Abstract
Pregroups, introduced in Lambek [12], are a generalization of partially ordered groups. In [5], we have proven several theorems on pregroups and grammars based on the calculus of free pregroups, in particular, the weak equivalence of these grammars and context-free grammars. In the present paper, we obtain further results of that kind. We consider left and right pregroups, study concrete left and right pregroups consisting of monotone functions on a poset and of monotone relations on a poset, and adjust the equivalence theorem to grammars based on left (right) pregroups.
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Buszkowski, W. (2002). Pregroups: Models and Grammars. In: de Swart, H.C.M. (eds) Relational Methods in Computer Science. RelMiCS 2001. Lecture Notes in Computer Science, vol 2561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36280-0_3
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DOI: https://doi.org/10.1007/3-540-36280-0_3
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