Computed answer based on fuzzy knowledgebase
– a model for handling uncertain information –
Departement of Computer Science
University of Pécs, Faculty of Engineering
Pécs, Boszorkány u. 2, Hungary
The basic question of our study is how we
can give a possible model for handling
uncertain information. This model is worked
out in the framework of DATALOG. The
concept of fuzzy knowledge-base will be
defined as a quadruple of any background
knowledge; a deduction mechanism; a
connecting algorithm, and a decoding set of
the program, which help us to determine
the uncertainty level of the results. A
possible evaluation strategy is given also.
Keywords: fuzzy knowledgebase, fuzzy
The large part of human knowledge can’t be
modelled by pure inference systems, because this
knowledge is often ambiguous, incomplete and
vague. When knowledge is represented as a set of
facts and rules, this uncertainty can be handled by
means of fuzzy logic.
A few years ago in  and  there was given a
possible combination of Datalog-like languages and
fuzzy logic. In these works there was introduced the
concept of fuzzy Datalog by completed the Datalog-
rules and facts with an uncertainty level and an
implication operator. In  there was given an
extension of fuzzy Datalog to fuzzy relational
Parallel with these works, there were researches on
possible combination of Prolog language and fuzzy
logic also. Several solutions were arisen for this
problem. These solutions propose different methods
for handling uncertainty. Most of them use the
concept of similarity, but in various ways. More
essays deal with fuzzy unification and fuzzy
resolution, for example , , , .
In this paper, continuing our former concept, we
give other possible model for handling uncertain
information, based on the extension of fuzzy
Datalog. According to our former papers, in the next
chapter we describe the concept of fuzzy Datalog, in
the further chapters we discuss our actually new idea
about fuzzy knowledgebase. We build the model of
fuzzy knowledge-base as a quadruple of any kind of
background knowledge; a deduction mechanism; a
connecting algorithm and a decoding set.
2. The fuzzy Datalog
A Datalog program consists of facts and rules. In
fuzzy Datalog, we can complete the facts by an
uncertainty level, and the rules by an uncertainty
level and an implication operator. Applying this
operator, the uncertainty level of rule’s head can be
determined from the uncertainties of rule’s body and
the rule. For example if in the program
the implication operator is the Gödel-operator
(I(x,y) = 1 if x ≤ y; otherwise I(x,y) = y),
then the level of the rule-head can be calculate as the
minimum of the level of the rule-body and the level
of the rule. For John and Mary it does:
that is John likes Mary at least 0.7 level.
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According to the previous paragraph, there are three
kind of nodes in depth 3k+2 (k=1,2,…): an unified
body of a rule; an unified fact with ordinary ground
term arguments; or the symbol NO. In the first case
the successors are the members of the body. They
are in AND connection, which is not important in
our context, but maybe important for a possible
future development. If the body has only one literal,
then the length of evaluating path would be reduce
one, but it would be damage for the view of
homogeneous treatment. In the second case the
successors are the symbol YES or NO, depending on
whether the unified fact is among the ground atoms
of the program. These nodes have not successors.
From the construction of searching graph, it is
Let X0 be the set of ground facts being in parent-
nodes of symbols YES. Starting from X0, the
fixpoint of mNTP contains the answer for the query.
From the viewpoint of the query, this fixpoint may
contains more superfluous ground atom, but
generally it is smaller then the consequence of
knowledge-base. More reduction of the number of
superfluous resulting facts is the work of a possible
Let us consider the knowledge-base of example 3!
(Now it is enough to consider only the program and
the background knowledge.)
Let the goal be li(M,x), where x is a variable.
Then the searching graph is:
The algorithm of searching the starting facts based
on the above construction is being in press.
In this paper there is given a possible model of
handling uncertain information by defining fuzzy
knowledge-base as a quadruple of a background
knowledge, a deduction mechanism, a decoding set
and some modifying algorithm, which connects the
background knowledge to the deduction mechanism.
There was also given a possible evaluation strategy.
Possibly this evaluation strategy can be improved, or
maybe there is a better modifying algorithm. To find
these better solutions will be the work of a possible
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