Subsequent work on referring expression generation has expanded the logical framework to allow reference by negation (the dog that is not black) and references to multiple entities (the brown or black dogs) (van Deemter, 2002), explored different search algorithms for finding the minimal description (e.g., Horacek (2003)) and offered different representation frameworks like graph theory (Krahmer et al., 2003) as alternatives to AVMs.
all these approaches are based on very similar formalisations of the problem, and all make the following assumptions: 1.