Bennett, B.

Mallenby, D.

Third, A.

English

White Rose Research Online

promoting access to White Rose research papers    White Rose Research Online   Universities of Leeds, Sheffield and York http://eprints.whiterose.ac.uk/    White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/7831/     Conference paper Third, A., Bennett, B. and Mallenby, D. (2007) Automatic grounding of vague geographic ontology in data. In: Demšar, U., (ed.) Proceedings of the 9th International Conference on Geocomputation. GeoComputation 2007, 3rd - 5th September 2007, Maynooth, Ireland. eprints@whiterose.ac.uk  Automatic Grounding of Vague Geographic Ontology inDataAllan Third, Brandon Bennett and David Mallenby?School of Computing, University of Leeds, Leeds, LS2 9JT, UK{thirda,brandon,davidm}@comp.leeds.ac.uk1 IntroductionIn constructing an ontological theory of a domain such as geography, it is important notonly to take account of the vagueness and ambiguity which is inherent in many of therelevant concepts, but also to be able to relate the high-level definitions of the theoryto actual sets of data of varying kinds. Any attempt to ignore or remove vaguenessand ambiguity risks errors and conflict in the ontological theory with the knowledge ofdifferent domain experts, while an inability to ground the theory in real data limits itspractical use. We present here a means of structuring such a theory to handle these issuesin a principled manner, which lends itself to concrete implementation. We illustrate withreference to several examples from the domain of hydrography.We say that a term is vagueif there exist entities to which it is unclear whether thatterm applies or not. For example, in the hydrographic domain, the distinction between“stream” and “river” is vaguely defined — there are water features which it seems ac-ceptable to classify as either large streams or small rivers. We could make these termsprecise by stipulating a dividing line between their interpretations, but to do so is tomove away from their actual use in the real world, in which vagueness is a real phe-nomenon.Many terms in natural language are ambiguous — that is to say, they have two ormore meanings. Ambiguity can often arise from different perspectives on a domain.From the point of view of the production of maps, the surface of the Earth can beseen as the surface of solid material with only air or water above it, whereas such adefinition would omit regions such as the floors of caves, and so on, which would beconsidered part of the Earth’s surface by an individual person walking. Terms suchas “estuary” can be ambiguous between a feature of the two-dimensional geometry ofwater regions, and a region of water which has salinity lying within a certain range ofvalues [Cameron & Pritchard, 1963]. A particular set of data will reflect the perspectiveof those who design it, and so the available data can affect the choice of definitions it isappropriate to use when relating a theory to real data. We believe that having an explicitmodel of this kind of ambiguity can make it possible to draw useful conclusions basedon multiple sets of data embodying different perspectives on the domain in question.Given a suitable set of data, and a high-level ontological theory, it is possible to pro-vide an explicit mapping from individual data points and their attributes to the primitivesymbols of the theory, in such a way that the data generate a model of that theory. We? The authors gratefully acknowledge the support of EPSRC grant no. EP/D002834/1refer to this process as “grounding” the theory on the data. For example, given a data-setconsisting of points in space with the attributes of being either “land” or “water”, a the-ory of hydrography defining terms such as “river” and “lake” can be grounded in thosedata by specifying which sets of points together constitute individual rivers and lakes.Grounding can simplify automated reasoning by providing a single explicit model of atheory which can be used to assist deduction.We propose a way of structuring an ontological theory in such a way as to main-tain the flexibility to handle vagueness and ambiguity. We also illustrate how such anapproach can simplify the automation of the grounding process.2 A Layered TheoryLet us divide an ontological theory of geography into three layers: a general layer, agrounding layer and a data layer. The general layer is intended, as the name suggests,to contain the definitions and axioms governing the use of high-level terms, close to thelevel of natural language. For example, it might define terms such as “river”, “lake”,“estuary”, and so on. Where terms are ambiguous, their definitions in the general layerare intended to capture the meaning common to all contexts of use, where such a com-mon meaning exists. For example, in any context, the term “river” denotes some kindof channel which can contain flowing water. The general layer might also define funda-mentals, such as the relevant spatio-temporal logic and the overall structure of the globeand the various matter types which make it up.The data layer, by contrast, is highly specific, and represents the contents of anindividual data-set. It thus contains a set of ground formulae stating which attributeshold of which data point, and which relations hold between which data points. Forexample, it might contain formulae stating, for a set of regions in space, whether thoseregions represent, say, water or land on the Earth’s surface. The data layer can alsorepresent properties which can be computed straightforwardly from the data, such asspatial relations like “part-of” and “overlap” holding between regions of space, andcomputed geometric predicates such as whether a given region of water is considered“linear”.Between the general and data layers lies the grounding layer, which is intended toserve as a bridge between the two. The grounding layer takes the primitive predicates ofthe general layer, such as “water-channel”, and provides definitions for them in termsof the predicates of the data layer, such as “water” and “linear”. By taking all of theselayers together, it is straightforward to see how the data provides a model for the high-level terms of the general layer, and it is possible to draw useful conclusions about thevarious concepts and facts represented in the theory.Different grounding layers can be used to relate the general layer to different kindsof data-set, and can be chosen to represent the meanings of ambiguous terms in thegeneral layer. A general term such as “estuary” can be grounded in the kind of exampledata layer described above by defining it in terms of the two-dimensional geometry ofwater regions. However, should a data-set be available which contains information onsalinity, a grounding layer can be constructed which defines estuary along the lines of[Cameron & Pritchard, 1963]. It is thus possible to handle multiple perspectives on asingle term within the framework of one theory. As a consequence, it is possible touse the common terms of the general layer to draw conclusions which can be appliedcorrectly to such different data sets simultaneously.Another benefit of such a division is that analysis of definitions in the groundinglayer can suggest ways of automating the grounding process. For example, given agrounding definition of a river in two-dimensional data as being a vaguely linear re-gion of water, one can construct software which can identify such regions in data andaugment the data layer accordingly.3 VaguenessWe base our treatment of vagueness on supervaluation semantics [Fine, 1975]. It isargued in [Bennett, 2001a] and [Bennett, 2001b] that many vague geographic terms aresuch that, given a partial definition of a term — for example, the set of clear-cut casesof “river” — there remain many “acceptable” ways of making that term precise. Thatis to say, one interpretation may include certain borderline cases of “river” as genuinerivers, and another may not, without either interpretation contradicting our intuitiveunderstanding of the term.The applicability of the vague terms in which we are interested turns out to be de-pendent on certain precise properties which can take a range of values. For example, itseems clear that a river should be longer and wider than a stream, even if it is unclearat precisely which specific values of length and width the boundary between them lies.We can model this phenomenon in terms of threshold values on the relevant properties.Thus a specification of unique values for each threshold corresponds to one way of mak-ing all vague terms precise. Specifying a range of values for thresholds therefore fixes aset of ways in which those terms can be made precise. By building such thresholds intothe formal definitions of vague terms, we acquire a straightforward means of control-ling the set of admissible interpretations for those definitions, and, when grounding suchdefinitions in real data, we can experiment with appropriate ranges for those thresholdsand quantify over them to be able to carry out reasoning and draw conclusions respect-ing the vagueness of the relevant terms. Detailed discussion of this particular approachto the logic of vagueness can be found in [Bennett, 2006].4 ConclusionWe have outlined a general approach to the structure of ontological theories whichhandles vagueness and ambiguity arising from different perspectives on the relevantdomain, as well as lending itself to convenient automation of the grounding process.Our approach allows results regarding the high-level terms of an ontology to be appliedto data arising from a range of different sources, and therefore allows the unificationof such data sources at the conceptual level, while maintaining an understanding of theperspectives and goals implicit in the creation of each.We have implemented our theory in software, and have successfully grounded anontological theory of the hydrographic domain in real-world data sources, augmentedwith geometric analysis software to identify the interpretations of predicates such as“linear”. For details of this software, particularly the grounding level, see [Mallenby, forthcoming]and [Mallenby, submitted].References[Bennett, 2001a] Bennett, B. 2001a. Application of supervaluation semantics to vaguely de-fined spatial concepts. In Montello, D., ed., Proceedings of the fifth international Conferenceon Spatial Information Theory (COSIT’01), number 2205 in LNCS, 108–123. Morro Bay:Springer.[Bennett, 2001b] Bennett, B. 2001b. What is a forest? on the vagueness of certain geographicconcepts. Topoi 20(2):189–201.[Bennett, 2006] Bennett, B. 2006. A theory of vague adjectives grounded in relevant observ-ables. In Doherty, P.; Mylopoulos, J.; and Welty, C. A., eds., Proceedings of the Tenth Interna-tional Conference on Principles of Knowledge Representation and Reasoning, 36–45. AAAIPress.[Cameron & Pritchard, 1963] Cameron, W. M., and Pritchard, D. W. 1963. Estuaries. In Hill,M. N., ed., The Sea: The Composition of Sea-water, volume 2. Harvard University Press.[Fine, 1975] Fine, K. 1975. Vagueness, truth and logic. Synthe`se 30:263–300.[Mallenby, forthcoming] Mallenby, D. forthcoming. Grounding a geographic ontology on ge-ographic data. In 8th International Symposium on Logical Formalizations of CommonsenseReasoning.[Mallenby, submitted] Mallenby, D. submitted. Preparing geographical data to facilitate geo-graphical ontology grounding. Computers and Geosciences.

Automatic grounding of vague geographic ontology in data

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Automatic grounding of vague geographic ontology in data

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