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This paper provides a set of cut-free complete sequent-style calculi for deontic STIT (‘See To It That’) logics used to formally reason about choice-making, obligations, and norms in a multi-agent setting. We leverage these calculi to write a proof-search algorithm deciding deontic, multi-agent STIT logics with (un)limited choice and introduce a loop-checking mechanism to ensure the termination of the algorithm. Despite the acknowledged potential for deontic reasoning in the context of autonomous, multi-agent scenarios, this work is the first to provide a syntactic decision procedure for this class of logics. Our proofsearch procedure is designed to provide verifiable witnesses/certificates of the (in)validity of formulae, which permits an analysis of the (non)theoremhood of formulae and act as explanations thereof. We show how the proof system and decision algorithm can be used to automate normative reasoning tasks such as duty checking (viz. determining an agent’s obligations relative to a given knowledge base), compliance checking (viz. determining if a choice, considered by an agent as potential conduct, complies with the given knowledge base), and joint fulfillment checking (viz. determining whether under a specified factual context an agent can jointly fulfill all their duties). [ABSTRACT FROM AUTHOR]

Nominal schemas have been proposed as an extension to Description Logics (DL), the knowledge representation paradigm underlying the Web Ontology Language (OWL). They provide for a very tight integration of DL and rules. Nominal schemas can be understood as syntactic sugar on top of OWL. However, this naive perspective leads to inefficient reasoning procedures. In order to develop an efficient reasoning procedure for the language |${\mathcal {E}\mathcal {L}\mathcal {V}^{++}}$|⁠ , which results from extending the OWL profile language OWL EL with nominal schemas, we propose a transformation from |${\mathcal {E}\mathcal {L}\mathcal {V}^{++}}$| ontologies into Datalog-like rule programs that can be used for satisfiability checking and assertion retrieval. The use of this transformation enables the use of powerful Datalog engines to solve reasoning tasks over |${\mathcal {E}\mathcal {L}\mathcal {V}^{++}}$| ontologies. We implement and then evaluate our approach on several real-world, data-intensive ontologies, and find that it can outperform state-of-the-art reasoners such as Konclude and ELK. As a lesser side result we also provide a self-contained description of a rule-based algorithm for |${\mathcal {E}\mathcal {L}^{++}}$|⁠ , which does not require a normal form transformation. [ABSTRACT FROM AUTHOR]

The inexpressive Description Logic (DL) ${\cal F}{{\cal L}_0}$ , which has conjunction and value restriction as its only concept constructors, had fallen into disrepute when it turned out that reasoning in ${\cal F}{{\cal L}_0}$ w.r.t. general TBoxes is ExpTime-complete, that is, as hard as in the considerably more expressive logic ${\cal A}{\cal L}{\cal C}$. In this paper, we rehabilitate ${\cal F}{{\cal L}_0}$ by presenting a dedicated subsumption algorithm for ${\cal F}{{\cal L}_0}$ , which is much simpler than the tableau-based algorithms employed by highly optimized DL reasoners. Our experiments show that the performance of our novel algorithm, as prototypically implemented in our ${\cal F}{{\cal L}_0}$ wer reasoner, compares very well with that of the highly optimized reasoners. ${\cal F}{{\cal L}_0}$ wer can also deal with ontologies written in the extension ${\cal F}{{\cal L}_ \bot }$ of ${\cal F}{{\cal L}_0}$ with the top and the bottom concept by employing a polynomial-time reduction, shown in this paper, which eliminates top and bottom. We also investigate the complexity of reasoning in DLs related to the Horn-fragments of ${\cal F}{{\cal L}_0}$ and ${\cal F}{{\cal L}_ \bot }$. [ABSTRACT FROM AUTHOR]

The spatial footprints, historical or acquired in real time, help to understand the dynamics of their carriers. In a context of coastal maritime navigation, the research presented details the approach of setting up a knowledge model aimed at a semantic analysis of ship footprints. This model is defined on the basis of knowledge gathered from experts in this field, supplemented by textual and graphic descriptions. After having described these navigation principles, we present the stages leading to such a knowledge model. The research is completed by the formalization of rules relating to the visibility of landmarks. Finally, a reasoning leads to infer additional navigation knowledge on which the navigation footprints are confronted in order to identify the routes having semantics for the model and those devoid of semantics. [ABSTRACT FROM AUTHOR]

The main element of extended reality (XR) environments is behavior-rich 3D content consisting of objects that act and interact with one another as well as with users. Such actions and interactions constitute the evolution of the content over time. Multiple application domains of XR, e.g., education, training, marketing, merchandising, and design, could benefit from the analysis of 3D content changes based on general or domain knowledge comprehensible to average users or domain experts. Such analysis can be intended, in particular, to monitor, comprehend, examine, and control XR environments as well as users' skills, experience, interests and preferences, and XR objects' features. However, it is difficult to achieve as long as XR environments are developed with methods and tools that focus on programming and 3D modeling rather than expressing domain knowledge accompanying content users and objects, and their behavior. The main contribution of this paper is an approach to creating explorable knowledge-based XR environments with semantic annotations. The approach combines description logics with aspect-oriented programming, which enables knowledge representation in an arbitrary domain as well as transformation of available environments with minimal users' effort. We have implemented the approach using well-established development tools and exemplify it with an explorable immersive car showroom. The approach enables efficient creation of explorable XR environments and knowledge acquisition from XR. [ABSTRACT FROM AUTHOR]

The project "Semantic Technologies for Situation Awareness" was concerned with detecting certain critical situations from data obtained by observing a complex hard- and software system, in order to trigger actions that allow this system to save energy. The general idea was to formalize situations as ontology-mediated queries, but in order to express the relevant situations, both the employed ontology language and the query language had to be extended. In this paper we sketch the general approach and then concentrate on reporting the formal results obtained for reasoning in these extensions, but do not describe the application that triggered these extensions in detail. [ABSTRACT FROM AUTHOR]

The construction and maintenance of ontologies is an error-prone task. As such, it is not uncommon to detect unwanted or erroneous consequences in large-scale ontologies which are already deployed in production. While waiting for a corrected version, these ontologies should still be available for use in a "safe" manner, which avoids the known errors. At the same time, the knowledge engineer in charge of producing the new version requires support to explore only the potentially problematic axioms, and reduce the number of exploration steps. In this paper, we explore the problem of deriving meaningful consequences from ontologies which contain known errors. Our work extends the ideas from inconsistency-tolerant reasoning to allow for arbitrary entailments as errors, and allows for any part of the ontology (be it the terminological elements or the facts) to be the causes of the error. Our study shows that, with a few exceptions, tasks related to this kind of reasoning are intractable in general, even for very inexpressive description logics. [ABSTRACT FROM AUTHOR]

In the paper we present the results of experiment we performed to determine whether a contextual approach may be used to increase the performance of querying a knowledge base. For the experiments we have used a unique setting where we put much effort in developing a contextual and a non-contextual ontology which are as much close counterparts as possible. To achieve this we created a contextual version of a non-contextual ontology and reformulated the set of competency questions to reflect the contextual structure of the newly created knowledge base. The results of the experiment strongly suggest that using contexts might be advantageous for improving performance, and also show the further ways of development of the approach. [ABSTRACT FROM AUTHOR]

Analogical reasoning is a complex process based on a comparison between two pairs of concepts or states of affairs (aka. the source and the target) for characterizing certain features from one to another. Arguments which employ this process to support their claims are called analogical arguments. Our goals are to study the structure and the computation for their defeasibility in light of the argumentation theory. Our proposed assumption-based argumentation with predicate similarity ABA(p) framework can be seen as an extension of assumption-based argumentation framework (ABA), in which not only assumptions can be used but also similarity of predicates is used to support a claim. ABA (p) labels each argument tree with an analogical degree and different ways to aggregate numerical values are studied toward gullible/skeptical characteristics in agent reasoning. The acceptability of analogical arguments is evaluated w.r.t. the semantics of abstract argumentation. Finally, we demonstrate that ABA (p) captures the argumentation scheme for argument from analogy and provides an explanation when it is used for persuasion. [ABSTRACT FROM AUTHOR]

Description logic, as a logical foundation of knowledge representation and reasoning, plays an important role in the Semantic Web. In practical applications, many fields contain a large number of fuzzy spatio-temporal knowledge. With a large amount of fuzzy spatio-temporal knowledge and many corresponding applications being incorporated into the Semantic Web, description logic becomes an effective method to solve the problem of fuzzy spatio-temporal knowledge representation and reasoning. Currently, many efforts have been done on fuzzy spatio-temporal extensions of description logics, and the literature on fuzzy spatio-temporal description logic has been booming. To address these issues and more importantly, in this paper, we provide a comprehensive survey of the research literature that applies description logics techniques in fuzzy spatio-temporal representation and reasoning. The paper serves as helping readers grasp the main results and highlighting the direction of fuzzy spatio-temporal representation and reasoning based on description logics. [ABSTRACT FROM AUTHOR]

In applications of AI systems where exact definitions of the important notions of the application domain are hard to come by, the use of traditional logic-based knowledge representation languages such as Description Logics may lead to very large and unintuitive definitions, and high complexity of reasoning. To overcome this problem, we define new concept constructors that allow us to define concepts in an approximate way. To be more precise, we present a family τ EL (m) of extensions of the lightweight Description Logic EL that use threshold constructors for this purpose. To define the semantics of these constructors we employ graded membership functions m , which for each individual in an interpretation and concept yield a number in the interval [ 0 , 1 ] expressing the degree to which the individual belongs to the concept in the interpretation. Threshold concepts C ⋈ t for ⋈ ∈ { < , ≤ , > , ≥ } then collect all the individuals that belong to C with degree ⋈ t. The logic τ EL (m) extends EL with threshold concepts whose semantics is defined relative to a function m. To construct appropriate graded membership functions, we show how concept measures ∼ (which are graded generalizations of subsumption or equivalence between concepts) can be used to define graded membership functions m ∼. Then we introduce a large class of concept measures, called simi-d , for which the logics τ EL (m ∼) have good algorithmic properties. Basically, we show that reasoning in τ EL (m ∼) is NP/coNP-complete without TBox, PSpace-complete w.r.t. acyclic TBoxes, and ExpTime-complete w.r.t. general TBoxes. The exception is the instance problem, which is already PSpace-complete without TBox w.r.t. combined complexity. While the upper bounds hold for all elements of simi-d , we could prove some of the hardness results only for a subclass of simi-d. This article considerably improves on and generalizes results we have shown in three previous conference papers and it provides detailed proofs of all our results. [ABSTRACT FROM AUTHOR]

Abstract The fuzzy UML model has been introduced to enable the conceptual modeling of imprecise data in many applications. How to prevent, detect, and correct errors as early as possible in the modeling process by verifying the correctness of fuzzy UML models is desirable. But it is difficult to manually verify the correctness of the models. Thanks to the effective reasoning service of fuzzy Description Logics (DLs), they are considered as natural candidates for supporting the verification of fuzzy UML models. In this paper we propose a complete and practical approach for verifying fuzzy UML models with fuzzy DLs. In detail, we first propose an approach for transforming a fuzzy UML model into a fuzzy DL knowledge base. Then we further reduce the verification tasks of the fuzzy UML model to reasoning problems of the transformed fuzzy DL knowledge base. Also, the correctness of the approach is proved, and a running example is provided to explain the approach in detail. Final we implemented a prototype that can transform fuzzy UML models into fuzzy DL knowledge bases. Case studies show that the proposed approach is feasible and the prototype translator actually works. By means of our approach and tool, the transformed fuzzy DL knowledge base and reasoning tasks can be input into the existing fuzzy DL reasoners, and the reasoning results reported by the reasoners can be passed back to the designer to improve the quality of the fuzzy UML model. Graphical abstract Highlights • Proposing an approach to transform a fuzzy UML model into a fuzzy DL knowledge base. • Proposing an approach to reduce verification tasks from fuzzy UML to fuzzy DL. • Implementing a prototype transformation tool. • Giving formal proofs, running example , and case studies. • Improving the quality of the fuzzy UML models. [ABSTRACT FROM AUTHOR]

The paper presents a methodology to revise a Description Logic knowledge base when exceptions are detected. The approach exploits concepts and results from techniques developed for debugging Description Logic terminologies. Debugging an inconsistent terminology amounts to identifying a minimal subset of axioms responsible for the inconsistency (i.e., an error to be removed by a knowledge engineer). Exception handling, instead, requires to revise the axioms causing an inconsistency so that a new consistent knowledge base is obtained, encompassing the detected exception about an individual x. To this aim, we make use of a nonmonotonic extension of the Description Logic ALC based on the combination of a typicality operator and the well established nonmonotonic mechanism of rational closure, which allows one to deal with prototypical properties and defeasible inheritance. [ABSTRACT FROM AUTHOR]

In the current era of increased customization, changing manufacturing systems and business globalization, effective use of product design information and knowledge generated from the product model can facilitate the decision-making of an assembly sequence by providing feasible product relationships and a viable semantic foundation. To enrich such semantics, a geometryenhanced ontology modelling and reasoning framework is proposed in this paper to explicitly express relevant concepts for assembly sequence planning (ASP). A rule-based reasoning mechanism based on Ontology Web Language Description Logics (OWL-DL) and Semantic Web Rule Language (SWRL) is also suggested to clarify implicit relations by incorporating reasoning units (RUs) to process complex geometric information. This framework is then validated with a complex case study related to assembly sequence planning. [ABSTRACT FROM AUTHOR]

This paper reports on an investigation into the use of ontology technologies to support taxonomic functions. Support for taxonomy is imperative given several recent discussions and publications that voiced concern over the taxonomic impediment within the broader context of the life sciences. Taxonomy is defined as the scientific classification, description and grouping of biological organisms into hierarchies based on sets of shared characteristics, and documenting the principles that enforce such classification. Under taxonomic functions we identified two broad categories: the classification functions concerned with identification and naming of organisms, and secondly classification functions concerned with categorization and revision (i.e. grouping and describing, or revisiting existing groups and descriptions). Ontology technologies within the broad field of artificial intelligence include computational ontologies that are knowledge representation mechanisms using standardized representations that are based on description logics (DLs). This logic base of computational ontologies provides for the computerized capturing and manipulation of knowledge. Furthermore, the set-theoretical basis of computational ontologies ensures particular suitability towards classification, which is considered as a core function of systematics or taxonomy. Using the specific case of Afrotropical bees, this experimental research study represents the taxonomic knowledge base as an ontology, explore the use of available reasoning algorithms to draw the necessary inferences that support taxonomic functions (identification and revision) over the ontology and implement a Web-based application (the WOC). The contributions include the ontology, a reusable and standardized computable knowledge base of the taxonomy of Afrotropical bees, as well as the WOC and the evaluation thereof by experts. [ABSTRACT FROM AUTHOR]

Reasoning with inconsistencies is an important issue for Semantic Web as imperfect information is unavoidable in real applications. For this, different paraconsistent approaches, due to their capacity to draw as nontrivial conclusions by tolerating inconsistencies, have been proposed to reason with inconsistent description logic knowledge bases. However, existing paraconsistent approaches are often criticized for being too skeptical. To this end, this paper presents a non-monotonic paraconsistent version of description logic reasoning, called minimally inconsistent reasoning, where inconsistencies tolerated in the reasoning are minimized so that more reasonable conclusions can be inferred. Some desirable properties are studied, which shows that the new semantics inherits advantages of both non-monotonic reasoning and paraconsistent reasoning. A complete and sound tableau-based algorithm, called multi-valued tableaux, is developed to capture the minimally inconsistent reasoning. In fact, the tableaux algorithm is designed, as a framework for multi-valued DL, to allow for different underlying paraconsistent semantics, with the mere difference in the clash conditions. Finally, the complexity of minimally inconsistent description logic reasoning is shown on the same level as the (classical) description logic reasoning. [ABSTRACT FROM AUTHOR]

DL-Lite is one of the most important fragments of description logics that allows a flexible representation of knowledge with a tractable computational complexity of the reasoning process. This article investigates an extension of the main fragments of DL-Lite to deal with uncertainty associated with objects, concepts or relations using a possibility theory framework. Possibility theory offers a natural framework for representing uncertain and incomplete information. It is particularly useful for handling inconsistent knowledge. We first provide foundations of possibilistic DL-Lite, denoted by π-DL-Lite, by extending the DLLitecore logic, the core fragment of all DL-Lite logics, within possibility theory setting. We present syntax and semantics of π-DL-Litecore, study the reasoning tasks and show how to compute the inconsistency degree of a π-DL-Litecore knowledge base. We then extend our possibilistic approach to DL-LiteF and DL-LiteR, two important fragments of DL-Lite family. Finally, we address the problem of query answering over a π-DL-Lite knowledge base. An important result of the article is that the extension of the expressive power of DL-Lite is done without additional extra-computational costs. [ABSTRACT FROM AUTHOR]

In some application domains it is sometimes useful to reason about plausible but "not obvious" scenarios, excluding the most trivial ones. In this work we introduce nonmonotonic procedures for preferential Description Logics in order to reason about plausible but - in some sense - "surprising" scenarios. We consider an extension, called ALC + TRexp, of the nonmonotonic logic of typicality ALC + TR by inclusions of the form T(C) ⊆d D, where d is a degree of expectedness. We consider a notion of extension of an ABox, in order to assume typicality assertions about individuals satisfying cardinality restrictions on concepts, then we define a preference relation among such extended ABoxes based on the degrees of expectedness, then we restrict entailment to those extensions that are minimal with respect to this preference relation. We propose a decision procedure for reasoning in ALC + TRexp and we exploit it to show that entailment is in ExpTime as for the underlying ALC. Last, we introduce a further extension of the proposed approach in order to reason about all plausible extensions of the ABox, by restricting the attention to specific degrees of expectedness ranging from the most surprising scenarios to the most expected ones, and we show that entailment remains in ExpTime also in these cases. [ABSTRACT FROM AUTHOR]

Norms and policies are a fundamental component of nowadays open distributed systems operating on the Internet, and a crucial application is the field of Access Control. In such context, policies have been widely used to express data consumer permissions and prohibitions to get access to certain data, whereas obligations have been modelled and applied more infrequently. In this paper, we present a unified semantic model for specifying data consumer and data provider obligations in the context of an exchange of logically formalized information between agents, inside a Multiagent System. We explain how to specify those obligations, in a formal way; we present how to enforce the data provider obligations on the data released by the agent before returning it to the data consumer; we show how to monitor the fulfilment or violation of the specified data consumer obligations; all of that in the context of a complete reasoning-based obligation framework. [ABSTRACT FROM AUTHOR]

In the last years, fuzzy ontologies and fuzzy description logics (DLs) have been applied successfully to several real-world domains. Some recent results on fuzzy DLs show an increase in the theoretical complexity, even for not expressive languages. However, it still may be possible to obtain reasoning algorithms performing well in practice. This paper studies some cases where reasoning with a fuzzy ontology can be reduced to reasoning with a tractable classical language (an OWL 2 profile). Then, building on the assumption that not all concepts and roles in fuzzy ontologies are indeed fuzzy, we show that reasoning algorithms can be optimized by taking into account the existence of possible crisp concepts and roles. We also prove the usefulness on crisp representation reasoning algorithms over an empirical evaluation over fuzzy OWL 2 EL ontologies, and discuss some preliminary techniques to learn which elements should be considered to be crisp or noncrisp. [ABSTRACT FROM PUBLISHER]

Automata-based methods have been successfully employed to prove tight complexity bounds for reasoning in many classical logics, and in particular in Description Logics (DLs). Very recently, the ideas behind these automata-based approaches were adapted for reasoning also in fuzzy extensions of DLs, with semantics based either on finitely many truth degrees or the Gödel t-norm over the interval [ 0 , 1 ] . Clearly, due to the different semantics in these logics, the construction of the automata for fuzzy DLs is more involved than for the classical case. In this paper we provide an overview of the existing automata-based methods for reasoning in fuzzy DLs, with a special emphasis on explaining the ideas and the requirements behind them. The methods vary from deciding emptiness of automata on infinite trees to inclusions between automata on finite words. Overall, we provide a comprehensive perspective on the automata-based methods currently in use, and the many complexity results obtained through them. [ABSTRACT FROM AUTHOR]

Background: Reasoning over biomedical ontologies using their OWL semantics has traditionally been a challenging task due to the high theoretical complexity of OWL-based automated reasoning. As a consequence, ontology repositories, as well as most other tools utilizing ontologies, either provide access to ontologies without use of automated reasoning, or limit the number of ontologies for which automated reasoning-based access is provided. Methods: We apply the AberOWL infrastructure to provide automated reasoning-based access to all accessible and consistent ontologies in BioPortal (368 ontologies). We perform an extensive performance evaluation to determine query times, both for queries of different complexity and for queries that are performed in parallel over the ontologie. Results and conclusions: We demonstrate that, with the exception of a few ontologies, even complex and parallel queries can now be answered in milliseconds, therefore allowing automated reasoning to be used on a large scale, to run in parallel, and with rapid response times. [ABSTRACT FROM AUTHOR]

We present the first direct tableau decision procedure for graded PDL, which uses global caching and has ExpTime (optimal) complexity when numbers are encoded in unary. It shows how to combine checking fulfillment of existential star modalities with integer linear feasibility checking for tableaux with global caching. As graded PDL can be used as a description logic for representing and reasoning about terminological knowledge, our procedure is useful for practical applications. [ABSTRACT FROM AUTHOR]

Today's ontology applications require efficient and reliable description logic (DL) reasoning services. Expressive DLs usually have high worst case complexity while tractable DLs are restricted in terms of expressive power. This brings a new challenge: can users use expressive DLs to build their ontologies and still enjoy the efficient services as in tractable languages? Approximation has been considered as a solution to this challenge; however, traditional approximation approaches have limitations in terms of performance and usability. In this paper, we present a tractable approximate reasoning framework for OWL 2 that improves efficiency and guarantees soundness. Evaluation on ontologies from benchmarks and real-world use cases shows that our approach can do reasoning on complex ontologies efficiently with a high recall. [ABSTRACT FROM AUTHOR]

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Based on the high expressive powers and effective reasoning services of description logics (DLs, for short), DLs have been employed in data modeling to support the development and maintenance of data models. The basic idea is that once the correspondences between data models and DLs can be established, reasoning techniques from DLs become applicable to the reasoning of data models. This paper proposes a complete DL approach for representing and reasoning on EER (Enhanced Entity-Relationship) models. We develop an equivalence-preserving transformation approach and a prototype tool for transforming an EER model into a DL knowledge base, and propose methods to reduce reasoning on the EER model to reasoning on the transformed DL knowledge base. As one result, the reasoning capabilities of the DL can provide the basic reasoning services that are needed in EER modeling. In detail, we firstly propose a formal definition and semantic interpretation method of EER models, which summarizes and includes all features of EER models. Then , by analyzing the features of EER models, a DL called A L C Q I K is presented as the language of representing and reasoning on EER models. On this basis , we propose an approach for transforming EER models into A L C Q I K knowledge bases. The correctness of the transformation is proved and a transformation example is provided. Further , a prototype transformation tool is implemented. Case studies show that our approach and prototype tool actually work. Finally , based on the transformed A L C Q I K knowledge bases, we propose methods to reduce reasoning on EER models to reasoning on the transformed A L C Q I K knowledge bases. [ABSTRACT FROM AUTHOR]

Combining ontologies in expressive fragments of Description Logics in inherently distributed peer-to-peer settings with autonomous peers is still a challenge in the general case. Although several modular ontology representation frameworks have been proposed for combining Description Logics knowledge bases, each of them has its own strengths and limitations. In this paper, we consider networks of peers, where each peer holds its own ontology within the $${\mathcal {SHIQ}}$$ fragment of Description Logics, and subjective beliefs on how its knowledge can be coupled with the knowledge of others. To allow peers to reason jointly with their coupled knowledge, while preserving their autonomy on evolving their knowledge, data, and subjective beliefs, we propose the $$E\text {-}{\mathcal {SHIQ}}$$ representation framework. The article motivates the need for $$E\text {-}{\mathcal {SHIQ}}$$ and compares it to existing representation frameworks for modular Description Logics. It discusses the implementation of the $$E\text {-}{\mathcal {SHIQ}}$$ distributed reasoner and presents experimental results on the efficiency of this reasoner. [ABSTRACT FROM AUTHOR]

By studying the features of event class and relations among event elements, this paper proposed an event instance checking method based on extended description logic. This method supplemented semantic information at first, and then it verified whether an event was an instance of a specific event class by using effective reasoning capability of extended description logic, such as concept subsumption and satisfiability. Finally, it carried out an experiment to evaluate this approach. The experimental results show that this method can achieve instance checking of event classes with an accuracy of 85.12 percents. [ABSTRACT FROM AUTHOR]

EL is a popular description logic, used as a core formalism in large existing knowledge bases. Uniform interpolants of knowledge bases are of high interest, e.g. in scenarios where a knowledge base is supposed to be partially reused. However, to the best of our knowledge no procedure has yet been proposed that computes uniform EL interpolants of general EL terminologies. Up to now, also the bound on the size of uniform EL interpolants has remained unknown. In this article, we propose an approach to computing a finite uniform interpolant for a general EL terminology if it exists. To this end, we develop a quadratic representation of EL TBoxes as regular tree grammars. Further, we show that, if a finite uniform EL interpolant exists, then there exists one that is at most triple exponential in the size of the original TBox, and that, in the worst case, no smaller interpolants exist, thereby establishing tight worst-case bounds on their size. Beyond showing these bounds, the notions and results established in this paper also provide useful insights for designing efficient ontology reformulation algorithms, for instance, within the context of module extraction. [ABSTRACT FROM AUTHOR]

In some cases one is provided with inconsistent information and has to reason about various consistent scenarios contained within that information. Our goal is to argue that filtered paraconsistent logics are not the right tool to handle such cases and that the problems generalise to a large class of paraconsistent logics. A wide class of paraconsistent (inconsistency-tolerant) logics is obtained by filtration: adding conditions to the classical consequence operation (for instance,is a weak Rescher–Manor consequence ofjust in casefollows classically from at least one maximally consistent subset of). We start by surveying the most promising candidates and comparing their strengths. Then we discuss the mainstream views on how non-classical logics should be chosen for an application and argue that none of these allows us to choose any of the filtered logics for action-guiding reasoning with inconsistent information, because such reasoning has to start with the selection of possible scenarios – and such a process does not correspond to any of the mathematical models offered by filtered paraconsistent logics. Finally, we criticise the recent attempt to defend explorative hypothetical reasoning by means of weak Rescher–Manor consequence operation in Meheus, Straßer, and Verdée (2014). [ABSTRACT FROM PUBLISHER]

Sylvan and Plumwood’sis therelevantDe Morgan minimal logic in the Routley-Meyer semanticswitha set of designated points. The aim of this paper is to define the logicand some of its extensions. The logicis thenon-relevantDe Morgan minimal logic in the Routley-Meyer semanticswithouta set of designated points. [ABSTRACT FROM PUBLISHER]

Abstract: Without data preparation, data mining algorithms cannot operate on data within the knowledge discovery in databases (KDD) process. In fact, the success of later KDD phases largely depends on the data preparation stage. The use of mechanisms for automatically preparing data saves a lot of time and resources within the KDD process. These resources will then be available for use at later, less automatable stages, for example, during results interpretation. We have proposed a general-purpose mechanism applicable to multiple domains in order to improve the data preparation phase in the KDD process. This mechanism processes and automatically converts input data to a suitable format for the application of different data preparation techniques based on a known syntax. It is based on the use of description logic. Taking a generic UML2 data model as a reference, this mechanism is able to check whether any XML data source whatsoever can be transformed and modelled as a subsumption or instance of the above UML2 model. Thus it automatically identifies a consistent, non-ambiguous and finite set of XLST transformations which are used to prepare the data for the application of data mining techniques, obviating the need to expend resources on the preliminary preparation and formatting stage. The proposed mechanism was applied on structurally complex data from four different domains. In order to test the validity of the proposal, we have applied data mining techniques to extract knowledge from the prepared data. The sound results of applying our proposal to several different domains confirm that it is applicable to any XML data source, as well as being correct, computationally efficient and saving time during the data preparation phase. [Copyright &y& Elsevier]

Fuzzy Description Logics (f-DLs) have been proposed as logical formalisms capable of representing and reasoning with vague/fuzzy information. They are envisioned to be helpful for many applications that need to cope with such type of information such as multimedia processing, decision making, automatic negotiation and more. Recent results have provided with many tableaux algorithms for supporting reasoning over quite expressive f-DLs. However, no (direct) tableaux algorithm for reasoning with fuzzy extensions of DLs such as $$\mathcal{SHOIQ } $$ and $$\mathcal{SROIQ } $$ exists today. $$\mathcal{SHOIQ } $$ and $$\mathcal{SROIQ } $$ are particularly interesting formalisms as they constitute the logical underpinnings of the Web ontology languages OWL DL and OWL 2 DL. In the current paper, we present an algorithm for reasoning with the fuzzy DLs f- $$\mathcal{SHOIQ } $$ and f- $$\mathcal{SROIQ } $$. In addition, we also provide a tableaux algorithm for fuzzy nominals, thus providing reasoning support for the fuzzy DL language (we call) f- $$\mathcal{SHO }_\mathtt{{f}}\mathcal{IQ }$$. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we investigate the consequence-based algorithms that are nowadays commonly used for subsumption reasoning with description logic ontologies, presenting the following novel results. First, we present a very general consequence-based reasoning algorithm that can be instantiated so as to capture the essential features of the known algorithms. Second, we use this algorithm to develop a novel framework for a quantitative and parametric analysis of the complexity of subsumption reasoning in description logic ontologies. Our approach is based on the notion of a decomposition—a graph-like structure that, roughly speaking, summarizes the models relevant during ontology reasoning. We identify width and length as decomposition parameters that determine the “level” of combinatorial reasoning. We prove that, when parameterized by a decomposition, our consequence-based algorithm runs in time that is fixed-parameter tractable in width and length. Third, we briefly discuss how length and width characterize the behavior of tableau algorithms. Fourth, we show that the width and length of existing ontologies are reasonably small, which, we believe, explains the good performance of consequence-based algorithms in practice. We thus obtain a sound foundation for a practical implementation of ontology reasoners, as well as a way to analyze the reasoners' performance. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to introduce and study model-theoretic notions of modularity in description logic and related reasoning problems. Our approach is based on a generalisation of logical equivalence that is called model-theoretic inseparability. Two TBoxes are inseparable w.r.t. a vocabulary Σ if they cannot be distinguished by the Σ-reducts of their models and thus can equivalently be replaced by one another in any application where only vocabulary items from Σ are relevant. We study in-depth the complexity of deciding inseparability for the description logics and and their extensions with inverse roles. We then discuss notions of modules of a TBox based on model-theoretic inseparability and develop algorithms for extracting minimal modules from acyclic TBoxes. Finally, we provide an experimental evaluation of our module extraction algorithm based on the large-scale medical TBox Snomed ct. [Copyright &y& Elsevier]

We present a logical system for reasoning about types of actions (processes) and about agent capabilities to execute types of actions. The syntax of the system is based on that of Propositional Dynamic Logic (PDL), though the semantics we define is different (interpreting process terms as types, i.e. sets of binary relations). The standard PDL syntax is extended with capabilities statements, as in the KARO framework, atomic process types specified as precondition-effect pairs, written as φ ⇒ ψ, as well as backwards possibility operators. The resulting system is shown (by filtration) to have a decidable satisfiability problem and a sound and complete Gentzen-style proof system is presented. [ABSTRACT FROM AUTHOR]

In this article, I present a procedure that generates proofs for finally derivable adaptive logic consequences. A proof procedure for the inconsistency adaptive logic CLuNr is already presented in [7]. In this article a procedure for CLuNm is presented and the results for both logics are generalized to all adaptive logics, on the presupposition that there exists a proof procedure for the lower limit logic. The generated proofs are so called goal-directed proofs, i.e. proofs that (i) start with the formula (the goal) of which one wants to know whether it is a consequence of a certain premise set and (ii) only consist of lines that may potentially be useful for proving or disproving the goal. The goal-directed proofs form good explications of actual problem-solving reasoning processes. [ABSTRACT FROM AUTHOR]