1. Arguing with Dimensions in Legal Cases
Trevor Bench-Capon
Department of Computer Science, University of Liverpool UK

2. Arguing With Legal Cases
Most systems draw upon HYPO (Rissland and Ashley) and CATO (Ashley and Aleven)
CATO represents cases using factors
Stereotypical patterns of facts which
Are either present or absent
Favour either the plaintiff or the defendant. The factor always favours the same party.
HYPO represents cases with dimensions
Dimensions may or may not apply to a case
Are a range, running from an extreme pro-plaintiff point to an extreme pro-defendant point
Which party is favoured varies according to where the case lies on the dimension, and may be argued about

3. Factors as Points on Dimensions
Land Ownership
Extreme Pro-P
Extreme Pro-D
Defendant
Freehold
Plaintiff
Freehold
Unowned
Defendant
Rent
Plaintiff
Rent
Other
Owner

4. Factors as Points on Dimensions
Factor points can be used as propositions in the premises of standard argumentation schemes
Approach of Henry Prakken, Adam Z. Wyner Trevor J. M. Bench-Capon, Katie Atkinson: A formalization of argumentation schemes for legal case-based reasoning in ASPIC+. Journal of Logic and Compututation 25(5): (2015)
Here will look at arguments based on the geometry

5. Where do the Factors favour Defendant?
Unowned land may favour plaintiff, defendant or neither
Extreme Pro-P
Extreme Pro-D
Defendant
Freehold
Plaintiff
Freehold
Unowned
Defendant
Rent
Plaintiff
Rent
Other
Owner
Where the line falls can be justified by precedents

6. Arguments in One Dimension
In Zone A we have a strong pro-plaintiff argument : no cases have been found for the defendant
In Zone B we have a weak argument for the plaintiff (cases found for both sides)
In Zone C we have no argument for the plaintiff A B C

7. Two Dimensions Extreme Pro-D Dim 2 H G I D E F Extreme Pro-P Dim 2 C AB
Extreme Pro-P
Dim 1
Extreme Pro-D
Dim 1

8. Two Dimensions
Assume the plaintiff has put forward an argument based on Dimension 1 So not in A,D or G.
Defendant responds using Dimension 2, so not D or G.
Response succeeds in Zone H
Response fails in Zone F
Depends on which dimension is given priority in Zone I
In Zone E we have a trade-off: we need to find a way of dividing the space between the parties

9. A Fortori Arguments
Defendant owns NW
P1 (D)
P2 (P)
Plaintiff owns SE

10. Arguments
Where there is no a fortori argument, we can use precedents to constrain the space, and argue that a current case should be treated similarly.
We can use hypothetical cases as well as actual precedents
Different combinations of dimensions can be tried
Some examples in the paper

11. Future
This very preliminary: little more than the idea of basing arguments about legal cases on the geometry of dimensions, rather than propositional factors
Need to:
Make the informal arguments sketched in the paper more formal
Explore whether dimensions can always be considered pairwise, or whether 3 or more may be needed simultaneously
Consider that sometimes dimensions supply thresholds for one another: can they interact in other ways?
Consider how to link the arguments into a dialectical exchange, such a dialogue game