A Fuzzy Spatial Description Logic for the Semantic Web

Tracking #: 1675-2887

Haitao Cheng
Zongmin Ma
Tao Li

Responsible editor: 
Thomas Lukasiewicz

Submission type: 
Full Paper
Spatial information is a crucial feature in many application domains. However, spatial information is often not crisp, but imprecise and uncertain. With the emergence of fuzzy spatial information, the representation and reasoning of fuzzy spatial knowledge have been a hot research topic. Currently, a large amount of fuzzy spatial information and many corresponding applications have been incorporated into the Semantic Web. To support representation and reasoning of fuzzy spatial knowledge in the Semantic Web, hence, in this paper, we propose a fuzzy spatial description f -ALC(S) which extends fuzzy ALC with fuzzy spatial concrete domain S. First, a fuzzy spatial concrete domain S including fuzzy spatial regions and fuzzy RCC relations is constructed. Then, the admissible concrete domain S is introduced to fuzzy description logic fuzzy ALC, and a new fuzzy spatial description logic f -ALC(S) is proposed. Furthermore, a formal definition of syntax, semantics, and knowledge base of the f -ALC(S) is given. Finally, we propose a tableau algorithm for reasoning fuzzy spatial knowledge, i.e., determining the consistency of f -ALC(S) ABox w.r.t an empty TBox. At the same time, we show the termination, soundness, and completeness of the tableau algorithm and analyze the complexity of the reasoning problem.
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Solicited Reviews:
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Review #1
Anonymous submitted on 31/Jul/2017
Review Comment:

The purpose of this submission is to provide an extension of description logics to
deal with fuzzy spatial information. To this extent, the authors propose to use fuzzy ALC
under Zadeh semantics, extended with a fuzzy variant of RCC8 to handle the spatial

As an application of DLs, and in particular fuzzy DLs, to a specific use, this could
be an interesting submission, if it focused more on the application and use part, and
the need for fuzzy spatial relations in a fully fuzzy DL. However, the paper focuses
more on the technical side, with the authors claiming to introduce a new logic, and
a new reasoning method for it. The issue, though, is that fuzzy DLs with fuzzy concrete
domains have been studied, in a much more general form, for more than 10 years. In
particular, the notions and the algorithm proposed are special cases of the work made
by Straccia in 2005 (see his UAI and DL papers from that year: http://ceur-ws.org/Vol-147/02-straccia.pdf and https://dslpitt.org/papers/05/p559-straccia.pdf ).

Moreover, the proposed algorithm can only handle ABoxes without a TBox, which is a very
strong limitation. Although the authors state clearly in the abstract that their method
works only with an empty TBox, the main content of the paper is a bit misleading in this
respect. The preliminaries introduce TBoxes in detail, and in the first paragraph of
Section 5.1 (where the algorithm is presented), the authors state:
"we focus on the decidable tableau algorithm for checling the f-ALC(S) ABox
consistency w.r.t. TBoxes"
Later, they say that they restrict to acyclic or unfoldable TBoxes, and two paragraphs
later they restrict to empty TBoxes. This is very confusing, to say the least.

For these reasons, I believe that this submission is not ready for publication in the
Semantic Web Journal.

Review #2
Anonymous submitted on 11/Oct/2017
Major Revision
Review Comment:

This paper proposes a fuzzy spatial description for the semantic web. The contribution is strongly built on existing work : [Straccia,FUZZ-IEEE2009] and [Schockaert,AI09] and the extensions of these works. As a consequence, one of the main concern of the paper is related to its novelty with respect to this state of the art.

Indeed, the paper proposes a fuzzy description logic that extends the fuzzy description logic proposed in [Straccia, UAI05] with a fuzzy spatial concrete domain built on the fuzzy region connection calculus [Schockaert,AI09]. The idea is not new since it was proposed in a paper of Straccia [Straccia,FUZZ-IEEE2009]. In particular, it is difficult to see in what the fuzzy spatial concrete domain proposed in this paper (Definition 2) is different from the one proposed in the previous paper. It seems that the only difference is the level of details given on the paper in the description of this fuzzy spatial concrete domain. However, one of the contribution of this paper is the proof that the proposed spatial fuzzy concrete domain is admissible. As a suggestion, the authors could have a look on the work of Merz et al [Merz,KI14] on fuzzy concrete domains in general.
In section 5, the authors propose a tableau-based approach for their description logics. Many works have been proposed in the litterature for reasoning with description logics with concrete domains and the position of the proposed approach towards these existing works is not clear.
Moreover, some points have to be explained better in this part. For instance the notion of subconcepts and sub-expressions is not clearly defined from my point of view. There are also in this part a lot of errors in the notation. For instance the use of \cap instead of \sqcap. The example chosen for the illustration of the procedure is to simple from my point of view and do not appeal for complex fuzzy spatial relationships. The notations have also to be verified in this part.

Other general concerns on the paper :
- The link with the semantic web is not clear except the use of description logics. The chosen example is close to image annotation.
_ There are several ankward assumptions in the introductive part of the paper. The first one is related to the notion of fuziness. For instance, I am not sure to understand "The emergence of fuzzy spatial information".
- The related work section seems complet except for the part on fuzzy description logics.
- In the preleminaries section, the given definition for implication does not correspond to Zadeh logics.
- In section 3.2, it seems that the definition of the fuzzy TBox and fuzzy ABox are not correct.

More generaly, the paper has to be checked since it contains many english errors.