83 research outputs found

    On the Turing completeness of the Semantic Web

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    The evidenced fact that “Linking is as powerful as computing” in a dynamic web context has lead to evaluating Turing completeness for hypertext systems based on their linking model. The same evaluation can be applied to the Semantic Web domain too. RDF is the default data model of the Semantic Web links, so the evaluation comes back to whether or not RDF can support the required computational power at the linking level. RDF represents semantic relationships with explicitly naming the participating triples, however the enumeration is only one method amongst many for representing relations, and not always the most efficient or viable. In this paper we firstly consider that Turing completeness of binary-linked hypertext is realized if and only if the links are dynamic (functional). Ashman’s Binary Relation Model (BRM) showed that binary relations can most usefully be represented with Mili’s pE (predicate-expression) representation, and Moreau and Hall concluded that hypertext systems which use the pE representation as the basis for their linking (relation) activities are Turing-complete. Secondly we consider that RDF –as it is- is a static version of a general ternary relations model, called TRM. We then conclude that the current computing power of the Semantic Web depends on the dynamicity supported by its underlying TRM. The value of this is firstly that RDF’s triples can be considered within a framework and compared to alternatives, such as the TRM version of pE, designated pfE (predicate-function-expression). Secondly, that a system whose relations are represented with pfE is likewise going to be Turing-complete. Thus moving from RDF to a pfE representation of relations would give far greater power and flexibility within the Semantic Web applications

    Changes under the hood - a new type of non-singleton fuzzy logic system

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    A major asset of fuzzy logic systems is dealing with uncertainties arising in their various applications, thus it is important to make them achieve this task as effectively and comprehensively as possible. While singleton fuzzy logic systems provide some capacity to deal with such uncertainty aspects, non-singleton fuzzy logic systems (NSFLSs) have further enhanced this capacity, particularly in handling input uncertainties. This paper proposes a novel approach to NSFLSs, which further develops this potential by changing the method of handling input fuzzy sets within the inference engine. While the standard approach is getting the maximum of the intersection between input’s and antecedent’s fuzzy sets (in the ”pre-filtering” stage), it is proposed to employ the centroid of the intersection as the basis of each rule’s firing degree. The motivation is to capture the interaction of input and antecedent fuzzy sets with high fidelity, thus making NSFLSs more sensitive to the input’s uncertainty information. The testbed is the common problem of Mackey-Glass time series prediction in the presence of input noise. Analyses of the results show that the new method outperforms the standard approach (by reducing the prediction error) and has potential for a more efficient uncertainty handling in NSFLS applications

    Are we talking about the same structure?: A unified approach to hypertext links, xml, rdf and zigzag

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    There are many different hypertext systems and paradigms, each with their apparent advantages. However the distinctions are perhaps not as significant as they seem. If we can reduce the core linking functionality to some common structure, which allows us to consider hypertext systems within a common model, we could identify what, if anything, distinguishes hypertext systems from each other. This paper offers such a common structure, showing the conceptual similarities between each of these systems and paradigms

    Exploring Constrained Type-2 fuzzy sets

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    Fuzzy logic has been widely used to model human reasoning thanks to its inherent capability of handling uncertainty. In particular, the introduction of Type-2 fuzzy sets added the possibility of expressing uncertainty even on the definition of the membership functions. Type-2 sets, however, don’t pose any restrictions on the continuity or convexity of their embedded sets while these properties may be desirable in certain contexts. To overcome this problem, Constrained Type-2 fuzzy sets have been proposed. In this paper, we focus on Interval Constrained Type-2 sets to see how their unique structure can be exploited to build a new inference process. This will set some ground work for future developments, such as the design of a new defuzzification process for Constrained Type-2 fuzzy systems

    Contrasting singleton type-1 and interval type-2 non-singleton type-1 fuzzy logic systems

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    Most applications of both type-1 and type-2 fuzzy logic systems are employing singleton fuzzification due to its simplicity and reduction in its computational speed. However, using singleton fuzzification assumes that the input data (i.e., measurements) are precise with no uncertainty associated with them. This paper explores the potential of combining the uncertainty modelling capacity of interval type-2 fuzzy sets with the simplicity of type-1 fuzzy logic systems (FLSs) by using interval type-2 fuzzy sets solely as part of the non-singleton input fuzzifier. This paper builds on previous work and uses the methodological design of the footprint of uncertainty (FOU) of interval type-2 fuzzy sets for given levels of uncertainty. We provide a detailed investigation into the ability of both types of fuzzy sets (type-1 and interval type-2) to capture and model different levels of uncertainty/noise through varying the size of the FOU of the underlying input fuzzy sets from type-1 fuzzy sets to very “wide” interval type-2 fuzzy sets as part of type-1 non-singleton FLSs using interval type-2 input fuzzy sets. By applying the study in the context of chaotic time-series prediction, we show how, as uncertainty/noise increases, interval type-2 input fuzzy sets with FOUs of increasing size become more and more viable

    Interpretability indices for hierarchical fuzzy systems

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    Hierarchical fuzzy systems (HFSs) have been shown to have the potential to improve interpretability of fuzzy logic systems (FLSs). In recent years, a variety of indices have been proposed to measure the interpretability of FLSs such as the Nauck index and Fuzzy index. However, interpretability indices associated with HFSs have not so far been discussed. The structure of HFSs, with multiple layers, subsystems, and varied topologies, is the main challenge in constructing interpretability indices for HFSs. Thus, the comparison of interpretability between FLSs and HFSs-even at the index level-is still subject to open discussion. This paper begins to address these challenges by introducing extensions to the FLS Nauck and Fuzzy interpretability indices for HFSs. Using the proposed indices, we explore the concept of interpretability in relation to the different structures in FLSs and HFSs. Initial experiments on benchmark datasets show that based on the proposed indices, HFSs with equivalent function to FLSs produce higher indices, i.e. are more interpretable than their corresponding FLSs
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