Memoization in Constraint Logic Programming

This paper shows how to apply memoization (caching of subgoals and associated answer substitutions) in a constraint logic programming setting. The research is is motivated by the desire to apply constraint logic programming (CLP) to problems in natural language processing that involve (constraint) interleaving or coroutining, such as GB and HPSG parsing.Comment: 11 page

Proof Nets and the Complexity of Processing Center-Embedded Constructions

This paper shows how proof nets can be used to formalize the notion of ``incomplete dependency'' used in psycholinguistic theories of the unacceptability of center-embedded constructions. Such theories of human language processing can usually be restated in terms of geometrical constraints on proof nets. The paper ends with a discussion of the relationship between these constraints and incremental semantic interpretation.Comment: To appear in Proceedings of LACL 95; uses epic.sty, eepic.sty, rotate.st

Type-driven semantic interpretation and feature dependencies in R-LFG

Once one has enriched LFG's formal machinery with the linear logic mechanisms needed for semantic interpretation as proposed by Dalrymple et. al., it is natural to ask whether these make any existing components of LFG redundant. As Dalrymple and her colleagues note, LFG's f-structure completeness and coherence constraints fall out as a by-product of the linear logic machinery they propose for semantic interpretation, thus making those f-structure mechanisms redundant. Given that linear logic machinery or something like it is independently needed for semantic interpretation, it seems reasonable to explore the extent to which it is capable of handling feature structure constraints as well. R-LFG represents the extreme position that all linguistically required feature structure dependencies can be captured by the resource-accounting machinery of a linear or similiar logic independently needed for semantic interpretation, making LFG's unification machinery redundant. The goal is to show that LFG linguistic analyses can be expressed as clearly and perspicuously using the smaller set of mechanisms of R-LFG as they can using the much larger set of unification-based mechanisms in LFG: if this is the case then we will have shown that positing these extra f-structure mechanisms is not linguistically warranted.Comment: 30 pages, to appear in the the ``Glue Language'' volume edited by Dalrymple, uses tree-dvips, ipa, epic, eepic, fullnam

Multiplicative structure of 2x2 tropical matrices

We study the algebraic structure of the semigroup of all $2 \times 2$ tropical matrices under multiplication. Using ideas from tropical geometry, we give a complete description of Green's relations and the idempotents and maximal subgroups of this semigroup.Comment: 21 pages, 5 figure