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Recent advances in AI -- including generative approaches -- have resulted in technology that can support humans in scientific discovery and decision support but may also disrupt democracies and target individuals. The responsible use of AI increasingly shows the need for human-AI teaming, necessitating effective interaction between humans and machines. A crucial yet often overlooked aspect of these interactions is the different ways in which humans and machines generalise. In cognitive science, human generalisation commonly involves abstraction and concept learning. In contrast, AI generalisation encompasses out-of-domain generalisation in machine learning, rule-based reasoning in symbolic AI, and abstraction in neuro-symbolic AI. In this perspective paper, we combine insights from AI and cognitive science to identify key commonalities and differences across three dimensions: notions of generalisation, methods for generalisation, and evaluation of generalisation. We map the different conceptualisations of generalisation in AI and cognitive science along these three dimensions and consider their role in human-AI teaming. This results in interdisciplinary challenges across AI and cognitive science that must be tackled to provide a foundation for effective and cognitively supported alignment in human-AI teaming scenarios.

Large Language Models bear the promise of significant acceleration of key Knowledge Graph and Ontology Engineering tasks, including ontology modeling, extension, modification, population, alignment, as well as entity disambiguation. We lay out LLM-based Knowledge Graph and Ontology Engineering as a new and coming area of research, and argue that modular approaches to ontologies will be of central importance.

Knowledge graphs (KGs) are increasingly utilized for data integration, representation, and visualization. While KG population is critical, it is often costly, especially when data must be extracted from unstructured text in natural language, which presents challenges, such as ambiguity and complex interpretations. Large Language Models (LLMs) offer promising capabilities for such tasks, excelling in natural language understanding and content generation. However, their tendency to ``hallucinate'' can produce inaccurate outputs. Despite these limitations, LLMs offer rapid and scalable processing of natural language data, and with prompt engineering and fine-tuning, they can approximate human-level performance in extracting and structuring data for KGs. This study investigates LLM effectiveness for the KG population, focusing on the Enslaved.org Hub Ontology. In this paper, we report that compared to the ground truth, LLM's can extract ~90% of triples, when provided a modular ontology as guidance in the prompts.

Geospatial Knowledge Graphs (GeoKGs) have become integral to the growing field of Geospatial Artificial Intelligence. Initiatives like the U.S. National Science Foundation's Open Knowledge Network program aim to create an ecosystem of nation-scale, cross-disciplinary GeoKGs that provide AI-ready geospatial data aligned with FAIR principles. However, building this infrastructure presents key challenges, including 1) managing large volumes of data, 2) the computational complexity of discovering topological relations via SPARQL, and 3) conflating multi-scale raster and vector data. Discrete Global Grid Systems (DGGS) help tackle these issues by offering efficient data integration and representation strategies. The KnowWhereGraph utilizes Google's S2 Geometry -- a DGGS framework -- to enable efficient multi-source data processing, qualitative spatial querying, and cross-graph integration. This paper outlines the implementation of S2 within KnowWhereGraph, emphasizing its role in topologically enriching and semantically compressing data. Ultimately, this work demonstrates the potential of DGGS frameworks, particularly S2, for building scalable GeoKGs.

KnowWhereGraph is one of the largest fully publicly available geospatial knowledge graphs. It includes data from 30 layers on natural hazards (e.g., hurricanes, wildfires), climate variables (e.g., air temperature, precipitation), soil properties, crop and land-cover types, demographics, and human health, various place and region identifiers, among other themes. These have been leveraged through the graph by a variety of applications to address challenges in food security and agricultural supply chains; sustainability related to soil conservation practices and farm labor; and delivery of emergency humanitarian aid following a disaster. In this paper, we introduce the ontology that acts as the schema for KnowWhereGraph. This broad overview provides insight into the requirements and design specifications for the graph and its schema, including the development methodology (modular ontology modeling) and the resources utilized to implement, materialize, and deploy KnowWhereGraph with its end-user interfaces and public query SPARQL endpoint.

ConceptLens is an innovative tool designed to illuminate the intricate workings of deep neural networks (DNNs) by visualizing hidden neuron activations. By integrating deep learning with symbolic methods, ConceptLens offers users a unique way to understand what triggers neuron activations and how they respond to various stimuli. The tool uses error-margin analysis to provide insights into the confidence levels of neuron activations, thereby enhancing the interpretability of DNNs. This paper presents an overview of ConceptLens, its implementation, and its application in real-time visualization of neuron activations and error margins through bar charts.

Integrating structured knowledge from tabular formats poses significant challenges within natural language processing (NLP), mainly when dealing with complex, semi-structured tables like those found in the FeTaQA dataset. These tables require advanced methods to interpret and generate meaningful responses accurately. Traditional approaches, such as SQL and SPARQL, often fail to fully capture the semantics of such data, especially in the presence of irregular table structures like web tables. This paper addresses these challenges by proposing a novel approach that extracts triples straightforward from tabular data and integrates it with a retrieval-augmented generation (RAG) model to enhance the accuracy, coherence, and contextual richness of responses generated by a fine-tuned GPT-3.5-turbo-0125 model. Our approach significantly outperforms existing baselines on the FeTaQA dataset, particularly excelling in Sacre-BLEU and ROUGE metrics. It effectively generates contextually accurate and detailed long-form answers from tables, showcasing its strength in complex data interpretation., Comment: We are withdrawing this paper to address foundational aspects that are critical for ensuring its accuracy and integrity before any potential resubmission

Depression is a common mental health issue that requires prompt diagnosis and treatment. Despite the promise of social media data for depression detection, the opacity of employed deep learning models hinders interpretability and raises bias concerns. We address this challenge by introducing ProtoDep, a novel, explainable framework for Twitter-based depression detection. ProtoDep leverages prototype learning and the generative power of Large Language Models to provide transparent explanations at three levels: (i) symptom-level explanations for each tweet and user, (ii) case-based explanations comparing the user to similar individuals, and (iii) transparent decision-making through classification weights. Evaluated on five benchmark datasets, ProtoDep achieves near state-of-the-art performance while learning meaningful prototypes. This multi-faceted approach offers significant potential to enhance the reliability and transparency of depression detection on social media, ultimately aiding mental health professionals in delivering more informed care.

Understanding how high-level concepts are represented within artificial neural networks is a fundamental challenge in the field of artificial intelligence. While existing literature in explainable AI emphasizes the importance of labeling neurons with concepts to understand their functioning, they mostly focus on identifying what stimulus activates a neuron in most cases, this corresponds to the notion of recall in information retrieval. We argue that this is only the first-part of a two-part job, it is imperative to also investigate neuron responses to other stimuli, i.e., their precision. We call this the neuron labels error margin.

A major challenge in Explainable AI is in correctly interpreting activations of hidden neurons: accurate interpretations would help answer the question of what a deep learning system internally detects as relevant in the input, demystifying the otherwise black-box nature of deep learning systems. The state of the art indicates that hidden node activations can, in some cases, be interpretable in a way that makes sense to humans, but systematic automated methods that would be able to hypothesize and verify interpretations of hidden neuron activations are underexplored. This is particularly the case for approaches that can both draw explanations from substantial background knowledge, and that are based on inherently explainable (symbolic) methods. In this paper, we introduce a novel model-agnostic post-hoc Explainable AI method demonstrating that it provides meaningful interpretations. Our approach is based on using a Wikipedia-derived concept hierarchy with approximately 2 million classes as background knowledge, and utilizes OWL-reasoning-based Concept Induction for explanation generation. Additionally, we explore and compare the capabilities of off-the-shelf pre-trained multimodal-based explainable methods. Our results indicate that our approach can automatically attach meaningful class expressions as explanations to individual neurons in the dense layer of a Convolutional Neural Network. Evaluation through statistical analysis and degree of concept activation in the hidden layer show that our method provides a competitive edge in both quantitative and qualitative aspects compared to prior work.

Explainable Artificial Intelligence (XAI) poses a significant challenge in providing transparent and understandable insights into complex AI models. Traditional post-hoc algorithms, while useful, often struggle to deliver interpretable explanations. Concept-based models offer a promising avenue by incorporating explicit representations of concepts to enhance interpretability. However, existing research on automatic concept discovery methods is often limited by lower-level concepts, costly human annotation requirements, and a restricted domain of background knowledge. In this study, we explore the potential of a Large Language Model (LLM), specifically GPT-4, by leveraging its domain knowledge and common-sense capability to generate high-level concepts that are meaningful as explanations for humans, for a specific setting of image classification. We use minimal textual object information available in the data via prompting to facilitate this process. To evaluate the output, we compare the concepts generated by the LLM with two other methods: concepts generated by humans and the ECII heuristic concept induction system. Since there is no established metric to determine the human understandability of concepts, we conducted a human study to assess the effectiveness of the LLM-generated concepts. Our findings indicate that while human-generated explanations remain superior, concepts derived from GPT-4 are more comprehensible to humans compared to those generated by ECII.

Ontology alignment, a critical process in the Semantic Web for detecting relationships between different ontologies, has traditionally focused on identifying so-called "simple" 1-to-1 relationships through class labels and properties comparison. The more practically useful exploration of more complex alignments remains a hard problem to automate, and as such is largely underexplored, i.e. in application practice it is usually done manually by ontology and domain experts. Recently, the surge in Natural Language Processing (NLP) capabilities, driven by advancements in Large Language Models (LLMs), presents new opportunities for enhancing ontology engineering practices, including ontology alignment tasks. This paper investigates the application of LLM technologies to tackle the complex ontology alignment challenge. Leveraging a prompt-based approach and integrating rich ontology content so-called modules our work constitutes a significant advance towards automating the complex alignment task.

The previously introduced Modular Ontology Modeling methodology (MOMo) attempts to mimic the human analogical process by using modular patterns to assemble more complex concepts. To support this, MOMo organizes organizes ontology design patterns into design libraries, which are programmatically queryable, to support accelerated ontology development, for both human and automated processes. However, a major bottleneck to large-scale deployment of MOMo is the (to-date) limited availability of ready-to-use ontology design patterns. At the same time, Large Language Models have quickly become a source of common knowledge and, in some cases, replacing search engines for questions. In this paper, we thus present a collection of 104 ontology design patterns representing often occurring nouns, curated from the common-sense knowledge available in LLMs, organized into a fully-annotated modular ontology design library ready for use with MOMo.

We subject GPT-4 to a number of rigorous psychometric tests and analyze the results. We find that, compared to the average human, GPT-4 tends to show more honesty and humility, and less machiavellianism and narcissism. It sometimes exhibits ambivalent sexism, leans slightly toward masculinity, is moderately anxious but mostly not depressive (but not always). It shows human-average numerical literacy and has cognitive reflection abilities that are above human average for verbal tasks., Comment: 16 pages, 8 tables, 1 code repository

This study evaluates the applicability and efficiency of ChatGPT for ontology alignment using a naive approach. ChatGPT's output is compared to the results of the Ontology Alignment Evaluation Initiative 2022 campaign using conference track ontologies. This comparison is intended to provide insights into the capabilities of a conversational large language model when used in a naive way for ontology matching, and to investigate the potential advantages and disadvantages of this approach.

A major challenge in Explainable AI is in correctly interpreting activations of hidden neurons: accurate interpretations would provide insights into the question of what a deep learning system has internally detected as relevant on the input, demystifying the otherwise black-box character of deep learning systems. The state of the art indicates that hidden node activations can, in some cases, be interpretable in a way that makes sense to humans, but systematic automated methods that would be able to hypothesize and verify interpretations of hidden neuron activations are underexplored. In this paper, we provide such a method and demonstrate that it provides meaningful interpretations. Our approach is based on using large-scale background knowledge approximately 2 million classes curated from the Wikipedia concept hierarchy together with a symbolic reasoning approach called Concept Induction based on description logics, originally developed for applications in the Semantic Web field. Our results show that we can automatically attach meaningful labels from the background knowledge to individual neurons in the dense layer of a Convolutional Neural Network through a hypothesis and verification process.

The Metadata Object Description Schema (MODS) was developed to describe bibliographic concepts and metadata and is maintained by the Library of Congress. Its authoritative version is given as an XML schema based on an XML mindset which means that it has significant limitations for use in a knowledge graphs context. We have therefore developed the Modular MODS Ontology (MMODS-O) which incorporates all elements and attributes of the MODS XML schema. In designing the ontology, we adopt the recent Modular Ontology Design Methodology (MOMo) with the intention to strike a balance between modularity and quality ontology design on the one hand, and conservative backward compatibility with MODS on the other.

We present an ontology design pattern for modeling Names as part of Roles, to capture scenarios where an Agent performs different Roles using different Names associated with the different Roles. Examples of an Agent performing a Role using different Names are rather ubiquitous, e.g., authors who write under different pseudonyms, or different legal names for citizens of more than one country. The proposed pattern is a modified merger of a standard Agent Role and a standard Name pattern stub., Comment: 6 pages, 5 Figures

One of the current key challenges in Explainable AI is in correctly interpreting activations of hidden neurons. It seems evident that accurate interpretations thereof would provide insights into the question what a deep learning system has internally \emph{detected} as relevant on the input, thus lifting some of the black box character of deep learning systems. The state of the art on this front indicates that hidden node activations appear to be interpretable in a way that makes sense to humans, at least in some cases. Yet, systematic automated methods that would be able to first hypothesize an interpretation of hidden neuron activations, and then verify it, are mostly missing. In this paper, we provide such a method and demonstrate that it provides meaningful interpretations. It is based on using large-scale background knowledge -- a class hierarchy of approx. 2 million classes curated from the Wikipedia Concept Hierarchy -- together with a symbolic reasoning approach called \emph{concept induction} based on description logics that was originally developed for applications in the Semantic Web field. Our results show that we can automatically attach meaningful labels from the background knowledge to individual neurons in the dense layer of a Convolutional Neural Network through a hypothesis and verification process., Comment: Submitted to IJCAI-23

Concept induction, which is based on formal logical reasoning over description logics, has been used in ontology engineering in order to create ontology (TBox) axioms from the base data (ABox) graph. In this paper, we show that it can also be used to explain data differentials, for example in the context of Explainable AI (XAI), and we show that it can in fact be done in a way that is meaningful to a human observer. Our approach utilizes a large class hierarchy, curated from the Wikipedia category hierarchy, as background knowledge.

Wikibase -- which is the software underlying Wikidata -- is a powerful platform for knowledge graph creation and management. However, it has been developed with a crowd-sourced knowledge graph creation scenario in mind, which in particular means that it has not been designed for use case scenarios in which a tightly controlled high-quality schema, in the form of an ontology, is to be imposed, and indeed, independently developed ontologies do not necessarily map seamlessly to the Wikibase approach. In this paper, we provide the key ingredients needed in order to combine traditional ontology modeling with use of the Wikibase platform, namely a set of \emph{axiom} patterns that bridge the paradigm gap, together with usage instructions and a worked example for historical data.

The importance of building neural networks that can learn to reason has been well recognized in the neuro-symbolic community. In this paper, we apply neural pointer networks for conducting reasoning over symbolic knowledge bases. In doing so, we explore the benefits and limitations of encoder-decoder architectures in general and pointer networks in particular for developing accurate, generalizable and robust neuro-symbolic reasoners. Based on our experimental results, pointer networks performs remarkably well across multiple reasoning tasks while outperforming the previously reported state of the art by a significant margin. We observe that the Pointer Networks preserve their performance even when challenged with knowledge graphs of the domain/vocabulary it has never encountered before. To the best of our knowledge, this is the first study on neuro-symbolic reasoning using Pointer Networks. We hope our impressive results on these reasoning problems will encourage broader exploration of pointer networks' capabilities for reasoning over more complex logics and for other neuro-symbolic problems., Comment: 14 pages, 1 figures

Neuro-Symbolic Artificial Intelligence -- the combination of symbolic methods with methods that are based on artificial neural networks -- has a long-standing history. In this article, we provide a structured overview of current trends, by means of categorizing recent publications from key conferences. The article is meant to serve as a convenient starting point for research on the general topic., Comment: under review

Powered by new advances in sensor development and artificial intelligence, the decreasing cost of computation, and the pervasiveness of handheld computation devices, biometric user authentication (and identification) is rapidly becoming ubiquitous. Modern approaches to biometric authentication, based on sophisticated machine learning techniques, cannot avoid storing either trained-classifier details or explicit user biometric data, thus exposing users' credentials to falsification. In this paper, we introduce a secure way to handle user-specific information involved with the use of vector-space classifiers or artificial neural networks for biometric authentication. Our proposed architecture, called a Neural Fuzzy Extractor (NFE), allows the coupling of pre-existing classifiers with fuzzy extractors, through a artificial-neural-network-based buffer called an expander, with minimal or no performance degradation. The NFE thus offers all the performance advantages of modern deep-learning-based classifiers, and all the security of standard fuzzy extractors. We demonstrate the NFE retrofit to a classic artificial neural network for a simple scenario of fingerprint-based user authentication., Comment: 8 pages, 5 figures

We present a new approach to integrating deep learning with knowledge-based systems that we believe shows promise. Our approach seeks to emulate reasoning structure, which can be inspected part-way through, rather than simply learning reasoner answers, which is typical in many of the black-box systems currently in use. We demonstrate that this idea is feasible by training a long short-term memory (LSTM) artificial neural network to learn EL+ reasoning patterns with two different data sets. We also show that this trained system is resistant to noise by corrupting a percentage of the test data and comparing the reasoner's and LSTM's predictions on corrupt data with correct answers.

Pattern-based, modular ontologies have several beneficial properties that lend themselves to FAIR data practices, especially as it pertains to Interoperability and Reusability. However, developing such ontologies has a high upfront cost, e.g. reusing a pattern is predicated upon being aware of its existence in the first place. Thus, to help overcome these barriers, we have developed MODL: a modular ontology design library. MODL is a curated collection of well-documented ontology design patterns, drawn from a wide variety of interdisciplinary use-cases. In this paper we present MODL as a resource, discuss its use, and provide some examples of its contents.

Concept Induction refers to the problem of creating complex Description Logic class descriptions (i.e., TBox axioms) from instance examples (i.e., ABox data). In this paper we look particularly at the case where both a set of positive and a set of negative instances are given, and complex class expressions are sought under which the positive but not the negative examples fall. Concept induction has found applications in ontology engineering, but existing algorithms have fundamental performance issues in some scenarios, mainly because a high number of invokations of an external Description Logic reasoner is usually required. In this paper we present a new algorithm for this problem which drastically reduces the number of reasoner invokations needed. While this comes at the expense of a more limited traversal of the search space, we show that our approach improves execution times by up to several orders of magnitude, while output correctness, measured in the amount of correct coverage of the input instances, remains reasonably high in many cases. Our approach thus should provide a strong alternative to existing systems, in particular in settings where other systems are prohibitively slow., Comment: Accepted at AAAI-19

Semantic Web knowledge representation standards, and in particular RDF and OWL, often come endowed with a formal semantics which is considered to be of fundamental importance for the field. Reasoning, i.e., the drawing of logical inferences from knowledge expressed in such standards, is traditionally based on logical deductive methods and algorithms which can be proven to be sound and complete and terminating, i.e. correct in a very strong sense. For various reasons, though, in particular, the scalability issues arising from the ever-increasing amounts of Semantic Web data available and the inability of deductive algorithms to deal with noise in the data, it has been argued that alternative means of reasoning should be investigated which bear high promise for high scalability and better robustness. From this perspective, deductive algorithms can be considered the gold standard regarding correctness against which alternative methods need to be tested. In this paper, we show that it is possible to train a Deep Learning system on RDF knowledge graphs, such that it is able to perform reasoning over new RDF knowledge graphs, with high precision and recall compared to the deductive gold standard.

It has been argued that it is much easier to convey logical statements using rules rather than OWL (or description logic (DL)) axioms. Based on recent theoretical developments on transformations between rules and DLs, we have developed ROWLTab, a Protege plugin that allows users to enter OWL axioms by way of rules; the plugin then automatically converts these rules into OWL 2 DL axioms if possible, and prompts the user in case such a conversion is not possible without weakening the semantics of the rule. In this paper, we present ROWLTab, together with a user evaluation of its effectiveness compared to entering axioms using the standard Protege interface. Our evaluation shows that modeling with ROWLTab is much quicker than the standard interface, while at the same time, also less prone to errors for hard modeling tasks., Comment: Accepted at ESWC 2017

In our experience, some ontology users find it much easier to convey logical statements using rules rather than OWL (or description logic) axioms. Based on recent theoretical developments on transformations between rules and description logics, we develop ROWL, a Protege plugin that allows users to enter OWL axioms by way of rules; the plugin then automatically converts these rules into OWL DL axioms if possible, and prompts the user in case such a conversion is not possible without weakening the semantics of the rule., Comment: Accepted at ISWC 2016

Once the conceptual overview, in terms of a somewhat informal class diagram, has been designed in the course of engineering an ontology, the process of adding many of the appropriate logical axioms is mostly a routine task. We provide a Protege plugin which supports this task, together with a visual user interface, based on established methods for ontology design pattern modeling., Comment: Poster in ISWC 2016

We provide a detailed example for modular ontology modeling based on ontology design patterns.

Conjunctive query answering over expressive Horn Description Logic ontologies is a relevant and challenging problem which, in some cases, can be addressed by application of the chase algorithm. In this paper, we define a novel acyclicity notion which provides a sufficient condition for termination of the restricted chase over Horn-SRIQ TBoxes. We show that this notion generalizes most of the existing acyclicity conditions (both theoretically and empirically). Furthermore, this new acyclicity notion gives rise to a very efficient reasoning procedure. We provide evidence for this by providing a materialization based reasoner for acyclic ontologies which outperforms other state-of-the-art systems.

Many current methods to interpret convolutional neural networks (CNNs) use visualization techniques and words to highlight concepts of the input seemingly relevant to a CNN's decision. The methods hypothesize that the recognition of these concepts are instrumental in the decision a CNN reaches, but the nature of this relationship has not been well explored. To address this gap, this paper examines the quality of a concept's recognition by a CNN and the degree to which the recognitions are associated with CNN decisions. The study considers a CNN trained for scene recognition over the ADE20k dataset. It uses a novel approach to find and score the strength of minimally distributed representations of input concepts (defined by objects in scene images) across late stage feature maps. Subsequent analysis finds evidence that concept recognition impacts decision making. Strong recognition of concepts frequently-occurring in few scenes are indicative of correct decisions, but recognizing concepts common to many scenes may mislead the network., Comment: 10 pages (including references), 9 figures, paper accepted by NIPS IEVDL 2017

The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour, among the most prominent tools in the modelling of behaviour are computational-logic systems, connectionist models of cognition, and models of uncertainty. Recent studies in cognitive science, artificial intelligence, and psychology have produced a number of cognitive models of reasoning, learning, and language that are underpinned by computation. In addition, efforts in computer science research have led to the development of cognitive computational systems integrating machine learning and automated reasoning. Such systems have shown promise in a range of applications, including computational biology, fault diagnosis, training and assessment in simulators, and software verification. This joint survey reviews the personal ideas and views of several researchers on neural-symbolic learning and reasoning. The article is organised in three parts: Firstly, we frame the scope and goals of neural-symbolic computation and have a look at the theoretical foundations. We then proceed to describe the realisations of neural-symbolic computation, systems, and applications. Finally we present the challenges facing the area and avenues for further research., Comment: 58 pages, work in progress

Trees -- i.e., the type of data structure known under this name -- are central to many aspects of knowledge organization. We investigate some central design choices concerning the ontological modeling of such trees. In particular, we consider the limits of what is expressible in the Web Ontology Language, and provide a reusable ontology design pattern for trees., Comment: Proceedings of the 8th Workshop on Ontology Design and Patterns, WOP 2017, co-located with the 16th International Semantic Web Conference, ISWC2017, Vienna, Austria, October 2017. To appear

The ever increasing prevalence of publicly available structured data on the World Wide Web enables new applications in a variety of domains. In this paper, we provide a conceptual approach that leverages such data in order to explain the input-output behavior of trained artificial neural networks. We apply existing Semantic Web technologies in order to provide an experimental proof of concept.

There is a common need in astroparticle experiments such as direct dark matter detection, 0{\nu}\b{eta}\b{eta} (double beta decay without emission of neutrinos) and Coherent Neutrino Nucleus Scattering experiments for light detectors with a very low energy threshold. By employing the Neganov-Luke Effect, the thermal signal of particle interactions in a semiconductor absorber operated at cryogenic temperatures, can be amplified by drifting the photogenerated electrons and holes in an electric field. This technology is not used in current experiments, in particular because of a reduction of the signal amplitude with time which is due to trapping of the charges within the absorber. We present here the first results of a novel type of Neganov-Luke Effect detector with an electric field configuration designed to improve the charge collection within the semiconductor., Comment: 6 pages, 5 figures, submitted to Journal of Low Temperature Physics

We propose a novel, type-elimination-based method for reasoning in the description logic SHIQbs including DL-safe rules. To this end, we first establish a knowledge compilation method converting the terminological part of an ALCIb knowledge base into an ordered binary decision diagram (OBDD) which represents a canonical model. This OBDD can in turn be transformed into disjunctive Datalog and merged with the assertional part of the knowledge base in order to perform combined reasoning. In order to leverage our technique for full SHIQbs, we provide a stepwise reduction from SHIQbs to ALCIb that preserves satisfiability and entailment of positive and negative ground facts. The proposed technique is shown to be worst case optimal w.r.t. combined and data complexity and easily admits extensions with ground conjunctive queries., Comment: 38 pages, 3 figures, camera ready version of paper accepted for publication in Logical Methods in Computer Science

Research on integrated neural-symbolic systems has made significant progress in the recent past. In particular the understanding of ways to deal with symbolic knowledge within connectionist systems (also called artificial neural networks) has reached a critical mass which enables the community to strive for applicable implementations and use cases. Recent work has covered a great variety of logics used in artificial intelligence and provides a multitude of techniques for dealing with them within the context of artificial neural networks. We present a comprehensive survey of the field of neural-symbolic integration, including a new classification of system according to their architectures and abilities., Comment: 28 pages

Currently, the variety of expressive extensions and different semantics created for logic programs with negation is diverse and heterogeneous, and there is a lack of comprehensive comparative studies which map out the multitude of perspectives in a uniform way. Most recently, however, new methodologies have been proposed which allow one to derive uniform characterizations of different declarative semantics for logic programs with negation. In this paper, we study the relationship between two of these approaches, namely the level mapping characterizations due to [Hitzler and Wendt 2005], and the selector generated models due to [Schwarz 2004]. We will show that the latter can be captured by means of the former, thereby supporting the claim that level mappings provide a very flexible framework which is applicable to very diversely defined semantics., Comment: 17 pages

In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded semantics can formally be understood as a stratified version of the Fitting (or Kripke-Kleene) semantics. The constructions leading to this result, however, show a certain asymmetry which is not readily understood. We will study this situation here with the result that we will obtain a coherent picture of relations between different semantics for normal logic programs., Comment: 20 pages

Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched with notions such as approximation by computation or representability. The latter are commonly studied in denotational semantics and domain theory and captured most prominently by the notion of algebraicity, e.g. of lattices. In this paper, we explore the notion of algebraicity in formal concept analysis from a category-theoretical perspective. To this end, we build on the the notion of approximable concept with a suitable category and show that the latter is equivalent to the category of algebraic lattices. At the same time, the paper provides a relatively comprehensive account of the representation theory of algebraic lattices in the framework of Stone duality, relating well-known structures such as Scott information systems with further formalisms from logic, topology, domains and lattice theory., Comment: 36 pages

W.C. Rounds and G.-Q. Zhang (2001) have proposed to study a form of disjunctive logic programming generalized to algebraic domains. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with default negation, giving rise to a new nonmonotonic reasoning framework on hierarchical knowledge which encompasses answer set programming with extended disjunctive logic programs. We also show that the hierarchically structured knowledge on which programming in this paradigm can be done, arises very naturally from formal concept analysis. Together, we obtain a default reasoning paradigm for conceptual knowledge which is in accordance with mainstream developments in nonmonotonic reasoning., Comment: Short version appeared in Proceedings of the 27th German conference on Artificial Intelligence, KI'2004, Ulm, Germany, September 2004, Lecture Notes in Artificial Intelligence

Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking machinery with symbolic knowledge representation and reasoning paradigms like logic programming in such a way that the strengths of either paradigm will be retained. Current state-of-the-art research, however, fails by far to achieve this ultimate goal. As one of the main obstacles to be overcome we perceive the question how symbolic knowledge can be encoded by means of connectionist systems: Satisfactory answers to this will naturally lead the way to knowledge extraction algorithms and to integrated neural-symbolic systems., Comment: In Proceedings of INFORMATION'2004, Tokyo, Japan, to appear. 12 pages

The fixpoint completion fix(P) of a normal logic program P is a program transformation such that the stable models of P are exactly the models of the Clark completion of fix(P). This is well-known and was studied by Dung and Kanchanasut (1989). The correspondence, however, goes much further: The Gelfond-Lifschitz operator of P coincides with the immediate consequence operator of fix(P), as shown by Wendt (2002), and even carries over to standard operators used for characterizing the well-founded and the Kripke-Kleene semantics. We will apply this knowledge to the study of the stable semantics, and this will allow us to almost effortlessly derive new results concerning fixed-point and metric-based semantics, and neural-symbolic integration., Comment: 15 pages. Presented at the 18th Workshop on Logic Programming, Potsdam, Germany, March 2004

We relate two formerly independent areas: Formal concept analysis and logic of domains. We will establish a correspondene between contextual attribute logic on formal contexts resp. concept lattices and a clausal logic on coherent algebraic cpos. We show how to identify the notion of formal concept in the domain theoretic setting. In particular, we show that a special instance of the resolution rule from the domain logic coincides with the concept closure operator from formal concept analysis. The results shed light on the use of contexts and domains for knowledge representation and reasoning purposes., Comment: 14 pages. We have rewritten the old version according to the suggestions of some referees. The results are the same. The presentation is completely different

Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more successful and acknowledged than others. The rationales behind those various semantics have been manifold, depending on one's point of view, which may be that of a programmer or inspired by commonsense reasoning, and consequently the constructions which lead to these semantics are technically very diverse, and the exact relationships between them have not yet been fully understood. In this paper, we present a conceptually new method, based on level mappings, which allows to provide uniform characterizations of different semantics for logic programs. We will display our approach by giving new and uniform characterizations of some of the major semantics, more particular of the least model semantics for definite programs, of the Fitting semantics, and of the well-founded semantics. A novel characterization of the weakly perfect model semantics will also be provided., Comment: 29 pages. To appear in Theory and Practice of Logic Programming