Defeasibility in the law Giovanni Sartor EUI - European University - PowerPoint PPT Presentation

Defeasibility in the law Giovanni Sartor EUI - European University Institute of Florence CIRSFID - Faculty of law, University of Bologna Conference, April 10, 2018 G. Sartor (EUI-CIRSFID) Defeasibility 1 / 57

Defeasible rules in complex systems A defeasible process can be characterised a mechanism which responds to its normal inputs with certain default outcomes, but that may fails to respond in this way when the input is accompanied by certain additional exceptional elements. Default hierarchy: A default hierarchy has many fewer rules than a set of rules in which each rule is designed to respond to a fully specified situation. A higher-level rule [. . . ] is easier to discover (because there are fewer alternatives) and it is typically tested more often (because the rule’s condition is more frequently satisfied. The hierarchy can be developed level by level as experience accumulates (Holland 2012,122). G. Sartor (EUI-CIRSFID) Defeasibility 2 / 57

Defeasibility as nonmonotonicity “Defeasible inference relies on absence of information as well as its presence, often mediated by rules of the general form: given P , conclude Q unless there is information to the contrary.” (Horty 2001,337). Monotonic and conclusive inference: Deduction is monotonic-conclusive: as long as we accept all premises of a deductive inference, we must continue to accept its conclusion. By contrast, defeasible inferences are nonmonotonic-presumptive: when given additional information we may reject the conclusion of a defeasible inference while maintaining all of its premises The standard example Tweety is a bird [therefore it flies], But it is a penguin, therefore it does not fly. G. Sartor (EUI-CIRSFID) Defeasibility 3 / 57

Tweety flies Birds Tweety is a bird presumably fly Figure 1: The Tweety case: he is a bird G. Sartor (EUI-CIRSFID) Defeasibility 4 / 57

Tweety flies Tweety does not fly Birds Tweety is a Penguins do Tweety is a bird presumably penguin not fly fly Figure 2: The Tweety Case: but he is a penguin G. Sartor (EUI-CIRSFID) Defeasibility 5 / 57

Conclusive and defeasible arguments A valid argument can be said to consist of three elements: a set of premises, a conclusion, and a support relation between premises and conclusion. In a deductively valid argument, the premises provide conclusive support for the conclusion: if we accept the premises we must necessarily accept the conclusion. In a defeasibly valid argument , the premises only provide presumptive support for the conclusion: if we accept the premises we should also accept the conclusion, but only so long as we do not have prevailing arguments to the contrary. G. Sartor (EUI-CIRSFID) Defeasibility 6 / 57

Enthymemes and satured inferences Arguments in natural language usually have an enthymematic form, meaning that they may omit some of the premises that are needed to support their conclusions. Here I shall present all arguments in their saturated (completed) form, that is, as including all premises that are sufficient to conclusively or defeasibly establish their conclusion. G. Sartor (EUI-CIRSFID) Defeasibility 7 / 57

Enthymeme Saturated argument Tweety flies Tweety flies D D Birds Tweety is a bird ? Tweety is a bird presumably fly Figure 3: Enthymeme and saturated argument G. Sartor (EUI-CIRSFID) Defeasibility 8 / 57

Defeasible modus ponens Each elementary defeasible argument includes ( a ) a set of antecedent conditions, and ( b ) a defeasible conditional, called a default , according to which the (conjunction of the) conditions presumably determines the argument’s conclusion. Thus a saturated single-step defeasible argument has the form of a defeasible modus ponens inference: 1 P 1 , · · · , P n (the antecedent conditions), and 2 if P 1 and . . . and P n then presumably Q (the default, in formula: P 1 ∧ . . . ∧ P n ⇒ Q . therefore 3 Q . G. Sartor (EUI-CIRSFID) Defeasibility 9 / 57

A B Fido is not aggressive; Fido is a mammal; ¬ Aggressive(Fido) Mammal(Fido) C D All dogs are mammal; Fido is a dog; D 1 : Pet dogs are presumably ∀ x( Dog(x) → Mammal(x)) Dog ( Fido ) Fido is a pet dog; not aggressive; PetDog(Fido) PetDog(x) ⇒ ¬Aggressive (x) Figure 4: Conclusive and defeasible arguments G. Sartor (EUI-CIRSFID) Defeasibility 10 / 57

Linked and convergent arguments A linked argument includes, beside a conditional warrant, more than one premises. None of these premises is sufficient to trigger on its own the conjunctive antecedent of the conditional warrant. A convergent argument structure is a combination of multiple arguments, each leading to the same conclusion. Often, but not always a convergent argument structure provides a stronger support to the common conclusion of its component arguments than each of these arguments would do in isolation G. Sartor (EUI-CIRSFID) Defeasibility 11 / 57

John is subject to a € 100 fine D D : If one drives to the city P 1 : John drives P 2 : John’s speed centre and one’s speed through the city exceeds 50km per exceeds 50km per hour, then center hour one is subject to a € 100 fine Figure 5: Linked argument G. Sartor (EUI-CIRSFID) Defeasibility 12 / 57

C A Mary was on the B crime scene D D P 1 : Witness John D 1 : If a witness P 2 : Witness D 1 : If a witness says that Mary says something Lisa says that says something was on the crime then presumably it Mary was on then presumably scene is true the crime scene it is true Figure 6: Convergent factual argument G. Sartor (EUI-CIRSFID) Defeasibility 13 / 57

C I should not tell John A B that he should go to the left D D P 2 : Telling John D 2 : One P 1 : Telling John D 1 : One that he should should not do that he should go should not tell go to the left things that to the left is a lie lies would harm him harm others Figure 7: Convergent practical argument G. Sartor (EUI-CIRSFID) Defeasibility 14 / 57

Rebutting and undercutting An argument can be attacked in any of three ways: by attacking its premises, by attacking its conclusions (rebutting), or by attacking the support relation between premises and conclusions (undercutting) G. Sartor (EUI-CIRSFID) Defeasibility 15 / 57

Defeat An argument is defeated iff: its premises are attacked it is rebutted by a stronger argument it is undercut by an argument G. Sartor (EUI-CIRSFID) Defeasibility 16 / 57

A B Fido is not aggressive; Fido is aggressive; ¬ Aggressive(Fido) Aggressive(Fido) D D D 2 : Dobermans are D 1 : Pet dogs are Fido is a Doberman; Fido is a pet dog; presumably aggressive; presumably not aggressive; Doberman(Fido) PetDog(Fido) Doberman(x) ⇒ Aggressive (x) PetDog(x) ⇒ ¬Aggressive (x) Figure 8: Rebutting attack G. Sartor (EUI-CIRSFID) Defeasibility 17 / 57

A C Default D 1 does not apply to Tommy is not aggressive; Tommy; ¬D 1 ( Tommy ) ) ¬ Aggressive(Tommy) D D D 3 : Being raised an isolated Fido has been raised in D 1 : Pet dogs are presumably Fido is a pet dog; isolation; pet dog presumably does not not aggressive; support non-aggressivity, i.e., PetDog(Tommy) IsolatedPetDog(Tommy) PetDog(x) ⇝ ¬Aggressive (x) default D1 does not apply to pet dogs raised in isolation; IsolatedPetDog(x) ⇝ ¬ D1(x) Figure 9: Undercutting attack G. Sartor (EUI-CIRSFID) Defeasibility 18 / 57

D 3 : If there is a red light then p looking pink does not entail being pink (default D1 does not apply) Figure 10: Undercutting attack: defeasible perception G. Sartor (EUI-CIRSFID) Defeasibility 19 / 57

Rebutting and undercutting in the law Defeat in the law can result from different attacks the conclusion of the argument is contradicted by a non-weaker arguments (rebuttal) the default (rule) in the argument undercut by an exception the default (rule) in the argument is undercut by establishing an impeditive fact. G. Sartor (EUI-CIRSFID) Defeasibility 20 / 57

A B John is liable John is not liable; Liable(John) ¬Liable(John) D D D 1 : If one culpably D 2 : If one is incapable John is incapable; John culpably damaged Mary) damages another, then p Incapable(John) one, then p is not liable; CulpablyDamages(John, Tom) one is liable Incapable(x) ⇒ ¬Liable (x) CulpablyDamages(x, y) ⇒ Liable(x) C Default D 2 does not apply to John; ¬D 2 (John) D D 3 : If one’s incapability is due to John’s incapability is one’s fault then p it does not excuse, due to his fault; i.e., default D 2 does not apply; IncapableByFault ( John ) IncapableByFault ( x ) ⇒ ¬D 2 (x) Figure 11: Undercutting attack: inapplicability rule G. Sartor (EUI-CIRSFID) Defeasibility 21 / 57

A B John is liable John is not at fault Liable(John) D D D 1 : if a product The motorbike D 2 : If the product has no causes damage, then p The motorbike It is not produced by John the producer is liable, manufacturing defects produced by proved that has no unless it is proved and no design defects John caused John is not manufacturing that the producer is then presumably the damage to Tom at fault defeats and no not at fault producer is not at fault design defects Figure 12: Undercutting attack: impeditive fact G. Sartor (EUI-CIRSFID) Defeasibility 22 / 57