
Eliminating the unit constant in the Lambek calculus with brackets
We present a translation of the Lambek calculus with brackets and the un...
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Proof Search on Bilateralist Judgments over Nondeterministic Semantics
The bilateralist approach to logical consequence maintains that judgment...
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Unbounded productform Petri nets
Computing steadystate distributions in infinitestate stochastic system...
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The Logic for a Mildly ContextSensitive Fragment of the LambekGrishin Calculus
While contextfree grammars are characterized by a simple prooftheoreti...
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Optimum Depth of the Bounded Pipeline
The paper is devoted to studying the performance of a computational pipe...
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On the Elementary Affine LambdaCalculus with and Without Fixed Points
The elementary affine lambdacalculus was introduced as a polyvalent set...
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Cirquent calculus in a nutshell
This paper is a brief and informal presentation of cirquent calculus, a ...
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A polynomial time algorithm for the Lambek calculus with brackets of bounded order
Lambek calculus is a logical foundation of categorial grammar, a linguistic paradigm of grammar as logic and parsing as deduction. Pentus (2010) gave a polynomialtime algorithm for determ ining provability of bounded depth formulas in the Lambek calculus with empty antecedents allowed. Pentus' algorithm is based on tabularisation of proof nets. Lambek calculus with brackets is a conservative extension of Lambek calculus with bracket modalities, suitable for the modeling of syntactical domains. In this paper we give an algorithm for provability the Lambek calculus with brackets allowing empty antecedents. Our algorithm runs in polynomial time when both the formula depth and the bracket nesting depth are bounded. It combines a Pentusstyle tabularisation of proof nets with an automatatheoretic treatment of bracketing.
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