The Internet of Things (IoT) has become one of the most popular technologies in recent years. Advances in computing capabilities, hardware accessibility, and wireless connectivity make possible communication between people, processes, and devices for all kinds of applications and industries. However, the deployment of this technology is confined almost entirely to tech companies, leaving end users with only access to specific functionalities. This paper presents a framework that allows users with no technical knowledge to build their own IoT applications according to their needs. To this end, a framework consisting of two building blocks is presented. A friendly interface block lets users tell the system what to do using simple operating rules such as "if the temperature is cold, turn on the heater." On the other hand, a fuzzy logic reasoner block built by experts translates the ambiguity of human language to specific actions to the actuators, such as "call the police." The proposed system can also detect and inform the user if the inserted rules have inconsistencies in real time. Moreover, a formal model is introduced, based on fuzzy description logic, for the consistency of IoT systems. Finally, this paper presents various experiments using a fuzzy logic reasoner to show the viability of the proposed framework using a smart-home IoT security system as an example.

Minimizing fuzzy interpretations in fuzzy description logics by using crisp bisimulations

Fuzzy ontology-based approach for liver fibrosis diagnosis

Fuzzy description logics (FDLs) are useful for dealing with fuzzy terminological knowledge for domains with linked data. Logical similarity or indiscernibility between individuals with respect to a given FDL is a fuzzy measure, which becomes crisp when the logic is extended with the Baaz projection operator. The measure is closely related to bisimulation. While logical indiscernibility is defined semantically, its corresponding notion based on bisimulation enables the computation. In this article, we study crisp bisimulations between fuzzy interpretations in FDLs with the Baaz projection operator under a general semantics based on an abstract algebra of fuzzy truth values. We define such bisimulations for a large class of FDLs with a rich set of well-known concept and role constructors, including qualified/unqualified number restrictions, nominals and the role constructors that correspond to the program constructors of propositional dynamic logic. We formulate and prove their logical characterizations, including the invariance of concepts under crisp bisimulations and the Hennessy–Milner property of crisp bisimulations. Such logical characterizations do not depend on a concrete semantics, such as the Gödel, Łukasiewicz, and product semantics. Based on crisp bisimulations, we also study indiscernibility of individuals in FDLs with the Baaz projection operator. An interesting consequence of our results states that, when restricting to the considered FDLs and image-finite fuzzy interpretations that are witnessed and modally saturated, indiscernibility of individuals is independent from the underlying algebra of fuzzy truth values in the case without number restrictions, and it is the same for both the Gödel and product semantics in the case with number restrictions.

Abstract Shared conceptualization, in the sense we take it here, is as recent a notion as the Semantic Web, but its relevance for a large variety of fields requires efficient methods of extraction and representation for both quantitative and qualitative data. This notion is particularly relevant for the investigation into, and construction of, semantic structures such as knowledge bases and taxonomies, but given the required large, often inaccurate, corpora available for search we can get only approximations. We see fuzzy description logic as an adequate medium for the representation of human semantic knowledge and propose a means to couple it with fuzzy semantic networks via the propositional Łukasiewicz fuzzy logic such that these suffice for decidability for queries over a semantic-knowledge base such as “to what degree of sharedness does it entail the instantiation C(a) for some concept C” or “what are the roles R that connect the individuals a and b to degree of sharedness ε.”

Computing the fuzzy partition corresponding to the greatest fuzzy auto-bisimulation of a fuzzy graph-based structure under the Gödel semantics

Abstract In this paper we establish a link between fuzzy and preferential semantics for description logics and self-organizing maps (SOMs), which have been proposed as possible candidates to explain the psychological mechanisms underlying category generalization. In particular, we show that the input/output behavior of a SOM after training can be described by a fuzzy description logic interpretation as well as by a preferential interpretation, based on a concept-wise multipreference semantics, which takes into account preferences with respect to different concepts and has been recently proposed for ranked and for weighted defeasible description logics. Properties of the network can be proven by model checking on the fuzzy or on the preferential interpretation. Starting from the fuzzy interpretation, we also provide a probabilistic account for this neural network model.

Bisimulation is a well-known notion in modal logic and the theory of labeled transition systems. It is used for characterizing indiscernibility between states and has important applications in minimizing structures, separating expressive powers of modal and related logics, as well as concept learning in description logics (DLs). Fuzzy bisimulation is a counterpart of bisimulation for dealing with fuzzy structures. In this article, we present an efficient algorithm with a complexity $O((m+n)n)$ for computing the greatest fuzzy bisimulation between two finite fuzzy interpretations in the fuzzy DL $\mathit {f}\!\mathcal {ALC}$ under the Godel semantics, where $n$ is the number of individuals and $m$ is the number of nonzero instances of roles in the given fuzzy interpretations. We also adapt our algorithm for computing fuzzy bisimulations and simulations between fuzzy finite automata, as well as for dealing with other fuzzy DLs. The resulting algorithms are much more efficient than the previously known ones, as they reduce the complexity from $O(n^5)$ to $O((m+n)n)$ .

Fuzzy description logics, the formalism behind fuzzy ontologies, are an important mathematical method with applications in many artificial intelligence scenarios. This paper proposes the first specific algorithms to solve two reasoning tasks with respect to a fuzzy ontology: the instance retrieval and the realization problem. Our algorithms are based on a reduction of the number of optimization problems to solve by merging some of them. Our experimental evaluation shows that the novel algorithm to solve the instance retrieval outperforms the previous algorithm, and that in practice it is common to be able to solve a single optimization problem.

Abstract Security is a growing concern in developing software systems. It is important to face unknown threats in order to make the system continue operating properly. Threats are vague and attack methods change frequently. Coping with such changes is a major feature of an adaptive software. Therefore, designing an adaptive secure software is an appropriate solution to address software security challenges. Through estimation of maximum amount of system assets security, one can determine whether the system is protecting the assets or not; if not, reconfiguration can be employed. This paper proposes a new requirement model for secure adaptive systems using fuzzy, goal modeling and Description Logic concepts. The model contains three phases of modeling security aspects of the system, identifying formalizations and relations between the requirements and monitoring and adapting, when needed. To illustrate the relations between the requirements, goal modeling is used in the first phase and fuzzy Description Logic in the second phase. For the third phase, four algorithms are proposed to monitor and determine whether reconfiguration is needed or not. Theorems are given to prove concept satisfaction of the requirements. Furthermore, examples and case studies are discussed to evaluate and show applicability of the proposed model.

We study the problem of minimizing interpretations in fuzzy description logics (DLs) under the Gödel semantics by using fuzzy bisimulations. The considered logics are fuzzy extensions of the DL 𝒜ℒ𝒞 reg (a variant of propositional dynamic logic) with additional features among inverse roles, nominals and the universal role. Given a fuzzy interpretation ℐ and for E being the greatest fuzzy auto-bisimulation of ℐ w.r.t. the considered DL, we define the quotient ℐ/ E of ℐ w.r.t. E and prove that it is minimum w.r.t. certain criteria. Namely, ℐ/ E is a minimum fuzzy interpretation that validates the same set of fuzzy terminological axioms in the considered DL as ℐ. Furthermore, if the considered DL allows the universal role, then ℐ/ E is a minimum fuzzy interpretation bisimilar to ℐ, as well as a minimum fuzzy interpretation that validates the same set of fuzzy concept assertions in the considered DL as ℐ.

Bisimulation and bisimilarity for fuzzy description logics under the Gödel semantics

Fuzzy description logics (DLs) are extensions of DLs for dealing with imprecise and vague concepts. They found the logical basis for fuzzy ontologies, which are useful for practical applications. Bisimilarity is a natural notion of equivalence between individuals in DLs. In this paper, for the first time, we introduce the notion of bisimilarity in fuzzy DLs under the Zadeh semantics. It is defined using our notion of p-cut simulation between fuzzy interpretations. The considered logics are fuzzy DLs that extend the fuzzy version of the DL ALC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">reg</sub> (a variant of propositional dynamic logic) with features among inverse roles, the universal role, qualified number restrictions, nominals, and local reflexivity of a role. We provide results on preservation of information by the mentioned simulations, conditional invariance of ABoxes and TBoxes by bisimilarity between witnessed interpretations, as well as the Hennessy-Milner property for fuzzy DLs under the Zadeh semantics.

Abstract Fuzzy spatio‐temporal knowledge is required in a wide range of application fields, including GIS, spatio‐temporal database, and artificial intelligence. Ontology, as a formal method of knowledge representation, plays a key role in the Semantic Web. Therefore, how to extend ontologies to represent fuzzy spatio‐temporal knowledge needs to be solved. In this paper, we propose an approach for representing fuzzy spatio‐temporal knowledge with ontologies and investigate a formal construction of fuzzy spatio‐temporal ontologies based on fuzzy Petri nets. First, we propose a formal definition of fuzzy spatio‐temporal ontologies. In addition, based on fuzzy description logic, a description logic named the fuzzy spatio‐temporal description logic, which provides a logical basis for the fuzzy spatio‐temporal ontologies, is presented. Furthermore, a fuzzy spatio‐temporal web ontology language, which is fuzzy and spatio‐temporal extension of standard ontology language OWL, is proposed to make the fuzzy spatio‐temporal ontologies easy to use and support efficient reasoning. On the basis of fuzzy spatio‐temporal ontologies, we investigate a formal approach for constructing fuzzy spatio‐temporal ontologies from fuzzy spatio‐temporal Petri nets, ie, transforming fuzzy spatio‐temporal Petri nets (including Petri net model and Petri net instance) into fuzzy spatio‐temporal ontologies at both structure and instance levels. Finally, we prove the correctness of the transformation and provide a detailed transformation example.

A well-known family of logics for managing structured knowledge is Description logics (DLs). They form the basis for a wide variety of ontology languages. Experience with the use of DLs in applications has, however, shown that their capabilities are insufficient for some domains. In particular, the decision-making process requires the assessment of two, possibly contradictory, influences on decision factors. First, there are items belonging to certain classes or fulfillling certain roles within complex logical constructs, but these memberships are to some extent vague. Secondly, individual preferences may change depending on the person who controls the decision-making process. Therefore, the challenge in building a decision making framework is to appropriately account for these variable influences by depicting and incorporating both aspects. This paper shows how these influences can be best modeled using a combination of fuzzy description logic and weighted description logic. Fuzzy logic is used to represent vagueness and ambiguity in ontologies, weighted description logic expresses individual preferences. In addition, the paper shows how to engineer an appropriate architecture for the suggested model.

[full article, abstract in Russian; abstract in Lithuanian and English]&#x0D; In the paper an approach to recognition of old Slavonic symbols is proposed, which includes the stages of ternary segmentation, detecting edges of areas, synthesis of two skeleton variants, forming a fuzzy graph, creating a logical description in a fuzzy description logic, and recognition with help of a subsystem of formal automatic reasoning. Results of preliminary experiments are provided, which confirm the perspective of the proposed approach.

Vague information has been emerged as a main issue in Semantic Web community. Vagueness is traditionally represented by fuzzy set theory. Besides vagueness, Semantic Web queries often have to deal with information incompleteness, aka uncertainty. This kind of information can be represented through Dempster–Shafer theory, that also enables distributed information fusion. Vagueness along with information incompleteness are often referred to under the common term imprecise information . Imprecise information should be represented and manipulated under a common framework. We propose such a framework by defining a fuzzy Description Logic extended with Dempster–Shafer theory. Furthermore, we regard our method as a DL extension and we implemented it by a metaontology that captures Dempster–Shafer Fuzzy statements.

Verification of fuzzy UML models with fuzzy Description Logic

Reasoning within Fuzzy OWL 2 EL revisited

On the relationship between fuzzy description logics and many-valued modal logics