abduction vs. induction

[Pierre MARQUIS]

I have received a great deal of replies about differences between
abduction and induction and I want to thank their authors for answering
my question.

It seems that the proposed definitions of abduction and induction are
neither compatible nor convergent ones. I have tried to synthetize them and
here is a (non exhaustive) inventory of the uses and denotations of abduction
and induction.

As Christian de Sainte Marie told me, first definitions of abduction
and induction are apparently issued from Aristotle's first analytics. If I have
well interpreted them in a logical sense:

* induction is derivation of B -> A from C -> A and C -> B. If B has
no more extension that C (that is, I presumed, B -> C ?) then this derivation
is perfect induction (logically valid one). Otherwise, it is unperfect (and
interesting) one.

* abduction is derivation of C -> B from B -> A and C -> A so long as
B -> A is certain, C -> A only probable and C -> B more probable than C -> A.

Two pairs of definitions issued from Pierce's books have also been
proposed to me and, strangely, they are not compatible:

First ones,

* induction is derivation of A -> B from fact A and observation B
relative to A.

* abduction is derivation of fact A from observation B and rule
A -> B.

Second ones,

* induction is evaluation of hypotheses by experiments.

* abduction is a process for hypotheses construction so long as the
choice of a particular hypothesis is not based on its truth value.

More recently, in AI community, abduction and induction have been both
used to denote the hypotheses construction process.

In others words, abductive and inductive reasoning are construction of
formulae h such that Th, h |= f where f is the fact to be explained and Th the
theory of domain.

However, if we consider diagnosis as typical abductive reasoning and
learning from examples as typical inductive reasoning, we notice that many
distinctions can be made between these two kinds of reasoning:

* syntactic proprieties of facts to explain: we are interessed by
conjunctive and ground facts in diagnosis and by facts represented by Horn
clauses in learning from ex.

* syntactic proprieties of hypotheses: we are interessed by
conjunctive hypotheses in diagnosis and by disjunctive hypotheses in learning
from ex.

* semantic proprieties of hypotheses: we are interessed by minimal
hypotheses in diagnosis and by more specific hypotheses in learning from ex.

* uses of hypotheses: conclusions of diagnosis need not to have any
applicability outside the particular set of circumstances. On the other hand,
the hypotheses have to be enough general in learning from ex. in order to
contribute to knowledge acquisition.

* implementation level: derivation is backward chaining in diagnosis
and pattern searching in learning from ex. This distinction is available if
deduction relation used is not full logical deduction.

Any comments ?

Pierre MARQUIS
e-mail: mar...@loria.crin.fr
CRIN (Centre de Recherche en Informatique de Nancy)
Campus scientifique - B.P. 239
54505 Vandoeuvre les Nancy Cedex
FRANCE