Adding the example of unbounded monotone functions.
]]>Adding explicit definitions for preordered monoid and pomonoid. I hope this clears some of the confusion.
]]>link to posets
DavidWhitten
]]>I fixed the omission of the homomorphic image part in my previous edit and added the respective references to Kobele and Kracht.
]]>Very likely my bad due to a false recollection of their argument, thanks for giving it a reality check! Hopefully, I got at least the substance right, namely, that product pregroup grammars land you in type 0. I’ll attend to the paragraph as soon as I find a minute. Feel free to revise concerning the Kracht-Kobele paper as you have a better overview of the relevant literature hence how the pieces fit together.
]]>I expanded on product grammars and attributed some results here to Kobele-Kracht. Since I am unfamiliar with the Lambek and Genkin et al. source my way to weave them in is somewhat conjectural: feel free to correct me on this!
]]>Adding a mention of mildly context-sensitive pregroup grammars.
]]>Add linguistics context.
]]>fix typos
Richie
]]>Re #6: This blog post is saying something very similar, using a monoidal category for sentence derivations. “That is, a string is grammatical whenever there exists an arrow from the start symbol to in .” Morphisms in monoidal categories can be notated using string diagrams.
]]>It should be pointed out (somewhere, sometime) the relationship between pregroups and residuated lattices, which appears in much older work of Lambek dating back at least to the 60’s. This work of Lambek was all of a piece, connecting module theory to proof theory to linguistics. I would like to add some of this history at some point.
]]>removing capital letter
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