PP-2001-08: Analyzing the Core of Categorial Grammar

PP-2001-08: Areces, C and Bernardi, R. (2001) Analyzing the Core of Categorial Grammar. [Report]

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Even though residuation is at the core of Categorial Grammar, it is not always immediate to realize how standard logic systems like Multi-modal Categorial Type Logics (MCTL) actually embody this property. In this paper we focus on the basic system NL and its extension with unary modalities NL(\Diamond), and we spell things out by means of Display Calculi (DC). The use of structural operators in DC permits a sharp distinction between the core properties we want to impose on the logic system and the way these properties are projected into the logic operators. We will show how we can obtain Lambek residuated triple \backslash, / and \bullet of binary operators, and how the operators \Diamond and \Box^\downarrow introduced by Moortgat are indeed their unary counterpart. In the second part of the paper we turn to other important algebraic properties which are usually investigated in conjunction with residuation: Galois and dual Galois connections. Again, DC let us readily define logic calculi capturing them, and we will discuss different possibilities in which the logic operators so obtained can interact with those obtained from residuation. We also provide preliminary ideas on how to use them when modeling linguistic phenomena.

Item Type: Report
Report Nr: PP-2001-08
Series Name: Prepublication (PP) Series
Year: 2001
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/50

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