Abstract
In the constraint satisfaction problem (CSP) formulation
used in artificial
intelligence, the variables
related by the constraints may be initially unknown
within their domains but
are assumed to have some
exact value in each solution. This approach leads to
representational and
computational problems when
dealing with incompletely specified, i.e.,
underconstrained CSPs as the number
of solutions explodes
combinatorially or becomes infinite with infinite
domains. I argue that this
problem can be solved by
generalizing the CSP formulation into what is called
tolerance constraint
satisfaction problem. A new
reasoning scheme for solving the tolerance CSP, tolerance
propagation (TP), has
been designed and
implemented. The idea of the tolerance approach is to aim
at and reason with
solutions and value
assignments in which variables refer to sets and
intervals, i.e., to
tolerances, instead of exact values. This
makes it possible to represent and reason with incomplete
and partly
inconsistent knowledge in a
well defined way. Additional representational and
computational power is
obtained without losing the
possibility of dealing with exact values that can be
represented as singleton
tolerances. The tolerance CSP
cannot be solved by current constraint satisfaction
techniques that are based
on searching or synthesizing
exact value solutions by constraint propagation or can
find only locally
consistent solutions. It is shown
that the tolerance scheme generalizes current numerical
exact value propagation
systems and provides a
rigid foundation for interval labeling systems based on
interval arithmetic.
Application of the scheme to
propositional logics leads into logical tolerance
(constraint) systems that can
be used to produce more
intuitive results than ordinary two , multiple , or
multivalued logics when
dealing with incomplete
knowledge. In order to amalgamate numerical and logical
tolerance reasoning,
techniques are developed
for representing and solving tolerance CSPs represented
in first order
predicate logic. The resulting
system generalizes current constraint logic programming
systems by making it
possible to express
quantified underconstrained logical problems more freely
and to derive
generalized tolerance valued
solutions. Applications of tolerance systems include
numerical equation
solving, consistency maintenance
systems, support for mixed initiative consultation mode
in expert systems, and
support for stepwise
refinement in problem solving.
Original language  English 

Qualification  Doctor Degree 
Awarding Institution 

Award date  15 Feb 1991 
Place of Publication  Espoo 
Publisher  
Print ISBNs  9513839281 
Publication status  Published  1991 
MoE publication type  G4 Doctoral dissertation (monograph) 
Keywords
 artificial intelligence
 reasoning
 decision making
 constraints
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Cite this
Hyvönen, E. (1991). Constraint reasoning with incomplete knowledge: the tolerance propagation approach: Dissertation. VTT Technical Research Centre of Finland.