Displacement logic for anaphora
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The displacement calculus of Morrill, Valentín and Fadda (2011)  aspires to replace the calculus of Lambek (1958)  as the foundation of categorial grammar by accommodating intercalation as well as concatenation while remaining free of structural rules and enjoying Cut-elimination and its good corollaries. Jäger (2005)  proposes a type logical treatment of anaphora with syntactic duplication using limited contraction. Morrill and Valentín (2010)  apply (modal) displacement calculus to anaphora with lexical duplication and propose extension with a negation as failure in conjunction with additives to capture binding conditions. In this paper we present an account of anaphora developing characteristics and employing machinery from both of these proposals.
CitationMorrill, G.; Valentin Fernández, J. Displacement logic for anaphora. "Journal of computer and system sciences", Març 2014, vol. 80, núm. 2, p. 390-409.