Displacement logic for anaphora

• Logical grammar account of anaphora and binding principles.
• Both syntactic (limited contraction) and lexical (displacement logic) duplication.
• Combining additives, S4 modality, limited contraction and displacement logic.
• Proposal of negation as failure in categorial grammar.
• Proof-theoretical study including Cut-elimination and Curry–Howard labelling.

The displacement calculus of Morrill, Valentín and Fadda (2011) [25] aspires to replace the calculus of Lambek (1958) [13] 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) [11] proposes a type logical treatment of anaphora with syntactic duplication using limited contraction. Morrill and Valentín (2010) [24] 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.