1. Generation of Referring Expressions (GRE) The Incremental Algorithm Dale & Reiter (1995)

2. The task: GRE NLG can have different kinds of inputs: ‘Flat’ data (collections of atoms, e.g., in the tables of a database) Logically complex data In both cases, unfamiliar constants may be used, and this is sometimes unavoidable

3. No familiar constant available: 1. The referent has a familiar name, but it’s not unique, e.g., ‘John Smith’ 2. The referent has no familiar name: trains, furniture, trees, atomic particles, … ( In such cases, databases use database keys, e.g., ‘Smith$73527$’, ‘TRAIN-3821’ ) 3. Similar: sets of objects.

4. Natural Languages are too economic to have a proper name for everything Names may not even be most appropriate So, speakers/NLG systems have to invent ways of referring to things. E.g., ‘the 7:38 Trenton express’

5. Dale & Reiter: best description fulfils Gricean maxims. (Quality:) list properties truthfully (Quantity:) list sufficient properties to allow hearer to identify referent – but not more (Relevance:) use properties that are of interest in themselves * (Manner:) be brief * Slightly different from D&R 1995

6. D&R’s expectation: Violation of a maxim leads to implicatures. For example, [Quantity] ‘the black pitbull’ (when there is only one). [Manner] ‘Get the cordless drill that’s in the toolbox’ (Appelt). There’s just one problem: …

7. …people don’t speak this way For example, [Manner] ‘the red chair’ (when there is only one red object in the domain). [Quantity] ‘I broke my arm’ (when I have two). General: empirical work shows much redundancy Similar for other maxims, e.g., [Quality] ‘the man with the martini’ (Donellan)

8. Example Situation a, £100 b, £150 c, £100 d, £150 e, £? SwedishItalian

9. Formalized in a KB Type: furniture (abcde), desk (ab), chair (cde) Origin: Sweden (ac), Italy (bde) Colours: dark (ade), light (bc), grey (a) Price: 100 (ac), 150 (bd), 250 ({}) Contains: wood ({}), metal ({abcde}), cotton(d) Assumption: all this is shared knowledge.

10. Violations of … Manner: * ‘The £100 grey Swedish desk which is made of metal’ (Description of a) Relevance: ‘The cotton chair is a fire hazard? ?Then why not buy the Swedish chair?’ (Descriptions of d and c respectively)

11. Consider the following formalization: Full Brevity: Never use more than the minimal number of properties required for identification (Dale 1989) An algorithm:

12. Dale 1989: 1. Check whether 1 property is enough 2. Check whether 2 properties is enough …. Etc., until success {minimal description is generated} or failure {no description is possible}

13. Problem: exponential complexity Worst-case, this algorithm would have to inspect all combinations of properties. n properties combinations. Recall: one grain of rice on square one; twice as many on any subsequent square. Some algorithms may be faster, but … Theoretical result: algorithm must be exponential in the number of properties.

14. D&R conclude that Full Brevity cannot be achieved in practice. They designed an algorithm that only approximates Full Brevity: the Incremental Algorithm (IA).

15. Psycholinguistic inspiration behind IA (e.g. Pechmann 89; overview in Levelt 89) Speakers often include “unnecessary modifiers” in their referring expressions Speakers often start describing a referent before they have seen all distractors (as shown by eye-tracking experiments) Some Attributes (e.g. Colour) seem more likely to be noticed and used than others Some Attributes (e.g., Type) contribute strongly to a Gestalt. Gestalts help readers identify referents. (“The red thing” vs. “the red bird”) Let’s start with a simplified version of IA, which uses properties rather than pairs. Type and head nouns are ignored, for now.

16. Incremental Algorithm (informal): Properties are considered in a fixed order: P = A property is included if it is ‘useful’: true of target; false of some distractors Stop when done; so earlier properties have a greater chance of being included. (E.g., a perceptually salient property) Therefore called preference order.

17. r = individual to be described P = list of properties, in preference order P is a property L= properties in generated description (Recall: we’re not worried about realization today)

19. P = < desk (ab), chair (cde), Swedish (ac), Italian (bde), dark (ade), light (bc), grey (a), 100£ ({ac}), 150£(bd), 250£ ({}), wooden ({}), metal (abcde), cotton ({d}) > Domain = {a,b,c,d,e}. Now describe: a = d = e =

20. P = < desk (ab), chair (cde), Swedish (ac), Italian (bde), dark (ade), light (bc), grey (a), 100£ (ac),200£ (bd),250£ ({}), wooden ({}), metal (abcde), cotton (d) > Domain = {a,b,c,d,e}. Now describe: a = d = (Nonminimal) e = (Impossible)

21. Incremental Algorithm It’s a hillclimbing algorithm: ever better approximations of a successful description. ‘Incremental’ implies no backtracking. Not always the minimal number of properties.

22. Incremental Algorithm Logical completeness: A unique description is found in finite time if there exists one. (Given reasonable assumptions, see van Deemter 2002) Computational complexity: Assume that testing for usefulness takes constant time. Then worst-case time complexity is O(n p ) where n p is the number of properties in P.

23. Better approximation of Full Brevity (D&R 1995) Attribute + Value model: Properties grouped together as in original example: Origin: Sweden, Italy,... Colour: dark, grey,... Optimization within the set of properties based on the same Attribute

24. Incremental Algorithm, using Attributes and Values r = individual to be described A = list of Attributes, in preference order Def: = Value j of Attribute i L= properties in generated description

26. FindBestValue(r,A): - Find Values of A that are true of r, while removing some distractors (If these don’t exist, go to next Attribute) - Within this set, select the Value that removes the largest number of distractors - If there’s a tie, select the most general one - If there’s still a tie, select an arbitrary one

27. Example: D = {a,b,c,d,f,g} Type: furniture (abcd), desk (ab), chair (cd) Origin: Europe (bdfg), USA (ac), Italy (bd) Describe a: {desk, American} (furniture removes fewer distractors than desk) Describe b: {desk, European} (European is more general than Italian) N.B. This disregards relevance, etc.

28. Exercise on Logical Completeness: Construct an example where no description is found, although one exists. Hint: Let Attribute have Values whose extensions overlap.

29. Example: D = {a,b,c,d,e,f} Contains: wood (abe), plastic (acdf) Colour: grey (ab), yellow (cd) Describe a: {wood, grey,...} - Failure (wood removes more distractors than plastic) Compare: Describe a: {plastic, grey} - Success

30. Complexity of the algorithm n d = nr. of distractors n l = nr. of properties in the description n v = nr. of Values ( for all Attributes ) According to D&R: O(n d n l ) (Typical running time) Alternative assessment: O(n v ) (Worst-case running time)

31. Minor complication: Head nouns Another way in which human descriptions are nonminimal A description needs a Noun, but not all properties are expressed as Nouns Example: Suppose Colour was the most-preferred Attribute, and suppose target = a

32. Colours: dark (ade), light (bc), grey (a) Type: furniture (abcde), desk (ab), chair (cde) Origin: Sweden (ac), Italy (bde) Price: 100 (ac), 150 (bd), 250 ({}) Contains: wood ({}), metal ({abcde}), cotton(d) target = a Describe a: {grey} ‘The grey’ ? (Not in English)

33. D&R’s repair: Assume that Values of the Attribute Type can be expressed in a Noun. After the core algorithm: - check whether Type is represented. - if not, then add the best Value of the Type Attribute to the description

34. Versions of Dale and Reiter’s Incremental Algorithm (IA) have often been implemented Still the starting point for many new algorithms. But how human-like is the output of the IA really? The paper does not contain an evaluation of the algorithms discussed

35. Limitations of the algorithm 1. Redundancy exists, but not for principled reasons, e.g., for - marking topic changes, etc. (Corpus work by Pam Jordan et. al.) - making it easy to find the referent (Experimental work by Paraboni et al.)

36. Limitations of the algorithm 2. Targets are individual objects, never sets. What changes when target = {a,b,c} ? 3. Incremental algorithm uses only conjunctions of atomic properties. No negations, disjunctions, etc.

37. Limitations of D&R 4. No relations with other objects, e.g., ‘the orange on the table’. 5. Differences in salience are not taken into account. When we say “the dog”, does this mean that there is only one dog in the world? 6. Language realization is disregarded. 7. Logical completeness is violated when Attribute has overlapping Values

38. Limitations of D&R 8. Calculation of complexity is iffy Role of “Typical” run time and length of description is unclear Greedy Algorithm (GA) dismissed even though it has polynomial complexity GA: always choose the property that removes the maximum number of distractors

39. More fundamental assumptions Speaker and Hearer have shared knowledge This knowledge can be formalised using atomic statements (plus, implicitly, negations of atomic statements) The aim of GRE is to identify the target referent uniquely. (I.e., the aim is to construct a “distinguishing description” of the referent.) Linguistic Realisation comes after Content Determination

40. Discussion: How bad is it for a GRE algorithm to take exponential time choosing the best RE? How do human speakers cope? More complex types of referring expressions problem becomes even harder Restrict to combinations whose length is less than x problem not exponential. Example: descriptions containing at most n properties (Full Brevity)

41. Linguist’s view We don’t pretend to mirror psychologically correct processes. (It’s enough if GRE output is correct). So why worry if our algorithms are slow?

42. Mathematicians’ view structure of a problem becomes clear when no restrictions are put. Practical addition: What if the input does not conform with these restrictions? (GRE does not control its own input!)

43. A compromise view Compare with Description Logic: - Increasingly complex algorithms … - that tackle larger and larger fragments of logic … - and whose complexity is ‘conservative’ When looking at more complex phenomena, take care not to slow down generation of simple cases too much