Journal of Logic, Language and Information 13: 117–120, 2004. 117

Inference and Computational Semantics

What is computational semantics? And what is inference in computational seman-tics? It is easy to give general answers: computational semantics is that part ofcomputational linguistics concerned with developing methods for computing thesemantic content of natural language expressions, and the study of inference incomputational semantics focuses on the role that reasoning has to play in thisprocess.

But such general answers are not particularly helpful. For a start, semanticissues can crop up just about anywhere in computational linguistics. Moreover,inference is such a broad term, covering everything from probabilistic reasoning,to various kinds of logical inference, that the above characterisations do not seemto pin down a coherent area of research. So what links the papers in this specialissue?

In recent years a particular approach to computational semantics has begunto emerge as a sub-area in its own right. Roughly speaking, this approach takesas its starting point the tradition initiated by Richard Montague (that is, what isnow usually called formal semantics, or model-theoretic semantics) and exploresit computationally.

It is not hard to see why Richard Montague might be regarded as a pioneerof computational semantics: After all, Montague demonstrated that the processof constructing semantical representations could be formulated algorithmically. Inparticular, given a grammar for a fragment of natural language, Montague showedhow to use the typed lambda calculus to systematically construct logical repre-sentations for sentences. So his work provides two of the key ingredients neededfor computational semantics. First, his insight that semantic construction can beviewed as an algorithmic process using relatively simple mechanisms makes com-putational semantics a real possibility: If you have good grammars and parsingtools (and nowadays excellent ones exist) why not try combining them with asemantic construction component? Second, the fact that Montague showed howto systematically construct logical representations, opens the door to inference: Ifwe build logical representations why not try to use automated reasoning tools (suchas theorem provers and model builders) to actually carry out useful reasoning forus?

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Readers familiar with formal semantics may feel that the computational per-spective is in one respect rather unorthodox: It highlights the role of semanticrepresentations. A key theme in Montague’s writing is the eliminability of rep-resentations. For Montague, the generation of logical representations was merely aconvenient way to induce a model-theoretic interpretation on a fragment of naturallanguage. The interpretation was the important thing, translation into an interme-diate logical representation merely one way of reaching this goal.

Now, it is certainly true that the computational tradition takes intermediate rep-resentations very seriously indeed: After all, they are the entities which need to becomputed, and they provide the basis for reasoning. So it is hardly surprising that agreat deal of energy in computational semantics is devoted to thinking hard aboutwhat good representations actually are; recent research on underspecified semanticrepresentations is a good example of this line of research. Arguably, however, thisdifference with traditional formal semantic research is largely a matter of empha-sis – a tendency to take representations seriously has long been visible even inthe traditional formal semantics literature. For example, Robin Cooper’s approachto quantifier scope resolution (Cooper storage) works by adding more structureto semantic representations and specifying an algorithm to manipulate it. AndHans Kamp’s Discourse Representation Theory (DRT) makes use of the notionof accessibility (which is defined in terms of the way semantic sub-representationsare embedded) to constrain anaphoric possibilities. Thus the concern with repre-sentations characteristic of computational semantics is perhaps not such a radicaldeparture after all.

Of course, the emphasis on computation and inference certainly does lead toother changes of perspective. For start, in the formal semantic tradition it hasusually been tacitly assumed that the interesting task is to give detailed syntacticand semantic analyses. Computational linguists, on the other hand, are comfortablewith the idea that shallow analyses may be more useful for some purposes – andarguably the idea of shallower forms of inference has an important role to play incomputational semantics too. For example, instead of building semantic represen-tations in rich logics (such as first-order logic) why not build representations inweaker logics (such as description logic) which trade expressive power for deduc-tive efficiency? Such representations may not be able to capture the full contentof natural language expressions, but for many purposes they may capture what isinferentially important. And indeed, should one always think in terms of manipu-lating logical formulas? Resources such as WORDNET embody a vast amount ofsemantic content – maybe they can be used directly instead? Finally, it should bestressed that the computational perspective does not simply give rise to practicalquestions, it gives rise to new theoretical issues too. For example, what is the logicthat drives the semantic construction process? And, given that we are interested ininference, what is the complexity of the inference tasks that face us?

Bearing these remarks in mind, let us examine the contributions to this specialissue. The first paper, Analysing the Core of Categorial Grammar by Carlos Areces

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and Raffaella Bernardi, falls firmly on the theoretical end of the spectrum. Sincethe work of Richard Montague, categorial grammar has been a favourite tool ofsemanticists, largely because of the way it minimises the distance between syntaxand semantics. At the heart of categorial grammar lies the operation of residuation,the “cancellation” operation which drives the semantic construction process. Thispaper investigates the logic of residuation. It argues that Display Calculi provide aparticularly clear window on the logic of residuation, and indeed on a number ofother aspects of semantic construction.

The second paper, Computational Semantics in Discourse: Underspecification,Resolution and Inference, by Johan Bos, gives an overview of the approach to sys-tem development that the author has used in a number of applications. Bos has longadvocated the coupling of relatively standard components and methods (DiscourseRepresentation Structures, underspecification, compilation into first-order logic) asthe basis for system design. Perhaps the best known example of this approach inaction is his DORIS system, which implements the van der Sandt algorithm forpresupposition resolution, but Bos has used similar methods in a number of otherapplication areas such as autonomous robots and household automation. In thispaper Bos discusses the architecture which underlies such implementations.

The third paper, Semantic Opposition and WORDNET, by Sandiway Fong, re-ports on an experiment in computational lexical semantics. In particular, the paperinvestigates the use of WORDNET for determining adjective-verb opposition fortransitive change of state verbs and adjectivally modified grammatical objects. Thebasic idea is to check whether an antonym link is present in the shortest pathlinking two words. The investigation reveals some oddities in the organisation ofWORDNET, most notably with respect to colour terms.

The fourth paper, Relevant Answers to WH-questions, by Helen Gaylard andAllan Ramsay, discusses two issues in the semantics of WH-questions. First, whena WH-question is posed, the questioner already has some description of the entityof interest, namely the description embodied in the WH-question. So the ques-tioner is interested in an alternative description of the entity – but how is this tobe obtained? Secondly, when answering a question it is not always possible to becompletely specific – but a more general answer can still be helpful. How can onefind (suitable) more general answers? This paper describes a system that carriesout the required reasoning.

The charmingly titled Put My Galakmid Coin into the Dispenser and Kick It:Computational Linguistics and Theorem Proving in a Computer Game, by Alexan-der Koller, Ralf Debusmann, Malte Gabsdil and Kristina Striegnitz reports onexperiments with description logic. The setting is text-based adventure games. Insuch games the player interacts with the computer in natural language in an attemptto get to grips with the game world. However (as anyone who has tried such agame will be aware) such games can be frustrating because of their inability toperform any sort of inference (for example, to resolve referring expressions usedby the player). This paper describes a system in which the inferential capabilities

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of description logic are added to a text-based adventure. As the authors show, thisturns out to be an ideal way of experimenting with inference in computationalsemantics.

With Fragments of Language by Ian Pratt-Hartmann we return once again thetheoretical side of the spectrum, and in a decidedly novel way. Ian Pratt-Hartmannraises a simple question, but one that does not seem to have been considered before:How computationally complex is natural language inference? To answer this, hereturns to the method of fragments introduced by Richard Montague. In particular,he defines a series of fragments of English for which the complexity of the satis-fiability problem ranges from polynomial to undecidable. In a nutshell, this paperdetermines the intrinsic inferential complexity of certain parts of English. It opensthe door to a new line of research, one that is arguably of fundamental importanceto computational semantics.

The final paper, Dialogue Systems as Proof Editors, by Aarne Ranta and RobinCooper, investigates how to handle the kinds of inferences required for informationseeking dialogues, dialogues in which one partner has to ask for information fromthe other in order to carry out some task. The key idea is to use a proof editor,originally designed for carrying out mathematical proofs, to refine the dialogueplan.

The papers in this special issue are reworked versions of some of the papers pre-sented at the Third International Workshop on Computational Semantics (ICoS-3),which was held in Siena on 18–19 June 2001. We hope they will give the reader ataste of what computational perspectives on inference in semantics have to offer.

Patrick BlackburnINRIA LorraineE-mail: patrick.blackburn@loria.fr

Michael KohlhaseInternational University BremenE-mail: m.kohlhase@iu-bremen.de