COMPLEXITY OF THE INFINITARY LAMBEK CALCULUS WITH KLEENE STAR
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Abstract We consider the Lambek calculus, or noncommutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega $ -rule, and prove that the derivability problem in this calculus is $\Pi _1^0$ -hard. This solves a problem left open by Buszkowski (2007), who obtained the same complexity bound for infinitary action logic, which additionally includes additive conjunction and disjunction. As a by-product, we prove that any context-free language without the empty word can be generated by a Lambek grammar with unique type assignment, without Lambek’s nonemptiness restriction imposed (cf. Safiullin, 2007).
2009 ◽
Vol 53
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pp. 547-561
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2007 ◽
Vol 18
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pp. 1293-1302
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1970 ◽
Vol 16
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pp. 201-202
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2014 ◽
Vol 577
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pp. 917-920
2011 ◽
Vol 14
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pp. 34-71
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2013 ◽
Vol 24
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pp. 1067-1082
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