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Introduction to a Hypergraph Logic Unifying Different Variants of the Lambek Calculus

by   Tikhon Pshenitsyn, et al.

In this paper hypergraph Lambek calculus (HL) is presented. This formalism aims to generalize the Lambek calculus (L) to hypergraphs as hyperedge replacement grammars extend context-free grammars. In contrast to the Lambek calculus, HL deals with hypergraph types and sequents; its axioms and rules naturally generalize those of L. Consequently, certain properties (e.g. the cut elimination) can be lifted from L to HL. It is shown that L can be naturally embedded in HL; moreover, a number of its variants (LP, NL, NLP, L with modalities, L^∗(1), L^R) can also be embedded in HL via different graph constructions. We also establish a connection between HL and Datalog with embedded implications. It is proved that the parsing problem for HL is NP-complete.


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