For Donald Nute's volume on DEFEASIBLE DEONTIC LOGIC

Alchourron and von Wright on Conflict among Norms

In an impassioned defense of deontic logic, "Philosophical foundations
of deontic logic and the logic of defeasible conditionals," (in DEONTIC
LOGIC IN COMPUTER SCIENCE:  NORMATIVE SYSTEM SPECIFICATION, edited by 
J.J. Meyer and R. Wieringa, Wiley, 1993) Carlos Alchourron provided us
with a clear statement of many of his final positions on the subtle
relations between defeasibility, deontic modality, and belief revision.
Alchourron, the Argentine gentleman lawyer and polymath, stood at the
apex where met three of this half-century's most important developments
in reasoning and the mathematical modeling of reasoning.  His passing
must be marked with the particular sadness of the loss of the rare
opposing thinker worth forthrightly engaging (although it must be
confessed that this author never succeeded in doing so).

Alchourron understood defeasibility and its implications better than all
others who failed to embrace it.  (NOTE:  For example, Alchourron
understands that defeasibility is ampliative (p. 83), that it creates
"contributory" conditions rather than conditions necessary or sufficient
(p. 82), that it is not always reducible to probabilistic relations (p.
69), that it is fundamental to the philosophy of law (p. 67), that it
demotes its conclusions to a secondary status relative to its premises
(p. 83), that it militates against the modularity of rules (p. 67), that
it creates conditionals that lack truth values (p. 44) and that are not
falsifiable (p. 83), and that it is closely related to belief revision
(p. 83).  Inexplicably, Alchourron fails to note its burden-shifting,
its relativizing warrant to partial computation.)  Defeasibility was for
him a competitor.  It was an insurgent idea backed by the sheer volume
and number of formalists in artificial intelligence, knowledge
representation and non-monotonic reasoning, their incessance, their
unchecked onslaught.  It was floodwater.  It was to be opposed because
it was so plausible a substitute for Alchourron's own favorite logical
developments.  Of course, as a co-founder with Peter Gaerdenfors and
David Makinson of AGM belief revision, ("On the logic of theory change:
partial meet contraction and revision functions," JOURNAL OF SYMBOLIC
LOGIC 1985) and as co-author with Eugenio Bulygin on the understanding
of legal reasoning through deontic logic, (NORMATIVE SYSTEMS, Springer,
1971) Alchourron's loyalties were determined.

Unlike other opponents of defeasibility, Alchourron was a lawyer who had
every reason to know the origins of defeasibility in contract and
property law; he could appreciate the concepts of burden-shifting and
process, upon which a proper understanding of defeasibility depends.  In
his paper, we find the depth of his appreciation of defeasibility, and
through his concern with von Wright's conditional norms, we find the
source of his recalcitrance.

	Alchourron's Attack

Alchourron's text shows his obvious effort to restrain his concern over
the popularity of the newcomer.  His defense of deontic logic takes the
form of an attack on defeasibility.  Defeasibility invokes a "possible
confusion of logic and revision," (p. 69) providing new mechanisms for
which "there is no need" (p. 44), and which anyway hides its
"conceptually weaker conclusions" in a "quiet darkness." (p. 83)

The principal conclusion is that

	If x is a bird then (defeasibly) x flies

is not the proper way to "give formal expression of the cognitive
situations of ... incomplete knowledge".  When a bird is subsumed under
this rule, the defeasible conclusion thereby (defeasibly) warranted,
that it flies, has a questionable epistemic status.  To Alchourron, the
better approach is to use the Russell/Frege/Peirce conditional,

	If x is a bird then (materially) x flies

and to revise that conditional as necessary if and when conflict arises.
The revision of the conditional depends on the actual conflicts that the
epistemic agent has suffered; for Alchourron,

	If x is a bird and x is not a penguin and x is not Dead,

	then (materially) x flies

is a reasonable stage to reach post revision.

This move is of course well known (though not always well understood).
H.L.A. Hart, in the paper that brought defeasibility forward from
medieval English law to modern logico-linguistics, entertained such a
move in a footnote, regarding it as trivial at best and misleading at
worst.  (NOTE:  Alchourron cites other work by Hart and the prior work
of Sir W.D. Ross, but does not show an awareness of this principal work
of Hart.  "The ascription of responsibility and rights," in LOGIC AND
LANGUAGE, edited by A. Flew, Oxford, 1952.  W.D. Ross, THE RIGHT AND THE
GOOD, Oxford, 1930.  This is quite clear in Alchourron's analogy that
Dworkin is to Hart as Ross is to Kant:  the implication is that
Dworkin's principles, like Ross's prima facie duties, make room for
defeasibility while Hart's positive rules, like Kant's absolute duties,
do not.  This cannot be right.  No scholar would take Hart to be in
contrast to Ross, since Hart's paper on defeasible concepts is the
historical extension of Ross's prima facie duties.  Perhaps Alchourron
simply did not fully care, or could simply be following too closely
Dworkin's twisted prose.  Although Hart trades the defeasibility of the
conditional for the defeasibility of the predication, the sentiment is
the same, and is largely present in the work of Hart that Alchourron
cites:  Hart's CONCEPT OF LAW, Oxford, 1961 under the new term,
"open-texture".)  AI writers have built their industry on the correct
perception that the antecedent cannot thus be gerrymandered.  Something
that has become important about the intertwining of computation and
specification, about prima facie warrant's localization in a rule, about
the incompleteness of computation, accounts for the transformation's
failure.  In plain language,

	If x is a bird then (defeasibly) x flies and

	If x is a penguin then (defeasibly) x does not fly

is not equivalent to

	If x is a bird and x is not a penguin then (materially) x flies
	and

	If x is a penguin then (materially) x does not fly.

Neither do the pairs of rules behave the same at various levels of
computation, nor do they behave the same at various levels of epistemic
improvement.

This much is a standard lesson in knowledge representation and
reasoning.  The usual response among classically trained thinkers is
that logic should be about commitment, not computation, and that one who
uses the rule that birds fly without explicit commitment to whether the
bird is a penguin, implicitly asserts that it is not a penguin.  It is a
response that retraces its steps rather than steps forward.

Alchourron takes us farther.  He too embraces epistemic commitment as
the goal of logic and denies the importance of computation.  But he
understands that defeasibility is part of a constructive model of
belief.  Construction is different from constraint.  Defeasible rules
prescribe the construction of warrant based on what can be computed or
asserted so far.  Alchourron's model of belief revision can describe the
dynamics of belief, so he too can give an account of construction.  He
can do more than indulge the insistence of deductivists.  He can
supplement conditionals with revision.

Alchourron notes that what is at stake is ampliative reasoning.
Ampliative reasoning is the great logical territory unconquered by
earlier mathematical models.  Probabilists and inductivists thought they
had accounts of it, as did philosophers of scientific explanation.
Alchourron believed that his theory of revision (with Gaerdenfors and
Makinson) provided the best qualitative understanding of ampliative
reasoning.  Of course, AGM revision theory occurs shortly after
Gaerdenfors's feud with Isaac Levi on indeterminate decision;
historically and technically, I find belief revision's paternity in
Levi's work on confirmational conditionalization and non-Bayesian
shifts.  So perhaps AGM revision theory's ampliativity is not so
different from inductive ampliativity.

For Alchourron, the state of belief depends on the epistemic agent's
experience.  The posterior nature of the revised conditional is
important.  Adding the explicit conditions of the bird not being dead
and not being a penguin are for Alchourron dependent on the particular
conflicts and revisions that were endured at earlier times.  "It seems
to me unquestionable that the main [conditions] are the formal
representation of the revisions effectively performed by an agent and of
his dispositions to revise.  ... We will probably need different choice
functions [i.e., conditions] for the same sentences in different moments
of his life."  (p. 81)  In AGM, revisions are constrained but not
uniquely constrained.  There is some indeterminacy of the resulting
state of belief.  This indeterminacy together with the contingency of the
agent's revisions accounts for Alchourron's view of the result as
ampliative.  The result is certainly not contained wholly within the
language of the original, unrevised state of belief, and it is not
predictable even if one has been given the sentences that force
revisions.

Defeasible reasoning likewise permits indeterminacy of the result, a
freeing (or indexing) of the connection between input and output.  The
antecedent of a defeasible rule is a contributory condition, not a
sufficient condition.  Its sufficiency depends on what other conditions
might be found in conflicting rules.  This in turn depends on which
rules have been considered by the search and inference procedures which
are indeterminate, unspecified computations.  (NOTE:  Isaac Levi writes
that this view might merely reinforce our human irrationality, our bad
habits of reasoning.  THE FIXATION OF BELIEF AND ITS UNDOING,
Cambridge, 1991.  Levi, too, views logic as the specification of ideal
belief commitments, finding no place in the model for computation or
construction.  He does not say whether he thinks there can be analysis
of the canons for regulating the constructions that might be used in
case humans fall short of the ideals, in case societies insist on
procedural justice, in case rule-makers decide to write regulations for
constructions, or in case we discover that the classical ideals merely
affect our language but do not help fix our beliefs.)  There is no
question that the result of defeasible reasoning is an ampliative
procedure.  Computational indeterminacy permits entailments to be
independent of their premises in a sense that can be found in none of
the competing accounts of ampliative reasoning.  Defeasible entailments
are computationally ampliative.

Alchourron's claim in the paper, that there is no need for a logic of
defeasible norms, is more the consequence of his fancy for revision than
his fixation upon deontic modalities.  Nevertheless, we may find in von
Wright what is at stake for deontic logic, and what is surely a
precursor of Alchourron's view.

	von Wright's Stand

In "Norms, truth and logic," (originally in DEONTIC LOGIC, COMPUTATIONAL
LINGUISTICS, AND LEGAL INFORMATION SYSTEMS," edited by A.A. Martino,
North-Holland 1982; we refer to G.H. von Wright, PRACTICAL REASON:
PHILOSOPHICAL PAPERS V. I, Cornell, 1983), von Wright responds to
Roderick Chisholm's puzzle of Contrary-to-Duty imperatives.
("Contrary-to-Duty imperatives and deontic logic," ANALYSIS 24, 1963.)
According to the puzzle, it is possible that 

	O(p --> q), O(p --> r), and O(~p) 

can co-exist in a corpus.  Worse, 

	O(~p) technically entails O(p --> x) 

for any x!  von Wright goes to some length to distinguish deontic
obligation from technical, or derived obligation, to avoid this
representational embarrassment.  But the main point is that the norms
are not in conflict unless p, which is prohibited, occurs.  The addition
of p would require the subtraction of O(~p).  This would be a revision,
and the revision might as well include the resolution of whether q or r
(or x) is the appropriate sanction.  von Wright says as much (p. 157):

	[The coexistence] in itself, need not lead to trouble.  It only
	means that, if the prohibition is violated, the coordinated
	Contrary-to-Duty imperatives require, for their satisfaction,
	that both q and that r come true.  ... If  ... the conjunction
	of the two states that q and r is a logical impossibility ...,
	If a case like this occurred "in real life", the legislator
	would presumably take steps to remove the conflict -- say by
	derogating one of the conditional norms or by making them,
	somehow, consonant.  (p. 157)

von Wright presses further into the question of deontic modeling:

	Such contradictions cannot be "solved" in logic, only in the
	practice of norm-giving.  ... The legislator is well advised to
	amend legislation.  The *logician* cannot help him.  (p. 158)

In no less a pair of legal authorities than John Austin and Hans Kelsen
does von Wright find a distinction between laws that norm action, and laws
that specify sanctions for delicts.  Some laws delimit right and wrong.
Some laws specify consequences.  von Wright wishes here to keep them separate,
as primary and secondary norms, as two different deontic environments
between which one passes when one retracts an a priori O(~p) in favor of an
a posteriori p.

Alchourron likewise discusses a problem of conflicting norms (pp. 60-61):  from

	O(A | B);

	O(~A | C),

he derives 

	~(B & C).

That is, if B and C can co-occur, then the authority has inconsistently
normed.  Hence, conditional norms with inconsistent consequents B and C
cannot jointly apply because B and C cannot co-occur.

	A set of conditional general norms entails (in the logic of
	norms) a non-tautological sentence (has a factual or contradictory
	consequence) iff it follows in the logic for normative propositions
	that the authority has inconsistently normed some action for 
	some circumstance.  (p. 61)

The problem is that in real normative systems, conflicting norms seem to
occur.  In a legal code, conflicting norms might be the natural, most
literal interpretation of the "duties imposed."  The law might prohibit
people from making p true, and might additionally specify the sanctions
q and r in the case of p.  In case of a crime of one foreign national
upon another, perhaps one rule prescribes extradition while another
recommends imprisonment.  Sometimes the conflict is resolved by ordering
the rules, by considerations of jurisdiction, rank, or recency.
Sometimes the rules are unorderable and an adjudicator sets a precedent
with deliberation and opinion.  

This situation is the normal problem for juridical decision.  The
problem is not that two rules are in direct conflict.  The problem is
usually that the current fact situation can be subsumed under two (or
more) rules with equal probity.  The problem is not, as Richard
Wasserstrom muses in THE JUDICIAL DECISION (Stanford, 1961) as he
attempts to escape the dominant deductivism of the time, that there is
no precedent that governs a case.  The problem is that with no
disingenuity, two or more precedents can be brought to bear on the case
at hand.

In a slightly different example, p might be the killing of a person by
accident, for which there is one remedy for killing in general, and one
remedy for manslaughter in particular.  p is thus separable as p1 & p2,
stating the killing and the accidental nature of the killing,
respectively.  So the literal "duties" might be

	O(p1 --> q);

	O(p1 & p2 --> r).

Nevertheless, from O(p1 --> q), many can derive O(p1 & p2 --> q).
This is exactly the kind of situation in which the law's "lex specialis"
recommends the more specific rule.  The deference of one rule to the
other, or "derogation", can also be governed by (meta-)rule, principle,
or precedent.  In logics of defeasible reasoning the more specific
antecedent dominates (for example, Donald Nute, "LDR", unpublished
technical report of ACMC, University of Georgia, 1985) or else there are
rules that have as their consequents that one rule is preferred to the
other (for example, Henry Prakken and Giovanni Sartor, forthcoming issue
of ARTIFICIAL INTELLIGENCE AND LAW, 1996).

Instead of specifying in a mathematically precise way how this
deference, derogation, or defeat occurs, von Wright regards the question
as extra-logical.  Somehow, consistency is restored.  Alchourron hides
the defeat within the "choice functions" that arise during "contingent"
revisions.  Somehow, the legislator or adjudicator makes the right
revisions.  

"The particular details of the revisions (and the choice functions) are
never analyzed by a logician (as a logician), since at the logical level
any empirical analysis is out of question."  (Alchourron, p. 83).  The
alternative paradigm, says Alchourron, hides its conclusions in an
epistemic status that is tentative and subordinate.  Defeasibility is
sneaky science.  It is disrespectful of the status quo; it flaunts the
weaker status of its defeasible conclusions.

But the defeasible logics describe exactly how conflicting norms are
processed.  The defeasible logics do not need to pretend that there are
no conflicts, or that someone else will solve the problem somehow.  The
defeasible logics provide a place for computation.

Alchourron left us at this same point:  a choice between two paths,
neither of which he could ascertain to have a priori superiority.  Like
the revisions of the agents he proposes with Gaerdenfors and Makinson,
the only constraint is for the final snapshot to have the dignity of
consistency.  Alchourron could only hope that we would choose what he
would consider choosing well.  I however, am able to believe that
inquiry will reveal other conclusions.