Computational Argumentation 20202021 HC 12 Legal argumentation with

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Computational Argumentation 2020/2021, HC 12 Legal argumentation with cases (1) Henry Prakken October 21,

Computational Argumentation 2020/2021, HC 12 Legal argumentation with cases (1) Henry Prakken October 21, 2020

Pros and cons at three levels of legal reasoning n Determining the facts of

Pros and cons at three levels of legal reasoning n Determining the facts of the case n n Classifying the facts under the conditions of a statutory rule n n conflicting sources of evidence generalisations with exceptions … weighing factors conflicting interpretations based on legal principles or values … Applying the statutory rule n n n Conflicting rules Reasons not to apply the rule …

Legal reasoning is adversarial n n Legal reasoning forms leave room for doubt Legal

Legal reasoning is adversarial n n Legal reasoning forms leave room for doubt Legal cases involve clashes of interest Dispute n study constructing and attacking arguments

Two topics n n Classification/interpretation: Factorbased domains Interpretation and law making: decision making

Two topics n n Classification/interpretation: Factorbased domains Interpretation and law making: decision making

Modelling legal classification and interpretation in factor-based domains

Modelling legal classification and interpretation in factor-based domains

Factor-based reasoning n n In legal classification and interpretation there are often no clear

Factor-based reasoning n n In legal classification and interpretation there are often no clear rules Often there only are factors: tentative reasons pro or con a conclusion n n Often to different degrees Factors are weighed in cases, which become precedents n n But how do judges weigh factors? And how do precedents constrain new decisions? 6

Running example factors: misuse of trade secrets n Some factors pro misuse of trade

Running example factors: misuse of trade secrets n Some factors pro misuse of trade secrets: F 2 Bribe-Employee n F 4 Agreed-Not-To-Disclose n F 6 Security-Measures n F 15 Unique-Product n F 18 Identical-Products n F 21 Knew-Info-Confidential n n Some factors con misuse of trade secrets: F 1 Disclosure-In-Negotiations n F 16 Info-Reverse-Engineerable n F 23 Waiver-of-Confidentiality n F 25 Info-Reverse-Engineered n HYPO Ashley & Rissland 1985 -1990 CATO Aleven & Ashley 1991 -1997

HYPO Ashley & Rissland 1987 -1990 n Representation language: n n n Kevin Ashley

HYPO Ashley & Rissland 1987 -1990 n Representation language: n n n Kevin Ashley & Edwina Rissland Cases: decision (p or d) + p-factors and d-factors Current Fact Situation: factors Arguments: n n n Citing (for its decision) a case on its similarities with CFS Distinguishing a case on its differences with CFS Taking into account which side is favoured by a factor

Example with factors C 1 (p) C 2 (d) pp 11 pp 22 p

Example with factors C 1 (p) C 2 (d) pp 11 pp 22 p 3 dd 11 dd 22 CFS p 1 d 2 d 3 p 1 p 3 d 3

Example with factors C 1 (p) C 2 (d) pp 11 pp 22 pp

Example with factors C 1 (p) C 2 (d) pp 11 pp 22 pp 33 dd 11 dd 22 Distinguish! CFS p 1 d 2 d 3 p 1 p 3 d 3 Distinguish!

Example with factors C 1 (p) C 2 (d) p 1 d 2 d

Example with factors C 1 (p) C 2 (d) p 1 d 2 d 3 pp 11 pp 22 p 3 dd 11 dd 22 CFS Distinguish! p 1 p 3 d 3 Distinguish!

HYPO’s argument game n n Given: a case base and a current fact situation

HYPO’s argument game n n Given: a case base and a current fact situation Plaintiff starts with a citable case n n A case decided for plaintiff and sharing proplaintiff factors with the CFS Defendant: n n cites all counterexamples (cases citable for defendant) distinguishes citation in all possible ways n n n On pro-plaintiff factors of precedent lacking in CFS On new pro-defendant factors in the CFS Plaintiff distinguishes defendant’s counterexamples in all possible ways

Citing precedent n Mason v Jack Daniels Distillery (Mason) – undecided. F 1 Disclosure-In-Negotiations

Citing precedent n Mason v Jack Daniels Distillery (Mason) – undecided. F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures (p) n F 15 Unique-Product (p) n F 16 Info-Reverse-Engineerable (d) n F 21 Knew-Info-Confidential (p) n n Bryce and Associates v Gladstone (Bryce) – plaintiff F 1 Disclosure-In-Negotiations (d) n F 4 Agreed-Not-To-Disclose (p) n F 6 Security-Measures (p) n F 18 Identical-Products (p) n F 21 Knew-Info-Confidential (p) n

Citing precedent n Mason v Jack Daniels Distillery (Mason) – undecided. F 1 Disclosure-In-Negotiations

Citing precedent n Mason v Jack Daniels Distillery (Mason) – undecided. F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures (p) n F 15 Unique-Product (p) n F 16 Info-Reverse-Engineerable (d) n F 21 Knew-Info-Confidential (p) n n Plaintiff cites Bryce because of F 6, F 21 Bryce and Associates v Gladstone (Bryce) – plaintiff F 1 Disclosure-In-Negotiations (d) n F 4 Agreed-Not-To-Disclose (p) n F 6 Security-Measures (p) n F 18 Identical-Products (p) n F 21 Knew-Info-Confidential (p) n

Distinguishing precedent n Mason v Jack Daniels Distillery (Mason) – undecided. F 1 Disclosure-In-Negotiations

Distinguishing precedent n Mason v Jack Daniels Distillery (Mason) – undecided. F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures (p) n F 15 Unique-Product (p) n F 16 Info-Reverse-Engineerable (d) n F 21 Knew-Info-Confidential (p) n n Plaintiff cites Bryce because of F 6, F 21 Bryce and Associates v Gladstone (Bryce) – plaintiff F 1 Disclosure-In-Negotiations (d) n F 4 Agreed-Not-To-Disclose (p) n F 6 Security-Measures (p) n F 18 Identical-Products (p) n F 21 Knew-Info-Confidential (p) n Defendant distinguishes Bryce because of F 4, F 18 and F 16

Counterexample n Mason v Jack Daniels Distillery – undecided. F 1 Disclosure-In-Negotiations (d) n

Counterexample n Mason v Jack Daniels Distillery – undecided. F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures (p) n F 15 Unique-Product (p) n F 16 Info-Reverse-Engineerable (d) n F 21 Knew-Info-Confidential (p) n n Defendant cites Robinson because of F 1 Robinson v State of New Jersey – defendant. F 1 Disclosure-In-Negotiations (d) n F 10 Secrets-Disclosed-Outsiders (d) n F 18 Identical-Products (p) n F 19 No-Security Measures (d) n F 26 Deception (p) n

Distinguishing counterexample n Mason v Jack Daniels Distillery – undecided. F 1 Disclosure-In-Negotiations (d)

Distinguishing counterexample n Mason v Jack Daniels Distillery – undecided. F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures (p) n F 15 Unique-Product (p) n F 16 Info-Reverse-Engineerable (d) n F 21 Knew-Info-Confidential (p) n n Defendant cites Robinson because of F 1 Robinson v State of New Jersey – defendant. F 1 Disclosure-In-Negotiations (d) n F 10 Secrets-Disclosed-Outsiders (d) n F 18 Identical-Products (p) n F 19 No-Security Measures (d) n F 26 Deception (p) n Plaintiff distinguishes Robinson because of F 6, F 15, F 21 and F 10, F 19

K. D. Ashley. Modeling Legal Argument: Reasoning with Cases and Hypotheticals. MIT Press, Cambridge,

K. D. Ashley. Modeling Legal Argument: Reasoning with Cases and Hypotheticals. MIT Press, Cambridge, MA, 1990. Plaintiff: I should win because My case shares pro factors F 6 and F 21 with Bryce, which was won by plaintiff Defendant: Unlike the present case, Bryce had pro factors F 4 and F 18 Defendant: Unlike Bryce, the present case has con factor F 16 Plaintiff: Unlike Robinson, the present case has pro factors F 6, F 15 and F 21 Defendant: I should win because my case shares con factor F 1 with Robinson, which was won by defendant Plaintiff: Unlike the present case, Robinson had con factors F 10 and F 19

From two-valued to many-valued factors (dimensions) n Dimensions can have a value from an

From two-valued to many-valued factors (dimensions) n Dimensions can have a value from an ordered range of values n n Numbers Anything else that can be ordered Notation: (dimension, value) or (d, v) Dimensions have polarities: con < pro

Example dimensions in HYPO n Number of outsider disclosees (0, 1, …. ) pro

Example dimensions in HYPO n Number of outsider disclosees (0, 1, …. ) pro 0 1 2 3 4 con 5, …. .

Example dimensions in HYPO n Security measures (minimal measures, acces to premises controlled, entry

Example dimensions in HYPO n Security measures (minimal measures, acces to premises controlled, entry by visitors restricted, entry by employees restricted) con pro minimal < access controlled < entry visitors restr < entry employees restr

Example with dimensions n n Precedent – defendant n F 16 Info-Reverse-Engineerable (d) n

Example with dimensions n n Precedent – defendant n F 16 Info-Reverse-Engineerable (d) n F 21 Knew-Info-Confidential (p) n Fx Security measures = entry visitors restricted n Fy Number of disclosees = 10 New case – undecided F 16 Info-Reverse-Engineerable (d) n F 21 Knew-Info-Confidential (p) n Fx’ Security measures = access to premises controlled n Fy’ Number of disclosees = 6 n

Vincent Aleven 1991 -1997 (snapshot of) CATO Factor Hierarchy Misuse of Trade Secret (p)

Vincent Aleven 1991 -1997 (snapshot of) CATO Factor Hierarchy Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d) F 101: Info Trade Secret (p) F 102: Efforts to maintain secrecy (p) F 4: Agreed not to disclose (p) F 1: Disclosures in negotiations (d) F 104: Info valuable (p) F 6: Security measures (p) F 15: Unique product (p)

V. Aleven. Using background knowledge in case-based legal reasoning: a computational model and an

V. Aleven. Using background knowledge in case-based legal reasoning: a computational model and an intelligent learning environment. Artificial Intelligence 150: 183 -237, 2003. Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d) F 101: Info Trade Secret (p) F 102: Efforts to maintain secrecy (p) F 4: Agreed not to disclose (p) Distinguishing F 1: Disclosures in negotiations (d) F 104: Info valuable (p) F 6: Security measures (p) F 15: Unique product (p)

Emphasising distinctions Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d)

Emphasising distinctions Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d) F 101: Info Trade Secret (p) F 102: Efforts to maintain secrecy (p) F 4: Agreed not to disclose (p) F 1: Disclosures in negotiations (d) F 104: Info valuable (p) F 6: Security measures (p) F 15: Unique product (p)

Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d) F 101:

Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d) F 101: Info Trade Secret (p) F 102: Efforts to maintain secrecy (p) F 4: Agreed not to disclose (p) Downplaying distinctions F 1: Disclosures in negotiations (d) F 104: Info valuable (p) F 6: Security measures (p) F 15: Unique product (p)

Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d) F 101:

Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d) F 101: Info Trade Secret (p) F 102: Efforts to maintain Secrecy (p) F 4: Agreed not to disclose (p) Distinguishing F 1: Disclosures In negotiations (d) F 104: Info valuable (p) F 6: Security measures (p) F 15: Unique product (p)

Emphasising distinctions Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d)

Emphasising distinctions Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d) F 101: Info Trade Secret (p) F 102: Efforts to maintain Secrecy (p) F 4: Agreed not to disclose (p) F 1: Disclosures In negotiations (d) F 104: Info valuable (p) F 6: Security measures (p) F 15: Unique product (p)

Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d) F 101:

Misuse of Trade Secret (p) F 120: Info legitimately obtained elsewhere (d) F 101: Info Trade Secret (p) F 102: Efforts to maintain Secrecy (p) F 4: Agreed not to disclose (p) Downplaying distinctions F 1: Disclosures In negotiations (d) F 104: Info valuable (p) F 6: Security measures (p) F 15: Unique product (p)

Two further issues n Which decisions are allowed or forced by a body of

Two further issues n Which decisions are allowed or forced by a body of precedents? n n Precedential constraint Where do preferences come from?

John Horty A logical account of case-based reasoning in factor-based domains: Precedential constraint

John Horty A logical account of case-based reasoning in factor-based domains: Precedential constraint

Notation (factors) n n n Factors = Pro U Con Outcomes = {o, o’}

Notation (factors) n n n Factors = Pro U Con Outcomes = {o, o’} F Factors favours s Outcomes iff n n -s = o’ iff s = o -s = o iff s = o’ s = o and F Pro; or s = o’ and F Con n Fs F Factors = the subset of F favouring s n A case c = (Pro(c), Con(c), Outcome(c)) where: n n n Pro(c), Con(c) Factors Outcome(c) {o, o’} Pro(c) favours Outcome(c) Con(c) favours -Outcome(c) A fact situation is a nonempty subset of Factors

Precedential constraint: result model n n n For two fact situations X and Y:

Precedential constraint: result model n n n For two fact situations X and Y: X s Y iff Xs Ys and Y-s X-s Deciding fact situation F for s is forced iff there exists a precedent (X, Y, s) such that X U Y s F n And allowed iff deciding F for –s is not forced. J. Horty, Rules and reasons in theory of precedent. Legal Theory 17 (2011): 1 -33.

X s Y iff Xs Ys and Y-s X-s Deciding F for s is

X s Y iff Xs Ys and Y-s X-s Deciding F for s is forced iff there exists a precedent (X, Y, s) such that X U Y s F n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n Security measures (p 3) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) {p 1, p 3, d 1, d 3} p FS 1? n Case 2 – won by defendant n Bribe-Employee (p 2) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) {p 2, d 1, d 3} d FS 1? n FS 1 – n Bribe-Employee (p 2) n Security measures (p 3) n Info-Reverse-Engineerable (d 2) n Secrets-disclosed-outsiders (d 3) {p 2, p 3, d 2, d 3}

X s Y iff Xs Ys and Y-s X-s Deciding F for s is

X s Y iff Xs Ys and Y-s X-s Deciding F for s is forced iff there exists a precedent (X, Y, s) such that X U Y s F n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n Security measures (p 3) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) {p 1, p 3, d 1, d 3} p FS 1? No n Case 2 – won by defendant n Bribe-Employee (p 2) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) {p 2, d 1, d 3} d FS 1? n FS 1 – n Bribe-Employee (p 2) n Security measures (p 3) n Info-Reverse-Engineerable (d 2) n Secrets-disclosed-outsiders (d 3) {p 2, p 3, d 2, d 3}

X s Y iff Xs Ys and Y-s X-s Deciding F for s is

X s Y iff Xs Ys and Y-s X-s Deciding F for s is forced iff there exists a precedent (X, Y, s) such that X U Y s F n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n Security measures (p 3) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) {p 1, p 3, d 1, d 3} p FS 1? n Case 2 – won by defendant n Bribe-Employee (p 2) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) {p 2, d 1, d 3} d FS 1? No n FS 1 – n Bribe-Employee (p 2) n Security measures (p 3) n Info-Reverse-Engineerable (d 2) n Secrets-disclosed-outsiders (d 3) {p 2, p 3, d 2, d 3}

Relevant differences n Assuming cases c and f have the same outcome s: n

Relevant differences n Assuming cases c and f have the same outcome s: n n n D(c, f) = the pro-s factors in c that are not in f and the con-s factors in f that are not in c. = all differences that make f weaker for s than c Proposition: Deciding f for s is forced iff for some c in CB with outcome s: D(c, f) =

Example cases n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n

Example cases n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n Security measures (p 3) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) D(C 1, f) = n Case 2 – won by defendant n Bribe-Employee (p 2) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) D(C 2, f) = n FS – n Bribe-Employee (p 2) n Security measures (p 3) n Info-Reverse-Engineerable (d 2) n Secrets-disclosed-outsiders (d 3)

Example cases n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n

Example cases n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n Security measures (p 3) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) D(C 1, f) = {p 1} U {d 2} n Case 2 – won by defendant n Bribe-Employee (p 2) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) D(C 2, f) = n FS – n Bribe-Employee (p 2) n Security measures (p 3) n Info-Reverse-Engineerable (d 2) n Secrets-disclosed-outsiders (d 3)

Example cases n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n

Example cases n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n Security measures (p 3) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) D(C 1, f) = {p 1} U {d 2} n Case 2 – won by defendant n Bribe-Employee (p 2) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) D(C 2, f) = {p 3} U {d 1} n FS – n Bribe-Employee (p 2) n Security measures (p 3) n Info-Reverse-Engineerable (d 2) n Secrets-disclosed-outsiders (d 3)

Decisions as preferences between factor sets The Pro-factors of precedent are P The Con-factors

Decisions as preferences between factor sets The Pro-factors of precedent are P The Con-factors of precedent are C precedent was decided Pro P+ are preferred over C- (C- < P+ ) P+ = P plus zero or more additional pro-factors C- = C minus zero or more con factors H. Prakken & G. Sartor, Modelling reasoning with precedents in a formal dialogue game. Artificial Intelligence and Law 6 (1998): 231 -287.

Precedential constraint: reason model n n A case c express a preference between Pro(c)

Precedential constraint: reason model n n A case c express a preference between Pro(c) and Con(c) as in Prakken & Sartor (1998) A case base CB expresses a set of preferences CB is consistent if and only if there are no factor sets X and Y such that both X < Y and Y < X Assume < is consistent. A decision s in a new case C is: n n allowed by CB iff adding C with decision s to CB leaves < consistent. forced iff allowed and adding C with decision -s to CB makes < inconsistent J. Horty, Rules and reasons in theory of precedent. Legal Theory 17 (2011): 1 -33.

Example cases n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n

Example cases n Case 1 – won by plaintiff n Deceive-plaintiff (p 1) n Security measures (p 3) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) {d 1, d 3} < {p 1, p 3} n Case 2 – won by defendant n Bribe-Employee (p 2) n No-unique-product (d 1) n Secrets-disclosed-outsiders (d 3) {p 2} < {d 1, d 3} n FS 1 – n Bribe-Employee (p 2) n Security measures (p 3) n Info-Reverse-Engineerable (d 2) n Secrets-disclosed-outsiders (d 3) {p 2, p 3} ? {d 2, d 3}

Following, distinguishing and overruling precedents n n Let Prec have pro factors P and

Following, distinguishing and overruling precedents n n Let Prec have pro factors P and con factors C and decision pro. Let Curr have pro factors Pcurr such that P Pcurr. n n n Following Prec = deciding Curr pro Distinguishing Prec = deciding Curr con where deciding Curr either pro or con is allowed Overruling Prec = deciding Curr con where deciding Curr pro is forced

Example (1) n Precedent – plaintiff F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures

Example (1) n Precedent – plaintiff F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures (p) n F 21 Knew-Info-Confidential (p) n F 23 Waiver-of-Confidentiality (d) n n New Case – undecided F 21 Knew-Info-Confidential (p) n F 23 Waiver-of-Confidentiality (d) n F 25 Info-Reverse-Engineered (d) n {F 6, F 21} > {F 1, F 23}

Example (1) n Precedent – plaintiff F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures

Example (1) n Precedent – plaintiff F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures (p) n F 21 Knew-Info-Confidential (p) n F 23 Waiver-of-Confidentiality (d) n n {F 6, F 21} > {F 1, F 23} New Case – undecided F 21 Knew-Info-Confidential (p) n F 23 Waiver-of-Confidentiality (d) n F 25 Info-Reverse-Engineered (d) n Pro = {F 21} > {F 23, F 25} Con = {F 21} < {F 23, F 25}

Example (1) n Precedent – plaintiff F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures

Example (1) n Precedent – plaintiff F 1 Disclosure-In-Negotiations (d) n F 6 Security-Measures (p) n F 21 Knew-Info-Confidential (p) n F 23 Waiver-of-Confidentiality (d) n n {F 6, F 21} > {F 1, F 23} New Case – undecided F 21 Knew-Info-Confidential (p) n F 23 Waiver-of-Confidentiality (d) n F 25 Info-Reverse-Engineered (d) n Deciding pro follows precedent Deciding con distinguishes precedent Pro = {F 21} > {F 23, F 25} Con = {F 21} < {F 23, F 25} Both pro and con allowed

Example (2) n Precedent 1 – plaintiff n n n Precedent 2 – defendant

Example (2) n Precedent 1 – plaintiff n n n Precedent 2 – defendant n n F 1 Disclosure-In-Negotiations (d) F 6 Security-Measures (p) F 21 Knew-Info-Confidential (p) F 23 Waiver-of-Confidentiality (d) F 6 Security-Measures (p) F 21 Knew-Info-Confidential (p) F 25 Info-Reverse-Engineered (d) New Case – undecided n n n F 21 Knew-Info-Confidential (p) F 23 Waiver-of-Confidentiality (d) F 25 Info-Reverse-Engineered (d) {F 6, F 21} > {F 1, F 23} {F 6, F 21} < {F 25} Pro = {F 21} > {F 23, F 25} Con = {F 21} < {F 23, F 25}

Deciding pro overrules precedent 2 Deciding con follows precedent 2 Example (2) n Precedent

Deciding pro overrules precedent 2 Deciding con follows precedent 2 Example (2) n Precedent 1 – plaintiff n n n Precedent 2 – defendant n n F 1 Disclosure-In-Negotiations (d) F 6 Security-Measures (p) F 21 Knew-Info-Confidential (p) F 23 Waiver-of-Confidentiality (d) F 6 Security-Measures (p) F 21 Knew-Info-Confidential (p) F 25 Info-Reverse-Engineered (d) New Case – undecided n n n F 21 Knew-Info-Confidential (p) F 23 Waiver-of-Confidentiality (d) F 25 Info-Reverse-Engineered (d) {F 6, F 21} > {F 1, F 23} {F 6, F 21} < {F 25} Only con allowed Pro = {F 21} > {F 23, F 25} Con = {F 21} < {F 23, F 25}