Upload
warren-garrison
View
214
Download
0
Tags:
Embed Size (px)
Citation preview
1
Formal Specifications of Image Schemata for Interoperability in Geographic Information Systems
Andrew Frank
Department of Geoinformation
Technical University Vienna
2
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
3
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)
4
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)
5
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
6
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)
7
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
8
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
9
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)
10
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
11
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)
12
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’)
13
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?
14
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
16
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
18
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
19
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)]
20
Relations with Region
loc1
reg1
reg2
Location within Region
in* (loc1, reg2) <=> in (loc1, reg1) & in (reg1, reg2)
21
Relations with Boundaries
reg2
reg1
ba
Boundary Locations
boundaryBetween (a, b) <=> path (a, b) & notInSameRegion (a, b)
22
Persons
Move
scene2 = move (place1, scene1) move (p, a, b): in (p, a) & path (a, b)unestablish (in (p, a)), establish (in (p, b))
23
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
24
Examples from Table-Top Space (1)
„In“ Blocks Target of Movement
x ‘in’ y (in scene) => blocked (move z into x (in scene))
25
Examples from Table-Top Space (2)
Converse of „auf“ Blocks Object of Movement
x ‘auf’ y (in scene) => blocked (move y in scene)
26
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
27
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)
28
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…)
29
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!
30
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!
31
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