On legal reasoning, legal informatics and visualization. Transforming the problem of impossibility to achieve several goals into a weighing problem

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1 On legal reasoning, legal informatics and visualization Transforming the problem of impossibility to achieve several goals into a weighing problem Vytautas ČYRAS Vilnius University Faculty of Mathematics and Informatics Vilnius, Lithuania Vytautas.Cyras@mif.vu.lt Lecture slides

2 1. Legal reasoning. An example T. Bench-Capon, H. Prakken (2006) Justifying actions by accruing arguments. In: Computational Models of Argument Proceedings of COMMA 2006, pp IOS Press. Slides: 2

3 An example problem: legal punishment A judge must determine the best way to punish (pu) a criminal found guilty. He has three options: imprisonment (pr), a fine (fi) and community service (cs). Besides punishment there are three more goals at stake, deterring the general public (de), rehabilitating the offender (re) and protecting society from crime (pt). So pu will be the most important goal, but the method of punishment chosen (pr, fi or cs) will depend on other goals. Initial state ( ) Actions: 1. imprisonment (pr), pr fi cs 2. fine (fi) 3. community service (cs) Final state ( pu, de, pt, re ) Goals: 1. punishment (pu) main goal 2. deterrence (de) 3. rehabilitation (re) 4. protecting society (pt) pu re de pt 3

4 Causal knowledge 1. Imprisonment (pr) promotes both deterrence (de) [R4] and protection of society (pt) [R5], but demotes rehabilitation (re) [R6] of the offender. 2. Fine (fi) promotes deterrence (de) [R7] but has no effect on rehabilitation (re) or the protection of society (pt) since the offender would remain free. 3. Community service (cs) promotes rehabilitation (re) [R9] of the offender, but demotes deterrence (de) [R8] since this punishment is not feared. Causal rules (between actions and goals): R1: pr pu R2: fi pu R3: cs pu 3 actions: R4: pr de R5: pr pt R6: pr re imprisonment (pr) R5 R1 R4 R6 R7: fi de R8: cs de fine (fi) R7 R2 R8 R3 R9: cs re community service (cs) R9 4 goals: protection of society (pt) deterrence (de) punishment (pu) rehabilitation (re) 4

5 Evaluation of arguments for actions. Values of goals Judge s goal base G = { pu, de, pt, re } (more exactly, G = { D pu, D de, D pt, D re }, where D is a modality; standing for desire) A propositional modal logic is used All 4 goals cannot be achieved! See further Question: What is the best way to punish the offender? Answer: cs (see further) Reason: first, cs > pr, second, cs > fi Value (promoted, demoted) Score { pu, de, pt, re } v(pr + ) = ( {pu, de, pt}, {re} ) 3:1 (1, 1, 1, -1) v(fi + ) = ( {pu, de}, ) 2:0 (1, 1, 0, 0) v(cs + ) = ( {pu, re}, {de} ) 2:1 (1, -1, 0, 1) R1: pr pu R2: fi pu R3: cs pu R4: pr de R5: pr pt R6: pr re R7: fi de R8: cs de R9: cs re pr + fi + cs + 5

6 A sketch of reasoning for cs Step 1 pr + > 1 pr Reason: pu sways cs + > 2 cs Step 2: > 3 > 3 > 4 Extralogical choice: re is next to pu Hence re > 3 de + pt Step 3: > 4 Extralogical choice for rehabilitation: re de > 4 de pr + fi + cs + > 1 > 2 winner pr cs 6

7 Arguments on imprisonment Practical syllogism, originally see Aristotle 1. Agent P wishes to realise goal G. 2. If P performs action A, G will be realised. 3. Therefore, P should perform A. Both PPS and NPS are defeasible. D G A G D A Abduction positive (Positive practical syllogism, PPS) D G A G D A Abduction negative (Negative practical syllogism, NPS) Individual defeat l 1 D pr l 2 D pr l 3 D pr l 4 D pr pr pu D pu pr de D de pr pt D pt pr re D re R1 R4 R5 R6 7

8 Abduction and deduction Abduction From goal to facts Abductive reasoning Backward-chaining in Artificial Intelligence Goal R 3 R 1 R 2 R 4 Deduction From facts to goal Deductive reasoning Forward-chaining Facts D G A G D A Abduction positive A A G G modus ponens 8

9 Accruals on imprisonment. Then defeat Defeat > 1 : pu sways Accrual : pr + D pr pr D pr l 1 D pr l 2 D pr l 3 D pr l 4 D pr pr pu D pu pr de D de pr pt D pt pr re D re R1 R4 R5 R6 9

10 Accrual on fining Accrual : fi + D fi l 5 D fi l 6 D fi fi pu D pu fi de D de R2 R7 10

11 Accruals on community service Defeat > 2 : pu sways Accrual : cs + D cs cs D cs l 7 D cs l 8 D cs l 9 D cs cs pu D pu cs re D re cs de D de R3 R9 R8 11

12 The attack graph pr + > 1 pr Step 1. > 1 and > 2 Step 2. > 3 Value (promoted, demoted) v(pr + ) = ( {pu, de, pt}, {re} ) 3:1 v(cs + ) = ( {pu, re}, {de} ) 2:1 re > 3 de + pt More precisely, re de > 3 de + pt re proved above. fi + > 3 winner > 4 cs + > 2 cs Extralogical choice: re is next to pu Thus we (judge) make re the second most important goal Other choices, e.g. pro fine fi + are possible cs + D cs Defeat: > 3 pr + D pr l 7 D cs l 8 D cs l 1 D pr l 2 D pr l 3 D pr cs pu D pu cs re D re pr pu D pu pr de D de pr pt D pt R3 R9 R1 R4 R5 12

13 Step 3. Defeat > 4 We chose promoting rehabilitation re while demoting deterrence de over promoting deterrence de. Formally, re de > 4 de. Value (promoted, demoted) v(fi + ) = ( {pu, de}, ) 2:0 v(cs + ) = ( {pu, re}, {de} ) 2:1 re de > 4 de pr + fi + > 3 winner > 4 cs + > 1 > 2 pr Justification: given that we must punish, we choose to do so in a way which will aid rehabilitation. cs cs + D cs Defeat: > 4 fi + D fi l 7 D cs l 8 D cs l 5 D fi l 6 D fi cs pu D pu cs re D re fi pu D pu fi de D de R3 R9 R2 R7 13

14 Conclusions Limitations of this formalisation See Bench-Capon & Prakken of artificial intelligence in law formalising choice algorithmically undecidable problems NP-problems of mathematics 14

15 2. On the problem of infeasibility of achieving several goals 15

16 Example: drink vs. roll You have one coin and want to buy two items: drink roll of bread Initial state buydrink ( ) buyroll Final state ( drink, roll ) Buy one item for a coin. You cannot buy both items. One cannot eat it and keep it Impossible 16

17 Modeling with two rules 1) Rules: R1: coin drink & coin buydrink R2: coin roll & coin buyroll 2) Facts: coin Three alternative goals: 3) Goal: drink Path: R1 3) Goal: roll Path: R2 3) Goal: drink & roll Path: impossible coin R1 drink coin R2 roll 17

18 Geometrical explanation. Choice is extralogical Which action to choose: to buy a drink or alternatively a roll? (drink, 0) > (0, roll) or alternatively (drink, 0) < (0, roll)? No ordering of vectors, i.e. neither (1,0) > (0,1) nor (1,0) < (0,1) Formal logic cannot help here to make a choice Extralogical reasons have to be involved E.g., assign weight 2 to drink and 1 to roll. You are thirsty and prefer drink In other circumstances you might prefer roll roll (0,1) 0 1 roll (0,1) Impossible (1,1) (1,0) drink (2,1) Reasoning with the distance to the goal Distance from drink: (2,1) (2,0) = (0,1) = 1 Distance from roll: (2,1) (0,1) = (2,0) = 2 Smaller distance to goal, 1, is preferred to 2. Therefore drink wins 0 drink (2,0) 0 2 winner 18

19 The landscape metaphor in meansends analysis The end justifies the means (Der Zweck heiligt das Mittel). Kant s imperative: Who is willing the end, must be willing the means (Wer den Zweck will, muss das Mittel wollen). evaluation m weak = (0,1) positive 1 m right = (1,1) negative 0 0 false 1 true m wrong = (1,0) bringsabouttheend 3 means m wrong, m weak and m right 19

20 Thank you 20