Information and Knowledge Representation in Fusion Problems - Information Fusion in Signal and Image Processing - page 62

- the use of typical properties;
- possible exceptions;
- the closed world hypothesis, which will be discussed particularly in Chapters 7
and 8.

Non-monotonic logics rely on concepts of preferences (which world, which situa-
tion is more “normal” than others, what are the preferred goals if not all of them can
be met, etc.), belief changes or revisions (the well-known AGM postulates [ALC 85])
and of course a certain number of postulates that manage non-monotonicity, referred
to as rationality postulates. “Cautious” monotonicity, which is an example of such a
postulate, expresses the fact that if a base KB can be used to infer A → B and C ,

then it can be used to infer A ∧ C → B .

The concepts of contingency, i.e. of necessary or possible truth, are not well rep-
resented in traditional logic. Manipulating such objects requires the introduction of
modalities in logic. Modal logics [CHE 80, HUG 68] allow us to reason on propo-
sitions A ( A is true), A ( A is possible). Numerical forms of

these concepts are found in belief function theory in terms of belief and plausibility
(see Chapter 7), and in possibility theory in terms of necessity and possibility (see
Chapter 8). We will not discuss in detail the logical meanings of these concepts in this
topic.

A ( A is necessary), ♦

Finally, the concepts of imprecision and uncertainty, which we have already dis-
cussed extensively, can be represented in fuzzy and possibilistic logic, which will be
briefly described in Chapter 8.

5.7. Bibliography

[ALC 85] A LCHOURRÓN C.E., G ÄRDENFORS P. , M AKINSON D., “On the Logic of Theory
Change: Partial Meet Contraction and Revision Functions”, Journal of Symbolic Logic ,
vol. 50, p. 510-530, 1985.
[CHE 80] C HELLAS B., Modal Logic, an Introduction , Cambridge University Press, Cam-

bridge, 1980.
[CLE 93] C LÉMENT V. , T HONNAT M., “A Knowledge-Based Approach to Integration of
Image Processing Procedures”, CVGIP: Image Understanding , vol. 2, p. 166-184, 1993.
[DES 90] D ESACHY J., “ICARE: An Expert System for Automatic Mapping from Satellite
Imagery”, in L. F. P AU (ed.) Mapping and spatial modelling for navigation , vol. F65 of

NATO-ASI , Springer Verlag, Berlin, 1990.
[DUB 80] D UBOIS D., P RADE H., Fuzzy Sets and Systems: Theory and Applications , Aca-
demic Press, New York, 1980.
[DUB 88]

D UBOIS D., P RADE H., Possibility Theory , Plenum Press, New York, 1988.