Ag. Paraskevi 153 10, Athens, Greece
{konstant,apostolikas}@iit.demokritos.gr
Abstract. In this paper we describe a **fuzzy** **Description** **Logic** reasoner
which implements resolution in order to provide **reasoning** services for expressive **fuzzy** DLs. The main innovation of this implementation is the ability to reason **over** assertions with abstract (unspeciﬁed) **fuzzy** degrees. The answer to queries is, consequently, an algebraic expression involving the (unknown) **fuzzy** degrees and the degree of the query. We describe the implementation and discuss a use case in the domain of semantic meta-extraction where conventional DL **reasoning** is not applicable.

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Enterprises, especially virtual enterprises (VEs) are nowadays getting more knowledge intensive and adopting efficient Knowledge management (KM) systems to boost their competitiveness. The major challenge for KM for VEs is to acquire, extract and integrate new knowledge with the existing source. Ontologies have been proved to be one of the best tools for representing knowledge with class, role and other characteristics. It is imperative to accommodate the new knowledge in the current ontologies with logical consistencies as it is tedious and costly to construct new ontologies every time after acquiring new knowledge. This paper introduces a mechanism and a process to integrate new knowledge in to the current system (ontology). Separate methods have been adopted for **fuzzy** and concrete domain ontologies. The process starts by finding the semantic and structural similarities between the concepts using Wordnet and **Description** **logic** (DL). DL-based **reasoning** is used next to determine the position and relationships between the incoming and existing knowledge. The experimental results provided show the efficacy of the proposed Method.

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For **fuzzy** rule induction the FRL algorithm 1,12 was used as a basis. The algorithm constructs **fuzzy** clas- sification rules and can use nominal as well as nu- merical attributes. For the latter, it automatically extracts **fuzzy** intervals for selected attributes. One of the convenient features of this algorithm is that it only uses a subset of the available attributes for each rule, resulting in so-called free **fuzzy** rules. The KNIME implementation follows the published algo- rithm closely, allowing various algorithmic options to be set as well as different **fuzzy** norms. After ex- ecution, the output is a model **description** in a KN- IME internal format and a table holding the rules as **fuzzy** interval constraints on each attribute plus some additional statistics (number of covered pat- terns, spread, volume etc.). These KNIME repre-

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EL, DLP and DL-Lite, which also correspond to language fragments OWL EL, OWL RL
and OWL QL of the Web Ontology Language.
The EL family of **description** logics is characterised by allowing unlimited use of existential quantifiers and concept intersection. The original **description** **logic** EL allows only those features and ⊤ but no unions, complements or universal quantifiers, and no RBox axioms. Further extensions of this language are known as EL + and EL ++ . The largest such extension allows the constructors ⊓, ⊤, ⊥, ∃, Self , nominals and the univer- sal role, and it supports all types of axioms other than role symmetry, asymmetry and irreflexivity. Interestingly, all standard **reasoning** tasks for this DL can still be solved in worst-case polynomial time. One can even drop the structural restriction of regularity that is important for SROIQ. EL has been used to model large but lightweight ontologies that consist mainly of terminological data, in particular in the life sciences. A number of reasoners are specifically optimised for handling EL-type ontologies, the most recent of which is the ELK reasoner for OWL EL. 6

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ABSTRACT: Data mining is the method of extraction of hidden and useful information from huge data. It is a knowledge domain subfield of computer science and the computational process of discovering patterns in massive data sets. Classification is one of the ordinarily used tasks in data mining applications. It is used to predict membership for data instances. For the past decade, due to the increase of various privacy problems, many theoretical and practical solutions to the classification drawback have been proposed under completely different security models. However, with the recent popularity of cloud computing, users currently have the opportunity to outsource their data, in encrypted form, as well as the data mining tasks to the cloud. In existing the k-Nearest Neighbor (k-NN) classifier is used to encrypted data or information within the cloud. The k-NN classifier had less efficient when compared to the **fuzzy** **logic** classifier. The protocols are used in the existing k-NN classifier has less efficiency. The proposed **fuzzy** **logic** classifier protects the high confidentiality of information, privacy of users input query, and hides the data access patterns.And it secure encrypted data in the cloud. This paper reviews the cost and efficiency of the **fuzzy** **logic** classifier with k-NN classifier.

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Schema.org does neither formally specify the language in which its ontologies are formulated nor does it provide a for- mal semantics for the published ontologies. However, the pro- vided ontologies are extended and updated frequently and fol- low an underlying language pattern. This pattern and its mean- ing is described informally in natural language. Schema.org adopts a class-centric representation enriched with binary re- lations and datatypes, similar in spirit to **description** logics (DLs) and to the OWL family of ontology languages; the cur- rent version includes 622 classes and 891 binary relations. Partial translations into RDF and into OWL are provided by the linked data community. Based on the informal descrip- tions at https://schema.org/ and on the mentioned translations,

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we plan to accompany our explanations with details on the TBox **reasoning** involved, using the work of (Borgida, Cal- vanese, and Rodriguez-Muro 2008) on proofs of positive an- swers as a starting point. The difficulty of such proofs could provide an additional criteria for ranking explanations (cf. the work on the cognitive complexity of justifications (Hor- ridge et al. 2011)). Second, our experiments showed that an answer can have a huge number of explanations, many of which are quite similar in structure. We thus plan to inves- tigate ways of improving the presentation of explanations, e.g. by identifying and grouping similar explanations (cf. (Bail, Parsia, and Sattler 2013) on comparing justifications), or by defining a notion of representative explanation as in (Du, Wang, and Shen 2014). Third, we plan to experiment with other methods of generating explanations of negative answers, by comparing alternative encodings and using tools for computing hitting sets or diagnoses. Finally, it would be interesting to explore how explanations can be used to par- tially repair the data based upon the user’s feedback.

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Boundary layer is a thin layer of fluid that shows the effects of viscosity and is closed to the boundary surface. The boundary layer **over** a surface of boundary continuous in the growing as long as the gradient of pressure equals zero along the surface. The thickness of boundary layer increases severely when pressure gradient is reversed. Also this adverse gradient of pressure and shearing forces (due to viscous) tends to decrease the momentum in the boundary layer, and if any of these factors continues in influence along a certain length of the surface, the growth of boundary layer is stopped. This is called separation, and to avoid separation **over** an airfoil reattached or energise the boundary layer at halted regions must be achieved. If this performed boundary layer remain thin a drop pressure at the rear of the airfoil prevented, and subsequently, the drag coefficient decreases then lift increases .There are quite a few strategies and methods that have been followed or invented to minimize the effects of boundary layer separation. Fig. (1) shows the flow control strategy. All of these techniques and other which are used to improve the aerodynamic characteristics by energize of boundary layer in the stall region [1], [2]. Efforts and studies of previous researchers in the invention and improvement the methods that delay or preventing the separation of boundary layer from the upper surface of wings, have been touched in this study: Kuok -Yang Tu, et al . applied the **fuzzy** modelling for nonlinear boundary layer in design of a new **fuzzy** suction controller, and devoted this process to solve the chattering problem which usually occurred from a sliding- mode controller (SMC) system in unstable situations that system states cross **over** a switching line [3]. M. Goodarzi, et al. studied the principle of active flow controlling by blowing air from slot with (25%) of chord length width, made on the upper surface of NACA0015 airfoil act as fixed blowing jets at different location along the chord. Boundary condition were (Re=45500), attack of angle changed into six times from (12 to 17) degree, and jet speed ratios are (1, 2 and 6 time of free stream velocity). The important results were blowing help in increasing the lift and decreasing the drag coefficient [4]. You and Moin investigated the flow separation by artificial jets on an NACA 0015 aerofoil by using Large Eddy Simulation way. Results given that coefficient of lift (C L ) increased by 70% and the coefficient of drag decreased 18 % while

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Idea for accuracy assessment of ontological classification results comes from the manner the maximum likelihood accuracy assessment was performed: select random sample areas with known classes and then let **fuzzy** **logic** „say‟ what these samples are. With 100 random selected samples, results were as following:

Another sweeping criticism that can be leveled against the legitimacy of the theory of reasoning raises questions about "argument analysis as a plausible subject for stud[r]

In this paper, we experimentally analysed three simple computation rules, namely the A-strategy, the T-strategy and the DB-strategy, in a tableau-based, parallel lean rea- soning system for the ALC **description** **logic**. The sys- tem is implemented in the relational programming model in the Oz language and executed by the parallel search engine on distributed machines. Empirical evaluation of the rules, performed on the testing data coming from the benchmark set T98-sat, gives similar outcomes for the speedup. However, the DB-strategy is generally more ef- ficient than the remaining computation rules, since for the majority of tests it results in significantly shorter compu- tational times. Nevertheless, a comprehensive analysis of the issue considered requires more tests, particularly on realistic data. These tests are intended for the future.

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Peirce invented linear EG as a convenience for typesetting purposes.^^ However, he believed - and it has been noted by others^° - that it is less intuitive than the two-dimensional version. W hy should this be? And are graphs in linear EG sentences or diagrams? We can now say the following: since EG and linear EG are evidently isomorphic to each other, both will be homomorphic to their range, as described above. The fact o f homomorphism, though it makes both valuable in **reasoning**, does not in itself distinguish between them. So too for discretion. But the two can be clearly distinguished in terms o f assimilability. The linear notation does not contain the cut as such, but replicates it using brackets. It is much less evident in linear EG how far a graph is nested within another, and on what level a given graph stands; the brackets do not literally enclose areas within which insertions or eliminations may be made, but are packed together like letters in a word, as though the intervening area had no logical value. Moreover, they must be paired o ff and counted to ensure a graph o f any complexity is well-formed. Finally, the linear format makes it less clear whether or not two graphs are tokens o f the same type. Given that discretion is equal, “normal” E G ’s greater assimilability makes it more perspicuous than linear EG. And this fits with a pre-theoretical intuition that the latter is sentential and the former diagrammatic.

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We now analyse the above CTD scenario in the context of I/O **logic**. This is done is Fig. 1, which first presents, in lines 4-13, an SSE based implementation of I/O **logic** in Isabelle/HOL. 2 A possible world semantics is employed in this
embedding to adequately address an extensionality issue we have revealed in our previous work. This issue, and its solution, is discussed in more detail in a techni- cal report [9]. The prescriptive rules of the GDPR scenario are then modelled in lines 19-25, where the set of given Norms is defined as {(>, process data lawfully), ( ¬process data lawfully, erase data), (process data lawfully, ¬erase data))}. The given Situation, in which we have ¬process data lawfully, is defined in line 27. Subsequently, three di↵erent queries are answered by the **reasoning** tools in- tegrated with Isabelle/HOL. The first query asks whether the data should be erased in the given context. The ATPs integrated with Isabelle/HOL via the Sledgehammer tool [15] respond quickly: the SMT solver CVC4 [22] and the first-order prover Spass [16] return a proof within a few milliseconds. For queries 2 and 3 the ATPs fail (not shown here), but now the countermodel finder Nitpick [14] responds and presents counterarguments to both queries. That is, we receive the intended negative answers to queries 2 and 3 when the GDPR example is modelled in our preferred I/O **logic**. It is worth mentioning that I/O **logic** (and also DDL) have never been automated before.

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Eﬀective ARQ management is the key to both power management and ensuring acceptable video quality at the receiver device. However, it is a multifaceted control prob- lem, as account must also be taken of wireless channel conditions, and of the display/decode deadlines of the picture type slices being conveyed. This paper proposes **fuzzy** **logic** control (FLC) of ARQ, as a way of combining all three factors: (1) channel state; (2) display/decode deadline; and (3) power budget. In our earlier work [13], we did not consider the need to meet a power budget. We have adopted a modular scheme whereby a two-input FLC stage with a single output is concatenated with a second FLC stage, with the output from the original FLC and an additional “remaining power” input. The two inputs to the first FLC stage are buﬀer fullness and the deadline margin of the packet at the head of the Bluetooth send queue, which gives a direct measure of delay. Assuming a fixed power budget for the duration of a video clip streaming session, the declining power budget as the stream progresses has the eﬀect of modulating the ARQ retransmission count. A modular scheme reduces the construction complexity of the design and allows for future enhancements.

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In the past, various semantic and syntactic restrictions have been proposed in order to identify computationally easier or even tractable fragments (see, e.g., [Sti90,KS91,BEZ02]). This is the starting point of the present paper. We propose a systematic study of fragments of default **logic** defined by restricting the set of allowed propositional connectives. For instance, if we look at the fragment where we forbid negation and the constant 0 and allow only conjunction and disjunction, we show that while the first problem is trivial (there always is an extension, in fact a unique one), the second and third problem become coNP-complete. In this paper we look at all possible sets B of propositional connectives and study the three decision problems investigated by Gottlob when all involved formulae contain only connectives from B. The computational complexity of the problems then, of course, becomes a function of B. We will see that Post’s lattice of all closed classes of Boolean functions is the right way to study all such sets B. Depending on the location of B in this lattice, we completely classify the complexity of all three **reasoning** tasks, see Figs. 1 and 2. We will show that, depending on the set B of occurring connectives, the problem of determining the existence of an extension is either Σ p 2 -complete, ∆ p 2 -complete, NP-complete, P-complete, NL-complete, or trivial, while for the **reasoning** problems the trivial cases split up into coNP-complete, P-complete, and NL-complete ones (under constant-depth reductions).

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The standard approach to information flow in a multi-agent system has been presented in [8] but it does not present a formal **description** of epistemic programs and their updates. The first attempts to formalize such programs and updates were done by Plaza [19], Gerbrandy and Groeneveld [12], and Gerbrandy [10, 11]. However, they only studied a restricted class of epistemic programs. A general notion of epistemic programs and updates for DEL was introduced in [5]. In our papers [2, 3], we introduced an algebraic semantics based on the notion of epistemic systems and a sequent calculus for a version of DEL, but the completeness of the sequent calculus was still an open problem. In this paper, we summarize the material in [2, 3] and present an updated version of the sequent calculus for which we have proved the completeness theorem with regard to the algebraic semantics.

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Abstract In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of” – without using a stronger statement such as “Ann knows that Bill is aware of p and Ann is not aware of p”, for some particular p. In Halpern and Rˆego (2006, 2009b) (revisited in Halpern and Rˆego (2009a, 2013)) Halpern and Rˆego introduced a **logic** in which such statements about knowledge of unawareness can be expressed. The **logic** extends the traditional framework with quantification **over** formulae, and is thus very expressive. As a con- sequence, it is not decidable. In this paper we introduce a decidable **logic** which can be used to reason about certain types of unawareness. Our **logic** extends the tradi- tional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of. The **logic** is less expressive than Halpern’s and Rˆego’s **logic**. It is, however, expressive enough to express all of the motivating examples in Halpern and Rˆego (2006, 2009b). In addition to proving that the **logic** is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and com- plete.

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In this paper, a framework for non-conscious ways of reasoning has been presented based on fuzzy 305. multivalued logic, fuzzy semantics and frame oriented knowledge representation[r]

Obviously, although we do accept much of what we are told, we should not accept all of it. As Woods points out, in a situation when we are told something, there may be a trigger which indicates that before acceptance there should be a due dil- igence search. Woods sees such situations as rare. He does enu- merate some triggers for the due diligence exercise. That some interlocutor’s word is an evaluation, not a **description**, triggers ordinarily that it should not merely be accepted but only when properly defended. A perceptual report which involves misper- ception and is immediately corrected, an interpretation, e.g., “Mother Theresa had a generous disposition”, recognition of some unreliability about the subject matter, are all triggers that one should not simply accept what one has been told. However, Woods greater concern in this discussion is not with these trig- gers but with the fact that in mechanisms that generate beliefs which may become premises of our **reasoning**, there may be many conditions which may produce error but which are not ac- companied by triggers. Woods explains that when one acquires a belief either through perception, say-so, or inference, one is experiencing belief change. With perception or say-so, there may be a long chain to the eventual production of one’s belief. By contrast, an inferential chain may be short. Woods proposes talking about the number of steps leading to a belief in a particu- lar case as “the surface of a medium of belief-change” (330, ital- ics in original). “The larger the surface size of a medium of be- lief change, the greater the likelihood of error” (331). Woods proposes this hypothesis as intuitive and worthy of empirical test.

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