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