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Auteur: Daniel GUTZMANN

Towards true multi-dimensionality. A compositional logic for expressive content

Abstract/Résumé: Despite its impact, Potts's (2005) logic LCI and its offsprings (Gutzmann 2011; McCready2010) faces two problems regarding compositionality and the proliferation of types and combinatoric rules. Both can be solved by a reformulation of the framework. Composition in LCI can be sketched as follows. If an expressive reaches propositional status, it is isolated from the descriptive content and becomes inaccessible for further modification. To ensure that it is nonetheless interpreted, the entire tree is interpreted as a pair whose first projection is the truth-conditional content and whose second dimension is the collection of all dangling expressive propositions. As noted elsewhere, this is not compositional, as it uses mediate expressions to calculate the meaning of a complex expressions. There are some proposals to account for expressive content in a compositional way (Barker et al. 2010, Giorgolo/Asudeh 2012; Kubota/Uegaki 2011), but at the cost of introducing a mightier machinery. Instead, compositionality can be reached by true multidimensionality. The basic idea is that every natural language expression is associated with a 3-dimensional logical expression. The 1st dimension contains the descriptive content, while the 3rd dimension stores satisfied expressive content. The key component is the 2nd dimension which keeps track of expressions that are “active” for calculating expressive content. Crucially, if we have a pure descriptive expression, the 2nd dimension will be the same as the 1st. This makes a composition rule for multidimensional application possible in which we have functional application in the first two dimensions (and union in the third). In addition, we only need another rule for expressive elimination which “empties” the second dimension by shifting expressive propositions to the third dimension and copying the first to the second. (Compare this to McCready's LCI+, which uses four application and two elimination rules, and two new types, such that a lot of LCI's original simplicity gets lost). Since each dimension is present at every point of the derivation, the entire composition respects compositionality. To account for restrictions, we assume that lexical entries are at most 2 dimensional and that a set of lexical extension rules maps then on proper 3-dimensional objects. With these rules, we can analyze the cases problematic for LCI (mixed expressive, expressive modifiers) and additional problems that also the extensions of LCI cannot deal with (quantification, abstraction). Furthermore, we show that the framework can be extended to accommodate other multidimensional phenomena like appositives (which are non-expressive) or focus (which interacts with descriptive content).