cite as

Infinitary Action Logic: Complexity, Models and Grammars



Action logic of Pratt [21] can be presented as Full Lambek Calculus FL [14, 17] enriched with Kleene star *; it is equivalent to the equational theory of residuated Kleene algebras (lattices). Some results on axiom systems, complexity and models of this logic were obtained in [4, 3, 18]. Here we prove a stronger form of *-elimination for the logic of *-continuous action lattices and the \({\Pi_{1}^{0}}\) –completeness of the equational theories of action lattices of subsets of a finite monoid and action lattices of binary relations on a finite universe. We also discuss possible applications in linguistics.


Kleene algebra action algebra relation algebra categorial grammar 


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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceAdam Mickiewicz University in Poznań Research Group on Mathematical Linguistics Rovira i Virgili University in TarragonaPolandSpain
  2. 2.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznańPoland

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