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E LAW - MURDOCH UNIVERSITY ELECTRONIC JOURNAL OF LAW

ISSN 1321-8247

Volume 5 Number 3 (September, 1998)

File: allen53.txt

ftp://cleo.murdoch.edu.au/pub/elaw/issues/v5n3/allen53.txt

http://www.murdoch.edu.au/elaw/issues/v5n3/allen53.html

________________________________________________________________________

The Legal Argument Game of LEGAL RELATIONS

Layman E. Allen

University of Michigan

and

Charles S. Saxon

Eastern Michigan University

Contents

* Introduction

* Official Rules that Define the Games

* Sketch of Legal Argument Game 1B

* Brief Summary of The Legal Argument Game 1B

o Starting

o Playing and Ending

o Playing Mat

o Winning and Scoring

o Summary of Scoring at the End of the Match

* Conclusion

* References

* Appendix A - The Rules of Inference, Constraints, and Deontic LEGAL

RELATIONS Definitions

* Appendix B - Example of the Play of Some Matches of the Legal Argument

Game

Introduction

1. The Language of LEGAL RELATIONS (LLR) is a representation language for

expressing rules and arguments in the legal domain. [Allen & Saxon

1997] The fundamental legal conceptions of Wesley N. Hohfeld, one of

the foremost legal philosophers of the 20th Century, provide the first

giant step in the development of the LEGAL RELATIONS Logic (LRL) that

underlies LLR.[Hohfeld 1913] LRL is an extension, enrichment, and

formalization of the eight fundamental legal conceptions that Hohfeld

viewed as "the lowest common denominators of legal discourse that

could be used to describe every possible legal state of affairs and

every change in such states. [Allen 1995, 1996; Allen & Saxon 1995]

This robustness is actually achieved by LRL, along with its capacity

to represent every possible legal rule as well as every possible legal

argument.

2. The Legal Argument (LA) Games of LEGAL RELATIONS are part of a series

of games and puzzles designed to facilitate learners becoming fluent

in LRL. [Allen & Saxon 1997] There are a total of nine LA Games, three

different varieties, each at three different levels as summarized in

Figure 1.

Figure 1. The Varieties and Levels of the Nine Legal Argument

Games

Levels / A. Basic B. Deontic C. Wild_Cards

Varieties

1. Fundamental Fundamental_Basic Fundamental_Deontic Fundamental_Wild_Cards

2. Enriched Enriched_Basic Enriched_Deontic Enriched_Wild_Cards

3. More_Enriched_Basic More_Enriched_Deontic More_Enriched_Wild_Cards

More_Enriched

3. In this article we present various accounts of the Fundamental_Deontic

Legal Argument Game 1B to illustrate the nature of these LA games.

First the official rules that define the LA Game 1B are set forth;

next is a sketch of the LA Game 1B. This is followed by a brief

summary of it. Then, in the Appendix will be found an example match of

LA 1B which is described in full detail, including an account of each

player’s strategy in making each move.

4. These LA games, along with other games and puzzles that deal with the

acquisition of fundamental reasoning skills are being developed at a

site on the Internet called THINKERS ALLIANCE at

http://thinkers.law.umich.edu. The LA games are at this URL with the

suffix /files/Leg_Arg.htm . Eventually, the THINKERS ALLIANCE site

will have available practice matches in all the games and examples of

the puzzles with interactive capability for interested learners to

test their skills and facilities for making appointments to play

matches with others around the world in any of the games.

5. Official Rules that Define the Games

----------------------------------------------------------------------

A. Goal Rule

On your shake, you must set a Goal by moving sufficient of the

generated Resources to the Goal section of the playing mat. The

Goal must express a DUTY of the player who is the defendant to do

something for the player who is the plaintiff (goal-setter) or

some equivalent of such a DUTY. Plaintiff indicates that the Goal

has been completed by saying "Goal."

Comments

1. The Goal is the conclusion of an argument. A Solution is a

set of premisses from which the specified Goal can be

deduced by means of the rules of inference, constraints, and

definitions of the Fundamental_Deontic LA Game of LEGAL

RELATIONS. The plaintiff must set a Goal.

2. In The Fundamental_Deontic LA Game the Goal must be an

expression equivalent to the declaration of a RIGHT of the

player who is the plaintiff that the defendant do something.

In more advanced versions the Goal is allowed to be the

declaration of any LEGAL RELATION.

3. The Goal is not changed after it has been set in The LA

Games.

B. Move Rule

After the Goal has been set, play progresses in a clockwise

direction. When it is your turn to play, you must either

challenge or transfer zero or more Resources from the remaining

pool of Resources to one or more of the Forbidden, Permitted, or

Essential Sections (F, P or E) of the Playing Mat.

Comments

1. Plaintiff's move consists of any one of the following four

options:

1. transfer a maximum of any five Resources to F, P, or E,

2. shift one Resource from F, P, or E to F, P, or E, AND

transfer a maximum of any three Resources to F, P, or

E, OR

3. shift two Resources from F, P, or E to F, P, or E, AND

transfer a maximum of any one Resource to F, P, or E,

4. make a challenge.

2. Defendant's move consists of any one of the following two

options:

1. transfer a maximum of any three Resources to F, P, or

E, OR

2. make a challenge.

3. By their moves, the players shape the Solution.

C. Solution Rule

For the plaintiff a Solution is a set of premisses from which the

Goal may be deduced by means of the rules of inference,

constraints, and definitions of The LA Game. For the defendant a

Solution is a set of premisses from which the NEGATION of the

Goal can be deduced. In attempting to build a Solution:

1. you must not use any of the Resources in the Forbidden

section; AND

2. you may use as many of the Resources in the Permitted

section as you like; AND

3. you must use all of the Resources in the Essential section

in an essential manner; AND

4. on an A-claim challenge or a C-claim challenge that stems

from a previous A-claim violation (see the Flubbing Rule

below), you may use the combination of transfers and shifts

that the next player can transfer on her turn; AND you may

insert parentheses and commas wherever you want to put them.

Comments

1. Since several Resources may be the same, it is possible to

have a DUTY in Forbidden which must not be used in the

Solution at the same time that there is a DUTY in Essential

which must be used.

2. That each Resource in Essential must be used in an essential

manner means that it cannot be so that a premiss in which

that Resource is used can be deleted from the set of

premisses offered as a Solution and the Goal still be

deduced from the remaining premisses without that deleted

premiss. In other words, an Essential Resource must be used

in a premiss essential (in the set of premisses offered as a

Solution) for reaching the Goal.

D. D. Flubbing Rule

You have flubbed, if your move violates the A-claim or the

C-claim that you are making when you make a move.

1. A-claim: If possible, I am [A]voiding by this move allowing

a Solution to be built with the Resources that the next

player can transfer or shift on her move.

2. C-claim: I [C]annot correctly challenge on this turn. The

prior Mover did not flub.

Comments

1. The A-claim means that you make an A-flub if you make a move

that [A]llows a Solution to be built with the Resources that

the next player can transfer or shift on her turn.

2. The C-claim means that once a flub is made, every subsequent

move is a flub because every subsequent Mover could have

[C]orrectly challenged. Since only the most recent flub may

be challenged, the C-claim makes it possible to win by

laying a trap: make a deliberate flub, and as soon as the

next player moves, challenge him for failing to challenge

you.

3. If a Mover by her move makes an A-flub, and then makes a

C-flub challenge of the next player's move and sustains the

Burden of Proof for that challenge, she makes a successful

Bold Challenge, the highest-scoring play possible in the LA

Game. She scores 18 for the successful Bold Challenge.

4. Bold Challengers deserve such high scores for laying the

trap by knowingly making the A-flub and taking the risk that

other players will detect their flub and challenge. Of

course, they also benefit by the high score when they do so

unknowingly and recover quick enough to challenge the next

Mover.

E. Challenge Rule

Whether or not it is your turn, you may at any time challenge the

other player who has just completed a move. You do so by saying

"challenge," and specifying which kind of flub you think the

Mover has made. The move of setting a Goal is completed when the

Mover says "Goal." The move of transferring Resources to

Forbidden, Permitted, or Essential is completed when the last of

the Resources is transferred. Prior flubs are insulated by later

ones; therefore, you cannot challenge any player except the one

who has just completed his play.

Comment

A challenge cannot be retracted once a player has said

"challenge."

F. Burden of Proof Rule

After a challenge, the Burden of Proof is upon the Challenger to

show that there is a Solution under the constraints imposed by

the moves made. If there has not been a challenge before all of

the Resources have been transferred to the Forbidden, Permitted,

or Essential sections, then the Burden of Proof is upon the

plaintiff to show that there is a Solution to the Goal. The

Burden of Proof is sustained by writing a Solution on a sheet of

paper or entering it into the computer within the specified time

limit (usually one or two minutes).

Comments

1. A Solution must, of course, satisfy the conditions imposed

by the Solution rule and the previous plays of the Resources

into the Forbidden, Permitted, or Essential sections.

2. The Burden of Proof will always be upon the Challenger.

G. Correctness Rule

After a challenge, a player is Correct if and only if:

1. he has the burden of proving the existence of a Solution,

AND he sustains it by writing the Solution, OR

2. he does not have the Burden of Proof (the other player has

it), AND the other player does not sustains that Burden of

Proof.

H. Scoring Rule

Whether or not there been a challenge,

1. Challenger scores 18 if Challenger is Correct on a Bold*

Challenge, and Challenger scores 10 if Challenger is Correct

on another kind of challenge, AND

2. Mover scores 10 if Mover is Correct, AND

3. if anyone is incorrect, then he scores 6.

4. (* A Bold Challenge is a C-challenge of the move immediately

following a move that was an A-flub by the Mover who made

the A-flub.)

Comment

The effect of this scoring rule is that one of the two

players scores 6, and the other scores either 10 or 18.

I. Stalling Rule

At any time any other player can call "stall" on the player who

1. deciding to set a Goal, or

2. deciding whether to move a Resource or to challenge, or

3. trying to build a Solution.

The stalling player then has some specified time (usually one to

two minutes) to complete what she is doing. If she fails to meet

the deadline, she loses one point, and another limited time

period begins. If she fails to meet the second deadline, she

loses another point; and so on.

(See also Appendix A - The Rules of Inference, Constraints, and

Deontic LEGAL RELATIONS Definitions)

----------------------------------------------------------------------

6. Given these rules that define the LA Game of LEGAL RELATIONS, the

mental activities that players of these games engage in during play

include

1. the formulation of premisses from the alphabet of resources that

are generated for each match from which the plaintiff’s claim

(the Goal) can be inferred by

2. arguments constructed using

3. specified inference rules, constraints, and definitions, in such

a way that

4. all essential resources are used, no forbidden resources are

used, and (possibly) some permitted resources are used in

specifying a Solution from the premisses formulated. The rules of

inference, constraints, and definitions that guide players’

formulations are set forth in Appendix A.

Sketch of Legal Argument Game 1B

Resources Limitations Legal Argument

DUTY NO_RIGHT PRIVILEGE RIGHT Forbidden Premiss 1 +

DISABILITY IMMUNITY POWER Permitted

LIABILITY CONDITIONAL DONE_BY Essential Premiss 2 +

DONE_FOR IF LS NEGATION OBLIGATORY

c1 c2 c3 p1 p2 p3 p4 s1 s2 s3 s4 Premiss 3 + ...

x1 x2

Premiss n =

Solution

Conclusion (Goal)

7. Plaintiff uses Resources to set the Goal, which is the conclusion of

an argument. The Goal is an expression equivalent to plaintiff's claim

of defendant's DUTY to do something for plaintiff.

8. Then, the players take turns transferring Resources to one or more of

the Limitations sections until somebody (1) challenges or (2) the

Resources are all transferred -- at which time the Burden of Proof is

on one player to show that a Solution can be built from resources in

Permitted and Essential.

9. The sustaining of the Burden of Proof (or failure to do so) determines

the scoring and ends the match.

Brief Summary of The Legal Argument Game 1B

Starting

10. In The LA Game the first player starts by using some of the Resources

to set the Goal. The Goal is a statement that expresses a DUTY or the

equivalent of a DUTY, and it will use from 4 to 7 Resources.

11. The Goal is the conclusion of an argument; a Solution is a set of

premisses from which the specified Goal can be deduced by means of the

rules of inference and definitions of the LA Game. For example,

plaintiff might set the Goal of "DUTY(s1,p1,p2)", which says that

defendant_p2 has a DUTY to plaintiff_p1 to see to it that

state_of_affairs_s1 is so. (Note that the expression in abbreviated

notation is written in the order: DUTY that s1 be so for p1 of p2.)

12. The Resources are the following words (or their abbreviations as shown

in enclosed parentheses) and alpha-numeric characters, which are made

available by the program:

a. Some of these Resources represent LEGAL RELATIONS, namely: DUTY,

NO_RIGHT, PRIVILEGE, RIGHT, DISABILITY, IMMUNITY, LIABILITY,

POWER, and CONDITIONAL (COND) when combined with a LEGAL

RELATION.

b. Some represent propositional connectives: IF and NEGATION (NEG).

c. Some represent action operators: DONE_BY (D2) and DONE_FOR (D4).

d. One represents a deontic operator: OBLIGATORY (O).

e. Some represent conditions: c1, c2, and c3.

f. Some represent persons: p1, p2, p3, and p4.

g. Some represent states of affairs (i.e., propositions about states

of affairs): s1, s2, s3, and s4.

h. And finally, some represent exercises of POWER: x1, and x2.

Playing and Ending

13. After the Goal is set, the players take turns transferring the

Resources to the Forbidden [F], Permitted [P], or Essential [E]

sections until (a) somebody precipitates the ending of the match by

Challenging or (b) all of the Resources have been transferred to F, P,

or E. On their turns, players can either move or challenge.

Defendant's move consists of transferring up to three Resources to the

F, P, or E sections. Plaintiff's move consists of transferring up to

five Resources or substituting a shift for a pair of transfers (or two

shifts for two pairs of transfers), where a shift is removing a

Resource already allocated to F, P, or E and putting it in one of the

other sections. What players should do on their turn to avoid making

flubs that will get them challenged is the following:

If the previous move allows a Solution on the next move,

the player whose turn it is should make an A-flub challenge,

but otherwise,

if the previous Mover could have correctly challenged,

a. the player whose turn it is should make a C-flub

challenge,

but otherwise,

b. it is safe to move, and the player whose turn it is

should move.

14. If a player makes a move to the Playing Mat, he is claiming that two

things are true, and there are consequences if either of his claims

are false.

a. By making a move the Mover is claiming about the situation in

which he moves and after the move: That's right, and there is no

Solution on the next move.

1. By claiming "That's right" the Mover is asserting the

C-claim, that is: because the previous move was not a flub,

I [C]annot correctly challenge on this turn.

2. By claiming "there is no Solution on the next move" the

Mover is asserting the A-claim: I am [A]voiding by this

move, allowing a Solution to be built on the next move.

b. If either of the Mover's claims are false, then he has flubbed.

1. For making a false C-claim he makes a C-flub.

2. For making a false A-claim he makes an A-flub.

c. By Challenging, the Challenger is saying to the Mover:

1. (C-flub) You could have correctly [C]hallenged (and should

have) instead of moving.

2. (A-flub) Your move has [A]Ilowed a Solution on the next

move.

Playing Mat

Forbidden Permitted Essential

The Resources The Resources The Resources transferred into this

played in this played in this section MUST be used in an essential way

section MUST section MAY, in the set of premisses offered as a

NOT be used in but NEED NOT, Solution. (A Resource is used essentially

the set of be used in the if and only if the conclusion can no

premisses set of longer be deduced from the remaining

offered as a premisses premisses when the premiss in which that

Solution. offered as a Resource is used is deleted from the set

Solution. of premisses offered as a Solution.

15. If a player challenges, he is declaring that the Mover has flubbed.

The Challenger has the Burden of Proof to show that the Mover flubbed.

a. The Challenger can sustain that Burden of Proof by writing a

Solution that shows that the Mover flubbed. The other player

(other than the Mover) is the one who can challenge.

b. Upon declaration of a C-flub the Challenger must show that there

was a Solution with the limitations imposed by the moves that had

been made when the prior A-flub occurred.

c. Upon declaration of an A-flub the Challenger must show that there

is a Solution on the next move with the limitations imposed by

the moves already made.

d. If the Challenger is plaintiff, the Solution is to the Goal set;

if the challenger is defendant, the Solution is to the NEGATION

of the Goal set.

e. If the match ends because all Resources have been transferred to

the Playing Mat, plaintiff has the Burden of Proof to show that

there is a Solution to the Goal.

Winning and Scoring

16. A player wins (and scores 18 or 10 points) if

1. she has the Burden of Proof and sustains it, or

2. she does not have the Burden of Proof, and nobody who has the

burden sustains it;

otherwise, a player loses (and scores 6 points).

Summary of Scoring at the End of the Match

Score of the Player Who Where Player with the Burden of Proof

Does Sustain it Does NOT Sustain

Has Burden of Proof on a Bold* 18 6

Challenge

Has Burden of Proof on a Regular 10 6

Challenge

Does NOT Have the Burden of Proof 6 10

* A C-flub challenge of the move immediately following an A-flub move.

Conclusion

17. The Legal Argument Game of LEGAL RELATIONS has been sketched briefly

and then described more completely, and the official rules that define

the game have been set forth in complete detail. The definitions of

both the deontic and CONDITIONAL LEGAL RELATIONS together with both

the assumed and some derived rules of inference and definitions that

are used in the reasoning in the LEGAL RELATIONS Language have been

presented (Appendix A). The strategies and course of play of the game

is illustrated in a play-by-play account of a pair of sample matches

of the LA Game (Appendix B).

18. As increasing numbers of workers in the legal domain become fluent in

the comprehensive and precisely-defined LEGAL RELATIONS Language, the

effects upon legal discourse and legal literature will unfold in step

with the increasing fluency. The LA Game is one of a variety of games

and puzzles that are now available as a means for accelerating the

process of becoming fluent in this language. These will be available

at the Internet site: http://thinkers.law.umich.edu/files/Leg_Arg.htm

19. The stimulation of the motivation of law students, practicing lawyers,

rules drafters, judges, legal scholars, and other toilers in the legal

vineyards to achieve such fluency in the LEGAL RELATIONS Language will

evolve as more examples of the usefulness of LRL are made public:

1. For law students, pictorial representations of LRL analysis of

appellate court opinions to deepen their understanding of the

implications and limitations of the courts’ decisions

2. For practicing lawyers, more comprehensive and precise tools for

structurally interpreting important legal documents, such as

their own professional liability insurance policies

3. For rules drafters, a means of checking the ambiguity in the

logical structure of regulations, statutes, constitutions,

corporate by-laws, contracts, and other sets of legal rules to

help assure that such ambiguity is deliberate, rather than

inadvertent

4. For appellate court judges, to craft written opinions that

precisely express the structure, scope, and limits of their

decisions

5. For legal scholars, a tool for the more precise and comprehensive

analysis and expression of legal doctrine for benefit of students

and others

6. Finally, for those other toilers who are seeking to build

computer systems to assist the legal profession, a representation

language for expert and other systems whose expressive power

covers all of legal discourse.

20. For those who are inclined to get started on this precise and

comprehensive language for law in the er-more-technological 21st

Century — a language that can precisely and completely

1. describe every possible legal state of affairs,

2. account for every possible change from one legal state to

another, and

3. represent every possible set of legal rules and every possible

legal argument — now is the time to begin the playing and solving

and learning. Challenge us to play a match of the LA Game!

References

Allen, Layman E. [1997] "Achieving Fluency in Modernized and Formalized

Hohfeld: Puzzles and Games for the LEGAL RELATIONS Language", Proceedings

of the Fifth International Conference on Artificial Intelligence and Law,

June 30 - July 3, 1997, The University of Melbourne Law School, Melbourne,

Victoria, Australia.

[1996] "From the Fundamental Legal Conceptions of Hohfeld to LEGAL

RELATIONS: Refining the Enrichment of Solely Deontic LEGAL RELATIONS", pp.

1-26 in DEONTIC LOGIC, AGENCY AND NORMATIVE SYSTEMS, (Edited by Mark A.

Brown and Jose Carmo), Springer and the British Computer Society, 1996.

Presented at DEON '96: Third International Workshop on Deontic Logic in

Computer Science, Sesimbra, Portugal, 11-13, January 1966. (Volume in the

WORKSHOPS IN COMPUTING Series edited by C. J. van Rijsbergen).

[1995] "Enriching the Deontic Fundamental Legal Conceptions of Hohfeld",

Invited paper presented at the 25th Anniversary Celebration of the

Norwegian Research Center for Computers and Law, March 15-17, l995, Oslo

University, Oslo, Norway, to be published in Anniversary Anthology in

Computers and Law, Edited by Jon Bing & O. Torvund, TANO-publ., Oslo.

Allen, Layman E. & Saxon, Charles S.[1995] "Better Language, Better

Thought, Better Communication: The A-HOHFELD Language for Legal Analysis",

Proceedings of the Fifth International Conference on Artificial

Intelligence and Law, May 21-24, 1995, University of Maryland, College

Park, Md.

[1991] "A-Hohfeld: A Language for Robust Structural Representation of

Knowledge in the Legal Domain to Build Interpretation-Assistance Expert

Systems", Invited paper for the First International Workshop on DEONTIC

LOGIC IN COMPUTER SCIENCE, Amsterdam, The Netherlands, December 11-13,

1991, published in DEONTIC LOGIC IN COMPUTER SCIENCE: Normative System

Specification (Edited by John-Jules Ch. Meyer and Roel J. Wieringa, John

Wiley & Sons, pp. 205-224 (1993).

[1986] "Analysis of the Logical Structure of Legal Rules by a Modernized

and Formalized Version of Hohfeld's Fundamental Legal Conceptions",

385-450, in Automated Analysis of Legal Texts: Logic, Informatics, Law,

Edited by Antonio A. Martino and Fiorenza Socci Natali, North-Holland,

Amsterdam.

Hohfeld, Wesley N. [1913] "Fundamental Legal Conceptions as Applied in

Judicial Reasoning," 23 YALE L. J. 16 (1913). Reprinted with a New Foreword

by Arthur L. Corbin by Yale University Press, London & New Haven (1964).

------------------------------------------------------------------------

Appendix A

The Rules of Inference, Constraints, and Deontic LEGAL RELATIONS

Definitions

A. The Five Rules of Inference of the Legal Argument Game

In the basis of the Logic of LEGAL RELATIONS the following five rule

schemata of inference are assumed. Each of these may be used by players in

The LA Games. They are all of the form:

A, ... N ----* S. This is an abbreviated way of saying: From the statements

A through N, it is valid to infer statement S.

There are four elements in the presentation of each rule schema (hereafter,

called rules) below:

(1) the name of the rule (2) an explanation of the

name

(3) statement of the rule in notation

(4) statement of the rule in text.

Rules:

D2o: Out-rule for the DONE_BY

operator

D2(s,p) ----* s

From "The state_of_affairs_s is brought about by (i.e.,

DONE_BY) person_p", it is valid to infer "The

state_of_affairs_s is so".

IFo: Out-rule for the IF operator

IF(r,s), r ----* s

From "IF the state_of_affairs_r is so, the

state_of_affairs_s is so" and "The state_of_affairs_r is

so", it is valid to infer "The state_of_affairs_s is so".

NEG-NEGo: Out-rule for double NEGATION

NEG(NEG(s)) ----* s

From "IT IS NOT SO THAT IT IS NOT SO THAT the

state_of_affairs_s is so", it is valid to infer "The

state_of_affairs_s is so".

POWERoD2oLRi: The out-out-in-rule for the

exercise of a POWER

POWER(D2(x,p),LR)), D2(x,p) ----* LR

From "Person_p has the POWER to create LEGAL_RELATION_LR

by exercising that POWER" and "Person_p exercises that

POWER (exercise_x of that POWER is DONE_BY Person_p)", it

is valid to infer "The LEGAL_RELATION_LR is so".

CONDITIONALoLRi: Out-in-rule for the

CONDITIONAL operator

CONDITIONAL(c,LR), c ----* LR

From "The CONDITIONAL (upon fulfillment of condition_c)

LEGAL_RELATION_LR is so" and "Condition-c has been

fulfilled, i.e., c is so", it is valid to infer

"LEGAL_RELATION_LR is so".

From these five rules two others can be derived that are used frequently in

the play of the LA Game to infer some LEGAL RELATION from the legally

determined exercise of a POWER or the legally determined fulfillment of the

condition of a CONDITIONAL LEGAL RELATION. These are the POWERoD2oD2IFoLRi

and CONDITIONALoD2IFoLRi rules.

POWERoD2oD2IFoLRi: The out-out-out-in-rule for

the exercise of a POWER

POWER(D2(x,p),LR), D2(s,p), D2(IF(D2(s,p),D2(x,p)),LS)

----** LR.

From POWER(D2(x,p),LR) and D2(s,p) and

D2(IF(D2(s,p),D2(x,p)),LS), it can be derived that it is

valid to infer LR.

In other words, given (1) that person_p has the POWER to create

LEGAL_RELATION_LR and (2) that state_of_affairs_s is DONE_BY person_p and

(3) that the legal system determines that IF state_of_affairs_s is DONE_BY

person_p THEN the exercise of POWER is DONE_BY person_p, it can be derived

that it is valid to infer (4) that the LEGAL_RELATION_LR is created.

CONDITIONALoD2IFoLRi: Out-out-in-rule for the

CONDITIONAL operator

CONDITIONAL(c,LR), s, D2(IF(s,c),LS) ----** LR.

From CONDITIONAL(c,LR) and s and D2(IF(s,c),LS), it can be

derived that it is valid to infer LR.

In other words,, given (1) that CONDITIONAL_LEGAL_RELATION_LR (conditioned

upon fulfillment of condition_c) is so and (2) that state_of_affairs_s is

so and (3) that the legal systems determines that IF state_of_affairs_s is

so, THEN condition_c is fulfilled, it can be derived that it is valid to

infer (4) that LEGAL_RELATION_LR is created.

The two similar derivations of this pair of derived rules are shown in

Figure 2.

Figure 2. Proofs of Two Derived Rules of Inference

POWERoD2oD2IFoLRi CONDITIONALoD2IFoLRi

1 POWER(D2(x,p),LR) suppose 1 CONDITIONAL(c,LR) suppose

2 2

D2(s,p) s

suppose suppose

3 _ D2(IF(D2(s,p),D2(x,p),LS) suppose 3 _ D2(IF(s,c),LS)

suppose

4 IF(D2(s,p),D2(x,p) 4 IF(s,c)

3,D2o 3,D2o

5 5

D2(x,p) c

4,2,IFo 4,2,IFo

6 LR 1,5,POWERoD2oLRi 6 LR 1,5,CONDITIONALoLRi

B. Constraints

In the reasoning in the LA Games there are also a pair of constraints upon

what can be assumed as premisses. These constraints are what make the

reasoning involved these games in accord with legal reality— specifically,

in accord with the jurisprudence of legal realism. The two constraints are

about what can be assumed as a premiss; they are the following:

1. s_to_c Constraint

IF_connections between s and c are relationships of a type that occur

between factual particulars and the general conditions of LEGAL RELATIONS.

Thus, IF(s,c) is a legal characterization. Such characterizations are

determined (i.e., DONE_BY) the legal system (and only by the legal system);

they cannot be assumed as premisses of a legal argument in the LA Games..

Thus, players of the LA Games cannot assume IF(s,c) as a premiss. If they

need IF(s,c) in their argument, what they must assume is that the legal

system determines IF(s,c), that is, D2(IF(s,c),LS).

2. D2(s,p)_to_D2(x,p) Constraint

Similarly, IF_connections between D2(s,p) and D2(x,p) are of a type that

occur between the factual particulars of what some specified person has

done and whether having done so constitutes an exercise of his POWER to

create a LEGAL RELATION -- another legal characterization that is only

DONE_BY the legal system. They, also, cannot be assumed as premisses of a

legal argument. Players of the LA Games cannot assume IF(D2(s,p),D2(x,p))

as a premiss. If they need IF(D2(s,p),D2(x,p)), what they must assume is

that the legal system determines IF(D2(s,p),D2(x,p)), that is,

D2(IF(D2(s,p),D2(x,p)),LS).

These rules of inference and constraints, in combination with the

definitions presented next, are the concepts players use in reasoning about

ways to reach their Goals in playing the LA Games.

C. Definitions of the Deontic (UNCONDITIONAL) and CONDITIONAL LEGAL

RELATIONS

1. Definitions of Deontic LEGAL RELATIONS

In the Basic variety of LA Games there are four deontic LEGAL RELATIONS

that do not explicitly use a deontic operator. Each of these is logically

equivalent to each of the others:

DUTY(sk,pi,pj) Person_pj has a DUTY to

person_pi to do sk.

RIGHT(sk,pj,pi) Person_pi has a RIGHT that

person_pj do sk.

IT IS NOT SO THAT person_pj

NEG(PRIVILEGE(NEG(sk),pi,pj)) has a PRIVILEGE with respect

to person_pi to do NOT sk.

IT IS NOT SO THAT person_pi

NEG(NO_RIGHT(sk,pj,pi)) has a NO_RIGHT that person_pj

do sk.

where i and j are different numerals from 1 to 4, and k is also a numeral

from 1 to 4.

In the Deontic variety of LA Games a fifth equivalent expression of a

deontic LEGAL RELATION is possible, one that uses the deontic operator, O,

namely:

IT IS OBLIGATORY THAT (sk be

O(D2(D4(sk,pi),pj)) DONE_FOR person_pi) be

DONE_BY person_pj.

The equivalence of these five deontic LEGAL RELATIONS result from the

following four definitions:

DUTYdf: DUTY(sk,pi,pj) =df O(D2(D4(sk,pi),pj))

RIGHTdf: RIGHT(sk,pi,pj) =df O(D2(D4(sk,pj),pi))

PRIVILEGEdf: PRIVILEGE(sk,pi,pj)) =df

NEG(O(D2(D4(NEG(sk),pi),pj)))

NO_RIGHTdf NO_RIGHT(sk,pi,pj)) =df NEG(O(D2(D4(sk,pj),pi)))

There are three other sets of five equivalent deontic LEGAL RELATIONS that

can be derived from these four definitions. All four sets are summarized in

Figure 3 below.

2. Definitions of Capacitive and Other CONDITIONAL LEGAL RELATIONS

CONDITIONAL LEGAL RELATIONS are of two types: capacitive and other. The

capacitive-type are POWER or POWER-equivalent LEGAL RELATIONS or their

NEGATIONS that are associated with changes in legal state that are brought

about by states of affairs DONE_BY legal persons (agentive). The other-type

of CONDITIONAL LEGAL RELATIONS are associated with changes in legal states

that are brought about by states of affairs that are NOT DONE_BY legal

persons (nonagentive).

Figure 3. Four Sets of Five Equivalent First-Level Deontic LEGAL RELATIONS

DUTY(s,pi,pj) NEG(DUTY(s,pi,pj))

RIGHT(s,pj,pi) NEG(RIGHT(s,pj,pi))

O(D2(D4(s,pi),pj)) NEG(O(D2(D4(s,pi),pj)))

NEG(NO_RIGHT(s,pj,pi)) NO_RIGHT(s,pj,pi)

NEG(PRIVILEGE(NEG(s),pi,pj)) PRIVILEGE(NEG(s),pi,pj)

DUTY(NEG(s),pi,pj) NEG(DUTY(NEG(s),pi,pj))

RIGHT(NEG(s),pj,pi) NEG(RIGHT(NEG(s),pj,pi))

O(D2(D4(NEG(s),pi),pj)) NEG(O(D2(D4(NEG(s),pi),pj)))

NEG(NO_RIGHT(NEG(s),pj,pi)) NO_RIGHT(NEG(s),pj,pi)

NEG(PRIVILEGE(s,pi,pj)) PRIVILEGE(s,pi,pj)

There are four capacitive LEGAL RELATIONS for which there are

definitions and two sets of four equivalent capacitive LEGAL

RELATIONS.

POWERdf: POWER(D2(x,p),LR) =df NEG(LR) & Ss(B(D2(s,p))&

(IF(D2(s,p),(D2(IF(D2(s,p),D2(x,p)),LS)&LR))))

"Person_p has POWER to create LEGAL_RELATION_LR." is equal to by

stipulated definition:

"1. LEGAL_RELATION_LR is NOT so, AND

2. there is some state_of_affairs_s such that,

A. it is naturally possible for state_of_affairs_s

to be DONE_BY person_p, AND

B. IF 1. state_of_affairs_s is DONE_BY

person_p

THEN 2. the legal system_LS will treat that s

being DONE_BY p as an exercise_x of

POWER DONE_BY person_p to

create LEGAL_RELATION_LR, AND

3. LEGAL_RELATION_LR is created".

The notational abbreviation: POWER(p,LR) =ab POWER(D2(x,p),LR)

is also available in LA Games (and similarly for the other capacitive

LEGAL RELATIONS). Note also that time relationships are left implicit

here in the LEGAL RELATIONS Language. However, in the Logic of LEGAL

RELATIONS underlying LRL time relationships are explicitly taken into

account.

[See Allen & Saxon 1986, 1991]

LIABILITYdf: LIABILITY(LR,D2(x,p) =df POWER(D2(x,p),LR)

"LEGAL_RELATON_LR has LIABILITY of being created by person_p" is equal

to by stipulated definition:

"Person_p has POWER to create LEGAL_RELATION_LR."

DISABILITYdf: DISABILITY(D2(x,p),LR) =df NEG(POWER(D2(x,p),LR))

"Person_p has DISABILITY to create LEGAL_RELATON_LR" is equal to by

stipulated definition:

"IT IS NOT SO THAT Person_p has POWER to create

LEGAL_RELATION_LR."

IMMUNITYdf: IMMUNITY(LR, D2(x,p)) =df NEG(POWER(D2(x,p),LR))

"LEGAL_RELATON_LR has IMMUNITY of being created by person_p" is equal

to by stipulated definition:

"IT IS NOT SO THAT Person_p has POWER to create

LEGAL_RELATION_LR."

From these four definitions there are two sets of four equivalent

deontic LEGAL RELATIONS that can be derived. Both sets are summarized

in Figure 4.

Figure 4. Two Sets of Four Equivalent Higher-Level Capacitive LEGAL

RELATIONS

POWER(D2(x,p),LR) NEG(POWER(D2(x,p,)LR))

LIABILITY(LR,D2(x,p)) NEG(LIABILITY(LR,D2(x,p)))

NEG(DISABILITY(D2(x,p),LR)) DISABILITY(D2(x,p),LR)

NEG(IMMUNITY(LR,D2(x,p))) IMMUNITY(LR,D2(x,p))

CONDITIONALdf: CONDITIONAL(c,LR) =df NEG(LR) & Ss(B(s) &

IF(s,D2(IF(s,c),LS)&LR))

"There is a CONDITIONAL_LEGAL_RELATION_CLR that LEGAL_RELATION_LR will

be created by the fulfillment of condition_c." is equal to by

stipulated definition:

"1. LEGAL_RELATON_LR is NOT so, AND

2. there is an state_of_affairs_s such that

A. it is naturally possible for state_of_affairs_s to occur,

AND

B. IF a. state_of_affairs_s occurs,

THEN b. the legal system will treat the occurrence of

state_of_affairs_s as fulfilling condition_c, AND

c. LEGAL_RELATON_LR is created."

Armed with these definitions, rules of inference, constraints, and

derived equivalencies we are ready to examine some examples of the

play of some matches of a LA 1B Game between a plaintiff and a

defendant in some detail.

------------------------------------------------------------------------

Appendix B

Example of the Play of Some Matches of the Legal Argument Game

Match 5A

Resources:

DUTY RIGHT IMMUNITY LIABILITY LIABILITY COND COND D2 D2 D2 D2 D2 D2 D2

D2 D2 D2 D2 D4 D4 D4 IF IF LS LS LS NEG NEG O O

c1 c1 c2 c2 c3 c3 p1 p1 p1 p1 p2 p2 p2 p2 p3 p3 p3 p3 p3 p3

s1 s1 s1 s2 s2 s3 s3 s3 s4 s4 s4 x1 x1 x2 x2 x2

Goal: DUTY(s3,p2,p3)

The 66 resources generated for Match 5A are shown above with four of them

underlined to indicate that they were selected by the first player

(plaintiff) to set the Goal of DUTY(s3,p2,p3). There are forms for matches

of the LA Game that can be downloaded from the Internet site for the LA

Game like Match 5A above. When these forms are printed out, they provide

materials for a paper and pencil version of the LA Game to be played

between two players. The moves of the players can be written into a summary

table provided like the one below.

After the Goal is set by the plaintiff, it is the defendant’s turn to

respond by transferring up to three of the Resources to one of the three

specified sections on the playing mat: the Forbidden section, the Permitted

are or the Essential section. In Match 5A defendant seeks to force

plaintiff to build a fourth-level Solution (one that uses three capacitive

operators and, thus, many more resources than are available in the

Resources section) by transferring IMMUNITY, LIABILITY, and LIABILITY from

the Resources into the Essential section. His objective in doing so is to

prevent the plaintiff from being able to construct a set of premisses from

which the Goal can be inferred. He indicates this Move 1 by underlining the

Resources that are being transferred and writing them in the Essential

column of Row 1.

Summary of Play after Goal is Set

Move Forbidden Permitted Essential

1 IMMUN* RIGHT IF LS IMMUN LIAB LIAB

3 LIAB* COND* O COND COND O

5 D4* D4* x2 D4 D4 D4

7 c1* c1 LS NEG c1 c2 c3

9 x1* x1 IF c2 x1 x2 x2

11 c3* c3 D2 D2 s1 s1 s1

13 D2 D2 D2 D2 D2 p1 p1 p1

15 s1* s2 s2 s3 s4 s4 s4

17 D2 D2 D2 Challenges, A-flub

18 s4* p1 p2 p3

The response of the plaintiff to defendant’s Move 1 is to shift the

IMMUNITY from the Essential section to the Permitted section and transfer

RIGHT, IF, and LS from the Resources to the Permitted section. (Recall that

plaintiffs can transfer the equivalent of five resources, where 1 shift = 2

transfers.) Her aim is to reduce the level of the Solution to a third-level

one (by shifting IMMUNITY) and to make available for use in her Solution

the RIGHT, IF and LS. She indicates her Move 2 by underlining the shifted

IMMUNITY (in Essential) and the transferred RIGHT, IF, and LS (in

Resources) and writes the four of them in the Permitted column of Row 2.

She also adds * to IMMUNITY to indicate that it was shifted.

After the first two moves have been made, six additional ones of the

Resources have been transferred to the playing mat. To indicate these

transfers each of the six are underlined so that the state of the Resources

that confronts the defendant as he prepares to make Move 3 is the

following:

Resources:

DUTY RIGHT IMMUNITY LIABILITYLIABILITY COND COND D2 D2 D2 D2 D2 D2 D2

D2 D2 D2 D2 D4 D4 D4 IF IF LS LS LS NEG NEG O O

c1 c1 c2 c2 c3 c3 p1 p1 p1 p1 p2 p2 p2 p2 p3 p3 p3 p3 p3 p3

s1 s1 s1 s2 s2 s3 s3 s3 s4 s4 s4 x1 x1 x2 x2 x2

The play continues in this manner with defendant making the odd-numbered

moves and the plaintiff making the even-numbered moves until one of the

players challenges or the Resources have all been transferred. The

motivation of the players for each move made for Moves 3 through 18 is

described in detail below.

Move 3. Defendant continues to seek to elevate the level of the

Solution by transferring COND and COND, to essential, forcing a

fifth-level Solution; he also seeks to force the use of the deontic

operator O in the Solution by transferring it to Essential.

Move 4. Plaintiff responds by shifting LIABILITY and COND from

Essential to Permitted, reducing the level of Solution that must be

built to a third-level one, and prevents defendant from forcing even

further use of deontic operators by transferring the only remaining O

from Resources to Permitted.

Move 5. Defendant seeks to force the use of two extra ‘D4's by

transferring D4, D4, and D4 to Essential.

Move 6. Plaintiff responds by shifting two of the ‘D4's from Essential

to Permitted, thereby eliminating the forced use of the two extra

‘D4's, and transfers one of the ‘x2's from Resources to Permitted to

prevent defendant from forcing the use of extra ‘x2's.

Move 7. Defendant seeks to force plaintiff to use extra ‘c’s by

transferring c1, c2, and c3 to Essential.

Move 8. Plaintiff eliminates the forced use of c1 shifting it from

Essential to Permitted, prevents defendant from forcing the use of the

remaining c1 and NEG by transferring them from Resources to Permitted,

and transfers LS from Resources to Permitted to be available for use

in a Solution.

Move 9. Defendant seeks to force the use of extra ‘x’s by transferring

x1, x2, and x2 to Essential.

Move 10. Plaintiff eliminates the forced use of x1 by shifting it from

Essential to Permitted, prevents defendant from forcing the use of the

remaining x1 by transferring it to Permitted, and transfers IF and c2

from Resources to Permitted to be available for use in a Solution.

Move 11. Defendant seeks to force the use of extra ‘s1’s by

transferring s1, s1, and s1 to Essential.

Move 12. Plaintiff eliminates the forced use of c3 (from Move 7) by

shifting it from Essential to Permitted, prevents defendant from

forcing the use of the remaining c3 by transferring it to Permitted,

and transfers D2 and D2 from Resources to Permitted to be available

for use in a Solution.

Move 13. Defendant seeks to force the use of extra ‘p1’s by

transferring p1, p1, and p1 to Essential.

Move 14. Plaintiff is aware that he can use all three of the ‘p1's in

a Solution that involves POWER and that he will need many ‘D2's for

such a Solution; so, he transfers five ‘D2's from Resources to

Permitted to make them available for use in a Solution.

Move 15. Defendant seeks to force the use of extra ‘s4’s by

transferring s4, s4, and s4 to Essential.

Move 16. Plaintiff eliminates the forced use of the extra s1 (from

Move 11) by shifting it from Essential to Permitted, prevents

defendant from forcing the use of an extra s3 by transferring it from

Resources to Permitted, and transfers s2 and s2 from Resources to

Permitted to make them available for use in a Solution (but also

blocking their being used by defendant to force use of extra ‘s2's in

the Solution.

At this stage of the play after Move 16, the state of the Resources is as

follows:

Resources:

DUTY RIGHT IMMUNITY LIABILITYLIABILITYCONDCONDD2D2D2D2 D2 D2 D2 D2 D2

D2 D2 D4D4 D4IFIFLS LS LS NEG NEG OO

c1 c1 c2 c2 c3 c3 p1p1p1 p1 p2 p2 p2 p2 p3 p3 p3 p3 p3 p3

s1 s1 s1 s2 s2 s3 s3 s3 s4 s4 s4 x1 x1 x2 x2 x2

The 50 underlined resources have been transferred to the playing mat, and

only the following 16 resources are available for further transfer: D2 D2

D2 D2 LS NEG p1 p2 p2 p2 p3 p3 p3 p3 p3 s3.

Move 17. Defendant seeks to prevent plaintiff from getting available

‘D2's needed for building Solutions of higher levels by transferring

D2, D2, and D2 to Forbidden.

Move 18. Plaintiff challenges, declaring that defendant by his last

move has made an A-flub; his move allows the plaintiff to achieve a

Solution on her next move.

On this kind of challenge the plaintiff has the Burden of Proof to show

that a Solution can be built by virtue of her next move. She indicates that

her move will consist of shifting the extra s4 (of Move 15) from Essential

to Permitted and transferring p1, p2, and p3 from Resources to Permitted.

She then writes as her Solution the following five premisses:

1. LIABILITY(COND(c2,O(D2(D4(s3,p2),p3))),D2(x2,p1))

2. D2(s1,p1)

3. D2(IF(D2(s1,p1),D2(x2,p1)),LS)

4. D2(IF(s4,c2),LS)

5. s4

using all 14 of the following resources in Essential: LIABILITY COND O

D4 c2 x2 x2 s1 s1 p1 p1 p1 s4 and s4. She also had available in

Permitted the following 16 other resources used in the five premisses:

IF LS LS IF c2 D2 D2 D2 D2 D2 D2 D2 s3 p1 p2 p3.

She then completes the proof to show that the conclusion,

DUTY(s3,p2,p3), i.e., the Goal, can be deduced from the Solution by

means of the rules of inference and definitions available,

6. POWER(D2(x2,p1),COND(c2,O(D2(D4(s3,p2),p3)))) 1,LIABILITYdf

7. COND(c2,O(D2(D4(s3,p2),p3))) 6,2,3,POWERoD2oD2IFoLRi

8. O(D2(D4(s3,p2),p3)) 7,5,4,CONDITIONALoD2IFoLRi

9. DUTY(s3,p2,,p3) 8,DUTYdf

Plaintiff has thus sustained her Burden of Proof on the challenge to show

that a Solution can be built after her next move. She scores 10 for this

match, and defendant scores 6. The match is over.

Now let us consider what might have happened under a different play of

Match 5, that is, a play with the same set of Resources as those for Match

5A, but with some different moves by the players. (This, incidentally,

illustrates that there can be many different plays with each of the sets of

Resources that can be downloaded from the LA Game site.) Suppose (1) that

in Match 5B, the same Goal is set as was set in Match 5A, and (2) that the

first 16 moves were the same so that the state of the Resources just after

Move 16 are the same as those shown above. It is defendant’s turn, and this

time he elects to pursue a different strategy at this stage.

Summary of Play after Goal is Set in Match 5B

Move Forbidden Permitted Essential

1 Same as the first 16 moves in Match 5A.

17: p3* p3* p3 p3 p3 p3

19 D2 p3* p3* D2 p3 p3

21 s4* p2* p1 p2 p2 p2

23 pass pass pass

24 Challenges, A-flub

p2*

Move 17. Instead of transferring the three ‘D2's to Forbidden,

defendant seeks to force plaintiff to use extra ‘p3's by transferring

p3, p3, and p3 to Essential.

Move 18. Plaintiff responds by (a) shifting two of the ‘p3's from

Essential to Permitted, reducing the number of ‘p3's that have to be

used in the Solution and (b) transferring one of the remaining ‘p3's

from Resources to Permitted to prevent defendant from forcing her to

use that one.

Move 19. Defendant seeks to force use of extra ‘p3's by transferring

p3, and p3 from Resources to Essential and to make unavailable a D2

that he thinks that Plaintiff might need by transferring D2 from

Resources to Forbidden.

Move 20. Plaintiff responds by shifting two of the extra ‘p3's from

Essential to Permitted and transferring a D2 from Resources to

Permitted to be available for use in a Solution.

Move 21. Defendant seeks to force the use of extra ‘p2’s by

transferring p2, p2, and p2 to Essential.

Move 22. Plaintiff eliminates the forced use of an extra s4 (from Move

15) by shifting an s4 from Essential to Permitted and also eliminates

the forced use of one of the ‘p2's by the same kind of shift of a p2.

She also makes available for use in the Solution the needed p1 by

transferring p1 from Resources to Permitted.

Move 23. In analyzing the situation defendant realizes (a) that

plaintiff does not need any of the remaining ‘D2's for a Solution (so,

there is no effective constraint imposed upon plaintiff by

transferring any of them to Forbidden, Permitted, or Essential) and

(b) that she also does not need the LS or NEG that remains nor will it

help to try to force her to use the LS or NEG (so, there is no point

in transferring either of them either). So, defendant passes, hoping

that plaintiff (a) will not recognize that she can build a Solution

after her next move and (b) will fail to challenge, and thus, enable

him to challenge her C-flub failure to challenge his A-flub when she

could have done so correctly.

Move 24. But plaintiff is not fooled. She challenges that there is an

A-flub, that is, that after defendant’s last move it is possible for

plaintiff to build a Solution after her next move. She then proceeds

to get rid of the last remaining extra p2 by shifting it from

Essential to Permitted.

Again she has the Burden of Proof on the A-flub challenge, and she

constructs the same Solution and proof of it as occurred in Match 5A. She

wins again in Match 5B, scoring 10 to defendant’s 6.

However, at Move 23 when defendant passed, he failed to realize that he

could have correctly made an A-flub challenge of Plaintiff’s prior move. By

simply transferring a D2 from Resources to Permitted, he could have reached

the NEGATION of the plaintiff’s Goal, that is NEG(DUTY(s3,p2,p3)). He then

could have constructed the following Solution:

1. LIABILITY(COND(c2,NEG(O(D2(D4(s3,p2),p3)))),D2(x2,p2))

2. D2(s1,p1)

3. D2(IF(D2(s1,p1),D2(x2,p1)),LS)

4. D2(IF(s4,c2),LS)

5. D2(D2(s4,p2),p2)

This would use all 17 of the following resource that are still in

Essential: LIABILITY COND 0 D4 c2 x2 x2 s1 s1 p1 p1 p1 s4 s4 p3 p2 and p2.

There would also be available in Permitted the following other 18 resources

used in the above Solution: NEG D2 D2 D2 D2 D2 D2 D2 D2 D2 IF IF LS LS c2

p2 p1 s3. The proof of the conclusion sought by defendant (i.e.,

NEG(DUTY(s3,p2,p3))) is the following:

6. POWER(D2(x2,p1),COND(c2,NEG(O(D2(D4(s3,p2),p3))))) 1,LIABILITYdf

7. COND(c2,NEG(O(D2(D4(s3,p2),p3)))) 6,2,3,POWERoD2oD2IFoLRi

8. D2(s4,p2) 5,D2o

9. s4 8,D2o

10. NEG(O(D2(D4(s3,p2),p3)))

7,9,4,CONDITIONALoD2IFoLRi

11. NEG(DUTY(s3,p2,p3)) 10,DUTYdf

After players have written out the proofs a few times, they will realize

that the proofs are all similar; they all involve repeated applications of

POWERoD2oD2IFoLRi and CONDITIONALoD2IFoLRi and definitions. That is why the

writing of proofs is NOT required in sustaining the Burden of Proof. Only

the writing of the Solution is required to sustain it.

By being careful and competent in his reasoning the defendant could have

won Match 5B. A similar strategy will work for those who aspire to become

fluent in the LEGAL RELATIONS Language. By carefully reading and following

the play of these two matches of the LA Game, step-by-step through each

match, such learners can get a good start on appreciating the nature and

strategies of playing the LA Games. This, in turn, will enable them to then

use the play of such games to enhance their fluency in the LEGAL RELATIONS

Language.