Spatial reasoning in a fuzzy region connection calculus (Q835806)

When I was asked to review this article, my first reaction was that the title is at least misleading. For it has been shown that the region connection calculus (RCC) is partial and flawed, see e.g. [\textit{T. Dong}, ``A comment on RCC: from RCC to RCC\(^{++}\)'', J. Philos. Log. 37, No. 4, 319--352 (2008; Zbl 1151.03005)]. Anyway, I contacted the corresponding author, as I hoped that the authors were aware of the problems of the RCC and aimed at providing a new solution to the flaws and even a new generalisation of the repaired theory. After several rounds of email exchanges, it is clear that the authors were not aware of that. In the abstract, the authors claim that they present a generalisation of the RCC based on fuzzy set theory. Let us examine this generalisation. In Section 2.1, the authors claim, ``throughout this paper, we will mainly be concerned with fuzzy sets in \(R^n\) representing vague regions'', and that for \(p \in R^n\), the membership function, \(A(p)\), reflects to what extent point \(p\) belongs to the vague region. In the same section, the complement of \(A\) is defined as the fuzzy set \(\text{co}A\) in \(X\) such that \(\text{co}A(x) = 1-A(x)\). Let us consider a region in RCC-8 theory. The membership function of this region can take on only two values, 0 and 1. That is, if \(q\) is a member of this region, \(A(q) = 1\), otherwise \(A(q)=0\). Based on the definition of the complement, we can deduce that its complement region, if it exists at all, will be determined by \(\text{co}A(q) = 1-A(q)\). We see that a region and its complement do not share a common point. However, in RCC theory a region connects with its complement -- this is the exact point where RCC theory is different from Clarke's work. Therefore, we found that if a region has a complement region, the presented work is NOT a generalisation of the RCC theory. If the presented work does not allow a region to have its complement region, we also CANNOT agree that the present work is a generalization of the RCC theory. For in RCC theory a region has its complement region. Section 1 briefly introduces the RCC theory, and presents motivations to define \(C\) as a fuzzy relation as follows: (1) vague regions exist, existence of vague regions forces the existences of vague topological relations. RCC theory makes no assumptions on the representation of regions. (2) spatial linguistic description in everyday life suggests that the topological relations between crisp regions can be vague. The first motivation suggests that the authors would do something to specify the RCC theory, for example, to give some representations of regions (representing vague regions) and define topological regions accordingly. The second motivation is based on the observation that people would describe two objects being connected, even if there is a small distance between them in reality. The aim of defining \(C\) as a fuzzy relation is to precisely explain the reality conveyed by languages. This observation mixes the objective physical world and the mental world described by language in everyday life. If they could not push further a cabinet against a wall, people would believe that the cabinet connects with the wall, and say the cabinet is located against the wall. Think about the case: the cabinet and the wall are made of magnetic stones, and you are pushing the north pole of the cabinet to the north pole of the wall while closing your eyes. You will believe they are connected, if you could not push the cabinet. However, in reality there can be a big distance between them. That is, spatial relations conveyed by our everyday language are about the world in mind, not the world in reality. The world in mind is a mixture of the world in reality and our psychology. Now think of reality again, cabinets and walls are made of atoms. Physicists tell us that there are big distances among atoms. Even if the cabinet is built inside the wall, there are big distances between them. In this sense, if the authors hope to develop a formal system which precisely explains reality, they might think about the disconnect relation. This discourages me to write a detailed technical review of this paper. A clear account of its contents is listed as follows: Section 2 presents fuzzy topological relations. The authors present the representation of fuzzy regions, and fuzzy topological relations between them. I would suggest readers to understand these formalism as a kind of specified generalisation of part of the RCC theory. Section 3 presents motivating examples. The authors use their formalism to represent meanings of spatial linguistic descriptions used in everyday life. See my comments above. Section 4 and Section 5 introduce the reasoning of RCC-8 in the literature, and their formalism, respectively. The reason tasks considered are satisfiability problems, computational complexity, entailment problem, best truth-value bound problem, inconsistency repairing problem. Section 6 and Section 7 show ways to reduce the presented formalism to the original RCC theory, and the relationship between the presented formalism and the Egg-Yolk calculus. These cases strengthen the argument that the presented formalism has potentiality of generalisation.