Abstract
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.
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Buszkowski, W., Palka, E. Infinitary Action Logic: Complexity, Models and Grammars. Stud Logica 89, 1–18 (2008). https://doi.org/10.1007/s11225-008-9116-7
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DOI: https://doi.org/10.1007/s11225-008-9116-7