1. Laws and Algebras – A Comparison
Gerhard Navratil
TU Vienna
Institute for Geoinformation

2. Contents Introduction Structure of a legal system
Structure of algebraic models
Similarities
Differences
Conclusions
Questions
REV!GIS-Meeting
Austria, 2001

3. Introduction Why is integration of data so difficult?
Different classification
Different resolution
....
Different view of reality
Different ontology
REV!GIS-Meeting
Austria, 2001

4. The five tiers (Frank) 0 The physical reality 1 Observable reality
2 Object world
3 Social reality
4 Cognitive agents
REV!GIS-Meeting
Austria, 2001

5. Influence of laws Laws define:
Meaning of objects (When do we call a piece of land a parcel?)
Procedures on objects (What must be done to subdivide a parcel?)
Effects on the social reality (A boundary line in a cadastral map means ...)
REV!GIS-Meeting
Austria, 2001

6. Structure of a legal system
System of rules that regulate the coexistence of the humans. The rules are enforced by the government
The rules define behaviour (commandments and prohibitions) – legal norms (laws)
REV!GIS-Meeting
Austria, 2001

7. Inconsistencies Apparent inconsistencies: Derogation
Real inconsistencies: Only solved by invalidating of one rule
REV!GIS-Meeting
Austria, 2001

8. Laws and computers Storing the law text in a database
„Stepping on a parcel“ – 217 times in 208 laws/contracts/decisions
Improvements? Phrases, synonyms, dictionary, ...
REV!GIS-Meeting
Austria, 2001

9. Expert systems Logic-based system (Lachmayer)
Representation language (McCarthy) Logic + Rules + Time + Actions
Agent-based system (Stamper)
Functional approach (Morscher, van Kralingen, Visser)
REV!GIS-Meeting
Austria, 2001

10. Algebraic models Consist of three elements:
Sets
Links
Axioms
Algebra Stack (Stack of a, a)
Links: Push, New, Pop, Top
Axioms: Top (Push a s) = a ...
REV!GIS-Meeting
Austria, 2001

11. Construction of an algebraic model
Definition of small pieces
Combination of these pieces
REV!GIS-Meeting
Austria, 2001

12. Similarities Description of models Subdivision into small pieces
Abstraction
Use of axioms
REV!GIS-Meeting
Austria, 2001

13. Differences
Laws use imprecise definitions (lawyers avoid explicit values)
Laws contain organisational aspects
Time (law is valid from)
Links to other laws
Enforced by somebody
Real inconsistencies
REV!GIS-Meeting
Austria, 2001

14. Conclusions Many similarities Differences come from
Method of modelling
Differences come from
Reality vs. mathematics
Transition (law -> algebra) is possible
REV!GIS-Meeting
Austria, 2001

15. Questions
Can we use algebras to help the user deal with legal aspects of data?
Can we compare legal situations in different countries? (European Union)
REV!GIS-Meeting
Austria, 2001