Foundations of Fuzzy Logic and Semantic Web Languages

Appendix H

Tableau Calculi for Fuzzy SHIF

g

As we have seen in Appendix C, the major issue introduced by functional roles

is that together with inverse roles they may cause a concept to be satisfiable

in an infinite model only as Example 60 illustrates. Of course, this property

applies to fuzzy SHIF

g

as well.

In order to cope with this issue, like for the crisp DLs case, we use the

so-called notion of pairwise blocking to guarantee the correct termination of

a tableau from which then we may build a possibly infinite model.

To start with, in this appendix, we restrict fuzzy RIAs in a fuzzy

RBox R to be of the form R

1

˜

vR

2

only.

Then the definitions of Inv(R),