To: hbe@math.ucla.edu
Subject: Re: review for jsl  (from Cathy)


Review of Prakken, Logical Tools for Modelling Legal Argument

for Journal of Symbolic Logic (solicited)

Mathematical models of defeasible reasoning and mathematical models of
argument tend to puzzle classical logicians.  Is a calculus of argument
a logic?  Is there no place left for an indefeasible, material
conditional?  Are procedural semantics really unavoidable?

Logics of argument and defeasible reasoning do seem to push farther
from the classical core than the usual nonstandard logics.  Their
models invariably include nonmonotonicity, resource limitation
(non-ideality), weak negation, dialogical and meta-logical relations,
and semantic ascent.  The mathematics is usually veiled in intellectual
historical invective, perhaps matching the acerbic tone of argument's
detractors (such as Alonzo Church, "there is no such thing as
dialectical logic," (JSL 18, 1958) or Jon Barwise, personal
communication, "but what have [the scholars of nondemonstrative
reasoning] actually produced?").

In the present book, Henry Prakken takes care to avoid controversy and
to explain why models of argument deviate so much from standard
logics.  He is content to survey the technical issues surrounding the
contemporary logical work on argument in and around artificial
intelligence.  Prakken's title refers to "logical tools" as opposed to
"logics", refers to "models" rather than "foundations", and restricts
its scope to "reasoning in the law" rather than the whole of
"commonsense reasoning".  In being so careful, Prakken has produced a
resource for those who want a quick, current, and authoritative
introduction to this body of work.  While the discussion does in fact
focus on the issues specifically raised in the modelling of legal
argument, no special interest in law is needed or supposed.
Meanwhile, Prakken would not be the first in the history of logic to
find patterns of legal argument logically fertile.

Mathematical defeasible reasoning in AI is of course the culmination of
work that had been known as "nonmonotonic reasoning", beginning with
inheritance hierarchies, closed-world databases, and the semantics of
negation-as-failure and logic programming.  Defeasibility is the main
competitor of belief revision for those who want to systematize
qualitative ampliative inference; it is the main competitor of deontic
logic in the ethical and policy fields.  It is a topic that makes
paraconsistent logic, dialogue logic, and belief revision each look
like one piece of a much larger puzzle.

The tradition of using a defeasible conditional (if p then q,
defeasibly, non-demonstratively, ceteris paribus, or prima facie) is as
old as any logical tradition.  What is new in this decade is (i) the
attempt to mathematize the subject, to understand its procedural
suppositions, to understand why it cannot be reduced to non-procedural
descriptive sentences, and (ii) the construction of reasoning patterns
on top of defeasible conditionals:  defeasible decisionmaking,
defeasible statistical inference, defeasible analogy, defeasible
deontic reasoning, and adversarial argument that employs defeasible
conditionals (which apparently includes legal reasoning).  Defeasible
reasoning has shown itself to be widely applicable, or more accurately,
applications of logic in the "representation of knowledge" have
frequently rewarded the use of defeasible conditionals.

To begin to appreciate the body of work that Prakken is studying, the
mathematical logician must first stipulate two assumptions that
distinguish defeasible reasoning.

First, the rule "if p then defeasibly q" might have procedural
content:  it need not just constrain co-occurrence of p-states of
affairs and q-states of affairs (not even in preferred possible
worlds).  It could instead say that an argument for p can be extended
into an argument for q (much as the PROLOG rule would say that one way
to derive q is to derive p).  Prakken has it matter-of-factly:

	knowledge representation formalisms have both procedural and
	declarative aspects, and the importance of logic lies in its
	ability to analyze the declarative aspects.  (p. 10)

Second, classical logic is to be used for its descriptive regularities,
not for its patterns of reasoning.  Logics are better at defining
useful representations than restricting the scope of rational
reasoning.  Prakken repeatedly says, on this point, that logic is a
tool for modeling often embedded within a greater framework (such as
dialogue or belief revision):

	... using logic does not commit to the 'axiomatic' or even to
	the 'naive deductivist' view on reasoning.  ... it leaves room
	for other reasoning activities, like induction, analogical
	reasoning and ways of arguing against a rule.  ... (p. 277)

With these two assumptions, the student of defeasible reasoning is
invariably constructivist and conventionalist:  unlike intuitionists,
the important division is between larger and smaller finite
constructions, not between countably and uncountably infinite
constructions.  As a conventionalist, believing that the appraisal of
the logic is rooted in the usefulness of its conventions, the student
of defeasible reasoning is resigned to a plethora of logical
systems much as database managers admit a plethora of database
languages.

Prakken begins by considering patterns of legal reasoning, where
exceptions to rules, priority among conflicting rules, and "open
texture" are fundamental phenomena that drive logical innovation.  An
exception to "if p then q" is "unless r".  A priority might be from
"lex specialis" (the more specific rule dominates), "if p then q; but
if p and r, then not q".  Open texture is the idea that "P(x)" might be
a predication such as "x is a reasonable person" which is subject to
defeasible patterns of reasoning and analogical argument.

Prakken then considers existing nonmonotonic approaches and the unusual
features that such nonmonotonic logics have:  their weak negation,
failure of antecedent-strengthening, contraposition, and cumulativity;
their fixed-point entailments and preferential semantics.  Prakken
surveys those approaches that permit a preference between rules or an
ordering of arguments.  This leads to a meta-theory of
nondeductive entailment, and one finds definitions such as 6.4.17, p.
162, (which can be found in any contemporary theory of argument):

	Defn.  (specificity defeat)  Let A1 and A2 be two arguments.
	A1 defeats A2  iff 
	1.  A1 attacks A2; and 
	2.  A2 is defeasible;
		and
		a.  A1 is strict or 
		b.  for some conflict pair (C1, C2) of (A1, A2) 
			it holds that
			C2 is not strictly more specific than C1.

The main novel technical contribution of the author is the extension of
existing argument systems to permit reasoning about the priorities
among rules.  In a PROLOG program, there is an implicit priority based
on the ordering of rules.  A more theoretically interesting implicit
priority is based on relative logical strength of each rule's protasis (as
in the above definition of "specificity").  Prakken's novelty permits a
dialogical move such as (p. 209):

	O2:  [  	d6:    ==> r,
		  	d7:  r ==> d1 < d2  ]

which says "rule d6:  by presumption, r; and rule d7:  given r, 
the rule d2 defeats the rule d1."  O2, d6, and d7 are just names:
the first names the argument; the latter name the rules.

The final contribution of this book is Prakken's overarching
"four-layered view" of argumentation (p. 270ff):

	Firstly, procedural models contain a _logic layer_ ... , for
	example, a party may not contradict himself ...; in addition,
	[they contain] a _dialectical layer_, at which such notions as
	'counterargument', 'attack', 'rebuttal', and 'defeat' are
	defined; ... finally, there is the _procedural layer_, which
	regulates how an actual dispute can be conducted ...

	... we can even identify a fourth level of what may perhaps be
	called _strategy_, at which ... tactics for playing the game are
	identified.

There is emerging consensus in the field that this multi-layered view
of argumentation is right.  It helps explain why logics of argument
venture so far from the usual logical picture.

In the end, Prakken has written the best current text with which the
interested logician can quickly study the main, surviving, applicable
ideas of nonmonotonic reasoning and can glimpse the themes that are
shaping current research in defeasible reasoning.



R. P. Loui 
Washington University in St. Louis