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Lambek Calculus with Conjugates

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Abstract

We study an expansion of the Distributive Non-associative Lambek Calculus with conjugates of the Lambek product operator and residuals of those conjugates. The resulting logic is well-motivated, under-investigated and difficult to tackle. We prove completeness for some of its fragments and establish that it is decidable. Completeness of the logic is an open problem; some difficulties with applying the usual proof method are discussed.

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Acknowledgements

This work is supported by the Czech Science Foundation Grant Number GJ18-19162Y. The authors are grateful to Wojciech Buszkowski, Tommaso Moraschini, audiences of the CLMPST 2019 and the North American meeting of the ASL 2019, and anonymous referees for a number of useful comments.

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  1. Institute of Computer Science, The Czech Academy of Sciences, Pod Vodárenskou věží 271/2, Prague, Czech Republic

    Igor Sedlár & Andrew Tedder

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  1. Igor Sedlár
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  2. Andrew Tedder
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Correspondence to Andrew Tedder.

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Sedlár, I., Tedder, A. Lambek Calculus with Conjugates. Stud Logica 109, 447–470 (2021). https://doi.org/10.1007/s11225-020-09913-2

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