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Formal Specifications of Image Schemata for Interoperability in Geographic Information Systems

Andrew Frank

Department of Geoinformation

Technical University Vienna

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Outline

• My background

• Spatial Cognition is Crucial

• Need to Formalize Semantics of Spatial Prepositions

• Principles of our Investigation

• Relations in Geographic Space

• Relations in Table-Top Space

• Current work

• Future: Cognitive Engineering

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My background

• Diploma in surveying engineering ETH Zurich

• Doctoral work on databases for spatial information ETH Zurich

• Research in GIS at University of Maine

• One of leaders of the National Center for Geographic Information and Analysis (NCGIA - UCSB, SUNY Buffalo, UMaine)

• Professor for Geoinformation, TU Vienna

• Initiation of series of conferences on Spatial Information Theory (COSIT)

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My past research

• Database management

• Formal data modeling methods

• Formalization and programming of geometric operations in a realistic environment (limited precision, rounding problems, errors)

• Bridging between formal research in geometry and cognitive and geographic investigation in human understanding of space (with David Mark)

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Spatial Cognition is Crucial

O’Keefe/Nadel • Hippocampus serves to construct a neural map

– (similar to the mental map/collage - B. Tversky)

• Humans use the left hippocampus for verbal problems

• Methods originally developed for spatial problem solving are transferred to the general (abstract) verbal domain

– navigation of semantic nets as a fitting metaphor

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Spatial Cognition is Crucial(Lakoff)

• Spatial metaphor abound in language (especially English)

– we are at crossroads, I’m feeling down

• Bodily experience provides grounding for the semantics of simple (primary experience) elements of language (Johnson)

• Metaphorical transfer links meaning of abstract terms to the bodily experience (Lakoff)

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Practical Need to Formalize Semantics of Spatial Prepositions

• Interoperability of GIS => Co-operation of different GIS

Requires:

• Standardization of Terms: Semantics Problem

• Different communities use terms very differently:

– width of a road

– parcel

– wood

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Practical issues

• Building of integrated European Land Use Databases (necessary for discussion of potential political action)

• Integrated Database for Town Administration: “one-stop” administrative procedures

• All require semantic integration from multiple domains

• Standardization efforts of industry:

– need to identify the building blocks that are universal

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Principles of Investigating Spatial Relations

Language allows to study (aspects of) spatial cognition:

Consider verbally expressed situations and what is implied (can be deduced) from the description (not just simple sentences).

Restrict to non-metaphoric usage (Montague?)

Very specific environment (only a single ‘space’, e.g., table-top space; to have influences from only one kind of bodily experiences)

Assume polysemy liberally (identification later)

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Spatial Prepositions investigated

Geographic Space and Table-Top Space

• Exclusion of Partial Spatial Relations

• Single Level of Detail

• Specific Environment and Single Language

– surprising amount of diversity within a single language (regional diversity)

• German: auf dem Tisch, Vienna: am Tisch

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Previous efforts: Formalizing Spatial Meaning

• Topological Relations based on formal considerations and some evidence of cognitive soundness (Egenhofer, Mark)

• Metric Relations (Cardinal Directions; discretized directions: Near, Far, etc.)

• What is universal?

• How much is left?

• Language encodes many other spatial relations (typically 50 to 100)

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Method of Formalization

• Formalize the meaning of several related spatial preposition (above/under)

• Static spatial prepositions can be modeled with (first order) predicate calculus (logic)

• If one includes movement and changing situations (including Talmy’s fictive motion) algebraic approaches lead to simpler formalizations.

• Need for a tool to maintain facts about the environment (‘database’)

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Executable Formalizations

• Formalizations are difficult to read and understand - and often contain errors.

• We currently use a formalization system (based on denotational semantics, category theory) packaged in a functional programming language.

• Our formalization is formally checked (for completeness, type conformance etc.) and can be ‘tested’ (run)

– do they produce the predicted output?

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Are Related Spatial Prepositions Image Schemata?

Image schemata are:

• Recurring, Imaginative Patterns based on People‘s Experiences

• Sufficient Internal Structure to Constrain People‘s Understanding and Reasoning

• More Abstract than Mental Pictures, Less Abstract than Logical Structures

• Source for metaphorical usage

• Accepted as a pragmatic concept (notion) for our research

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Image Schema PATH

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How to Formalize Spatial Image Schemata

• Predicate Calculus

– A above B => B under A

• Relation Calculusa (R;S) c = aRb and bSc

– A north of B and B north of C => A north of C

• Functionsf.g(x) = f(g(x))

– move out (Coin, (move in (Coin, Box) ) = isOutOf (Coin, Box)

• Model Based

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Example Geographic-Space-Image-Schemata

• LOCATION

• PATH

• REGION

• BOUNDARY

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Select Base Relations

• Location in Region

• Region inside Region

• Location directly connected to Location

• Region borders Region

– formal (but not cognitive) justification for the selection of base relations

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Location and Relation between Places

a

a1bn

b

Direct and Indirect Path

path (a, b) <=> path (b, a)ind-path (a, b) <=> [path (a, a1) & path (a1, a2) & path (a2, ...) & ... & path (..., bn) & path (bn, b)]

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Relations with Region

loc1

reg1

reg2

Location within Region

in* (loc1, reg2) <=> in (loc1, reg1) & in (reg1, reg2)

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Relations with Boundaries

reg2

reg1

ba

Boundary Locations

boundaryBetween (a, b) <=> path (a, b) & notInSameRegion (a, b)

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Persons

Move

scene2 = move (place1, scene1) move (p, a, b): in (p, a) & path (a, b)unestablish (in (p, a)), establish (in (p, b))

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Conclusions ‘Geographic Space’

• Extension of Relation Calculus to Function Calculus

• 5 Base Relations => 15 Meaningful Relations

• Formal Spatial Relations => Interoperability, Optimizing Spatial Queries

• Powerful Domain as Source for Metaphors

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Examples from Table-Top Space (1)

„In“ Blocks Target of Movement

x ‘in’ y (in scene) => blocked (move z into x (in scene))

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Examples from Table-Top Space (2)

Converse of „auf“ Blocks Object of Movement

x ‘auf’ y (in scene) => blocked (move y in scene)

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Conclusions ‘Table-Top space’

• Some relations are similar to geographic space; polysemy could be dropped and core of meaning identified

– (problems with formalization)

• Limit to specific environment is fruitful; next steps:

– spatial relations in image space

– spatial relations in city space

• Expectation: full formalization of all German spatial prepositions

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Our related research

• Models of environments and observers

• Simulate language expressions describing the environment for various observers

– problem perspective taking: “from your point of view, the coin lies just behind the box”

• Formalized concepts often described as deictic, intrinsic, absolute etc.

• Open issues: build models for effects like ‘imagined translation vs. imagined rotation’ (Klatzky)

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Current Work: Spatial Affordances

(student: Martin Raubal)

• Formal description what we understand by ‘affordance’

• Models of actors (persons) with tasks and objects

• Formalization as models of complex environments including actors having their own observation function and maintaining their own (temporal) knowledge base

• Open issue: effects of hierarchies in space and in the tasks (Timpf)

• (Formal complication: databases in databases…)

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Practical Application

• Predict navigation performance in complex built environments, in order to improve the built environment.

• Meaning:

– improve signage in airports so you find your gate and make it unlikely that you get lost in the transfer!

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Current Work: User Interface (with Werner Kuhn)

• Metaphor is keyword in graphical user interface research, but not well defined

• Formalize metaphor to construct metrics to assess the ‘cognitive load’ for learning and usage of an user interface

• Apply to design better user interfaces!

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Future: Cognitive Engineering

• Cognitive science can be successfully applied in a predictive mode: engineering

• Some differences in the methodology and approach between engineering and science:

– concentrate on primary influence before investigating secondary effects

– simplify problems and subdivide issues (Occam?)

– formalize to allow use in a predictive mode

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Open Questions

• Best Method for Formalization

• Are there Language Independent Primitives?

• Composition and Interaction of Image Schemata

• Integration of Image Schemata Across Domains

• Formalize Metaphorical Transfer