In the present paper, a word expert's knowledge will be expressed, not as Prolog clauses defining sense/2 directly, but as a sequence of transfor­mation rules. For example, here is how we spec­ify a word expert which is able to disambiguate occurrences of interest:

worcLexpert sense := sense:add 6 <- word:interest®[0] o sense:6>1 <- word: in@[l] o sense: 1>5 <- word: '%'Q[-1] o end.

The first rule works as a default rule, which sim­ply assigns the most frequent sense to the word interest (6 in this case). If no other rules apply, this is the tag that the word will eventually get. The other rules dictate when - based on the context - a word should have its tag changed. The second rule is to be read "replace the tag for sense 6 with the tag for sense 1, if the next word is in". The third rule says "replace the tag for sense 1 with the tag for sense 5, if the pre­vious 'word' is '%'." The o-symbol is a compo­sition operator, and (R o Rs) basically means that the output of applying the rule R forms the input to the application of the rules Rs. Thus, rules are strictly order-dependent. Note, for ex­ample, that the third rule is applicable only if the second rule is.

Needless to say, the above rules are not at all sufficient for the task of disambiguating all uses of interest But the number of rules can be increased, and typically a word expert will

xThis word was of course not used the Swedish task, but is used here for expository reasons. The sense tags are numbers: 1="readiness to give attention", 5= "a company share", 6= "money paid for the use of money", etc.

Interestingly, a sequence of transformation rules can be translated into a set of axioms, expressed in first-order predicate logic, defining relation­ships between positions in a text, word forms, and senses (Lager, 2000; Lager & Nivre, 2001). For example, the meaning of the rules from the previous section can be spelled out as follows:

The idea is that for each rule in the sequence a new predicate Si is introduced, where the sub­script indicates where in the sequence the rule belongs. Semantically, Si relates a position to a sense, and the formulas define this predicate in terms of the predicate Si~\ plus a number of other predicates. Each Si corresponding to a replacement rule is defined by two sentences -one stating the conditions under which a sense tag is replaced with another sense tag, the other one stating the conditions under which the old sense tag is kept.

Given a suitable logical representation of a text, such as and given a suitable constructive proof method, the exact identity of the sense of an occurrence of the word interest - say the word at position 12 - will follow as a logical consequence of the theory formed by taking the union of the pre­vious two sets of formulas. For example, the formula 3x[S(12,x)] is a theorem, for which we can construct (only) the example x —» 5, and we have thus formally proved that this partic­ular occurrence of interest means "a share in a company" .

What we have here is something that we like to think of as word sense disambiguation as de­duction, in analogy to the ideas of parsing as deduction due to Pereira and Warren (1983).

Since the above formulas have already logic pro­gramming form, it is straightforward to trans­late them into Prolog. For example, the second and the third formulas can be translated as fol­lows:

s2(P0,l) :- sl(P0,6), PI is PO+i, w(Pl,in). s2(P0,X) :- sl(PO.X), PI is P0+1, \+ w(Pi,in).

To write Prolog procedures such as these by hand for many rules would be tedious and prone to errors. Fortunately, since the formalism for transformation rules is compositional, it was straightforward to write a compiler that gener­ates word expert procedures from word expert specifications automatically.

There is an obvious choice of learning method for training Prolog Word Experts, namely Transformation-Based Learning (Brill, 1995). Of course, the fact that transformation rules can be learned from tagged corpora was a major rea­son for using them in the first place. The //-TBL system - described in detail in (Lager, 1999) -uses the search and database capabilities of the Prolog programming language to implement a generalized form of transformation-based learn­ing. Through its support of a compositional rule/template formalism and 'pluggable' algo­rithms, the //-TBL system can easily be tailored to different learning tasks.

Rules that can be learned in Transformation-Based Learning are instances of rule templates. For example, the second of the rules in our ex­ample PWE specification is an instance of the following template:

sense:A>B <~ word:CO[1].

for a word token with a particular sense (say 5) becomes a matter of constructively proving 3p[S(p,5)].

For the training of our simplest form of sense disambiguation expert, the following set of seven templates was used:

sense:A>B <- word:CO[-1] . sense :A>B <- word:C0[-l,-2] .

sense:A>B <- word:C0[l].

sense:A>B <- word:CO[1,2].

sense:A>B <- word:C0[l] & word:DO[2].

sense:A>B <- word:C0[-l] & word:DO[-2].

sense:A>B <- word:C0[-l] & word:D0[l].

The idea was to exploit a fact noted by many researchers in the field: that the sense of an occurrence of a word can fairly successfully be determined from just looking at the two previ­ous words and the two following words (cf. Ide &; Veronis, 1998). The choice of the above set of templates is based on a fairly thorough trail-and-error process and works well for most words that we have tried.

The idea here was to train five different PWEs for each lemma, and then to use a simple vot­ing mechanism to arrive at a final decision. The PWEs were different only in that they used different sets of templates during the train­ing. Templates looking forwards only, templates looking backwards only, and templates looking both forwards and backwards. Furthermore, one member in each committee was trained for using a bag-of-words approach to disambigua­tion, based on templates of the following form:

sense:A>B <- inBag:W0[0].

sense:A>B <- inBag:W10[0] & inBag:W20[0].

Finally, one PWE in each committee had access to a list of words extracted from the language examples provided by the GLDB.

In this section we describe the actions that we took in order to submit our entry in the compe­tition.

• In a preparatory step, the XML formatted training data was parsed and subsequently converted into the format required by the /i-TBL system.

• The training was performed, and resulted in one PWE specification per lemma. Training took between 5 seconds and a cou­ple of minutes per lemma, depending on the amount of training data available for the lemma in question.

• The PWE specifications were compiled into a set of PWE procedures, by means of the PWE compiler.

In the following table we show the results of our entry in the competition, copied from the Senseval-2 homepage.

Five groups and altogether eight systems par­ticipated in the Swedish lexical sample task. In terms of ranking, our PWE-vote came in sec­ond, after Yarowski's JHU system, and before the Göteborg team's best entry. However, we hasten to add that the step from Yarowski's (nearly 70%, fine grained evaluation) to our re­sults is a very significant 7%, and that the step down to Göteborg 's result is very small and probably statistically insignificant. Our simple Peewees shared the fourth place with Resnik et al.'s UMD-SST.

As can be seen from the table, the PWE com­mittees did slightly better than a single simple PWE. It is however dubious whether the small difference was really worth the trouble. It is quite possible that training a single PWE on the combination of corpus data and the exam­ples from the GLDB would have lead to a result almost as good, and with less work.