An FLP-Style Answer-Set Semantics for Abstract-Constraint Programs with Disjunctions

We introduce an answer-set semantics for abstract-constraint programs with disjunction in rule heads in the style of Faber, Leone, and Pfeifer (FLP). To this end, we extend the definition of an answer set for logic programs with aggregates in rule bodies using the usual FLP-reduct. Additionally, we also provide a characterisation of our semantics in terms of unfounded sets, likewise generalising the standard concept of an unfounded set. Our work is motivated by the desire to have simple and rule-based definitions of the semantics of an answer-set programming (ASP) language that is close to those implemented by the most prominent ASP solvers. The new definitions are intended as a theoretical device to allow for development methods and methodologies for ASP, e.g., debugging or testing techniques, that are general enough to work for different types of solvers. We use abstract constraints as an abstraction of literals whose truth values depend on subsets of an interpretation. This includes weight constraints, aggregates, and external atoms, which are frequently used in real-world answer-set programs. We compare the new semantics to previous semantics for abstract-constraint programs and show that they are equivalent to recent extensions of the FLP semantics to propositional and first-order theories when abstract-constraint programs are viewed as theories

Singular and Plural Functions for Functional Logic Programming

Functional logic programming (FLP) languages use non-terminating and non-confluent constructor systems (CS's) as programs in order to define non-strict non-determi-nistic functions. Two semantic alternatives have been usually considered for parameter passing with this kind of functions: call-time choice and run-time choice. While the former is the standard choice of modern FLP languages, the latter lacks some properties---mainly compositionality---that have prevented its use in practical FLP systems. Traditionally it has been considered that call-time choice induces a singular denotational semantics, while run-time choice induces a plural semantics. We have discovered that this latter identification is wrong when pattern matching is involved, and thus we propose two novel compositional plural semantics for CS's that are different from run-time choice. We study the basic properties of our plural semantics---compositionality, polarity, monotonicity for substitutions, and a restricted form of the bubbling property for constructor systems---and the relation between them and to previous proposals, concluding that these semantics form a hierarchy in the sense of set inclusion of the set of computed values. We have also identified a class of programs characterized by a syntactic criterion for which the proposed plural semantics behave the same, and a program transformation that can be used to simulate one of them by term rewriting. At the practical level, we study how to use the expressive capabilities of these semantics for improving the declarative flavour of programs. We also propose a language which combines call-time choice and our plural semantics, that we have implemented in Maude. The resulting interpreter is employed to test several significant examples showing the capabilities of the combined semantics. To appear in Theory and Practice of Logic Programming (TPLP)Comment: 53 pages, 5 figure

Constraint Functional Logic Programming over Finite Domains.

Abstract In this paper, we present our proposal to Constraint Functional Logic Programming over Finite Domains (CFLP (FD) ) with a lazy functional logic programming language which seamlessly embodies finite domain (FD) constraints. This proposal increases the expressiveness and power of constraint logic programming over finite domains (CLP (FD) ) by combining functional and relational notation, curried expressions, higher-order functions, patterns, partial applications, non-determinism, lazy evaluation, logical variables, types, domain variables, constraint composition, and finite domain constraints. We describe the syntax of the language, its type discipline, and its declarative and operational semantics. We also describe TOY(FD), an implementation for CFLP (FD) , and a comparison of our approach with respect to CLP (FD) from a programming point of view, showing the new features we introduce. And, finally, we show a performance analysis which demonstrates that our implementation is competitive with respect to existing CLP (FD) systems and that clearly outperforms the closer approach to CFLP (FD)

Multi-Context Reasoning in Continuous Data-Flow Environments

The field of artificial intelligence, research on knowledge representation and reasoning has originated a large variety of formats, languages, and formalisms. Over the decades many different tools emerged to use these underlying concepts. Each one has been designed with some specific application in mind and are even used nowadays, where the internet is seen as a service to be sufficient for the age of Industry 4.0 and the Internet of Things. In that vision of a connected world, with these many different formalisms and systems, a formal way to uniformly exchange information, such as knowledge and belief is imperative. That alone is not enough, because even more systems get integrated into the online world and nowadays we are confronted with a huge amount of continuously flowing data. Therefore a solution is needed to both, allowing the integration of information and dynamic reaction to the data which is provided in such continuous data-flow environments. This work aims to present a unique and novel pair of formalisms to tackle these two important needs by proposing an abstract and general solution. We introduce and discuss reactive Multi-Context Systems (rMCS), which allow one to utilise different knowledge representation formalisms, so-called contexts which are represented as an abstract logic framework, and exchange their beliefs through bridge rules with other contexts. These multiple contexts need to mutually agree on a common set of beliefs, an equilibrium of belief sets. While different Multi-Context Systems already exist, they are only solving this agreement problem once and are neither considering external data streams, nor are they reasoning continuously over time. rMCS will do this by adding means of reacting to input streams and allowing the bridge rules to reason with this new information. In addition we propose two different kind of bridge rules, declarative ones to find a mutual agreement and operational ones for adapting the current knowledge for future computations. The second framework is more abstract and allows computations to happen in an asynchronous way. These asynchronous Multi-Context Systems are aimed at modelling and describing communication between contexts, with different levels of self-management and centralised management of communication and computation. In this thesis rMCS will be analysed with respect to usability, consistency management, and computational complexity, while we will show how asynchronous Multi-Context Systems can be used to capture the asynchronous ideas and how to model an rMCS with it. Finally we will show how rMCSs are positioned in the current world of stream reasoning and that it can capture currently used technologies and therefore allows one to seamlessly connect different systems of these kinds with each other. Further on this also shows that rMCSs are expressive enough to simulate the mechanics used by these systems to compute the corresponding results on its own as an alternative to already existing ones. For asynchronous Multi-Context Systems, we will discuss how to use them and that they are a very versatile tool to describe communication and asynchronous computation

Kiel Declarative Programming Days 2013

This report contains the papers presented at the Kiel Declarative Programming Days 2013, held in Kiel (Germany) during September 11-13, 2013. The Kiel Declarative Programming Days 2013 unified the following events: * 20th International Conference on Applications of Declarative Programming and Knowledge Management (INAP 2013) * 22nd International Workshop on Functional and (Constraint) Logic Programming (WFLP 2013) * 27th Workshop on Logic Programming (WLP 2013) All these events are centered around declarative programming, an advanced paradigm for the modeling and solving of complex problems. These specification and implementation methods attracted increasing attention over the last decades, e.g., in the domains of databases and natural language processing, for modeling and processing combinatorial problems, and for high-level programming of complex, in particular, knowledge-based systems

Explainable methods for knowledge graph refinement and exploration via symbolic reasoning

Knowledge Graphs (KGs) have applications in many domains such as Finance, Manufacturing, and Healthcare. While recent efforts have created large KGs, their content is far from complete and sometimes includes invalid statements. Therefore, it is crucial to refine the constructed KGs to enhance their coverage and accuracy via KG completion and KG validation. It is also vital to provide human-comprehensible explanations for such refinements, so that humans have trust in the KG quality. Enabling KG exploration, by search and browsing, is also essential for users to understand the KG value and limitations towards down-stream applications. However, the large size of KGs makes KG exploration very challenging. While the type taxonomy of KGs is a useful asset along these lines, it remains insufficient for deep exploration. In this dissertation we tackle the aforementioned challenges of KG refinement and KG exploration by combining logical reasoning over the KG with other techniques such as KG embedding models and text mining. Through such combination, we introduce methods that provide human-understandable output. Concretely, we introduce methods to tackle KG incompleteness by learning exception-aware rules over the existing KG. Learned rules are then used in inferring missing links in the KG accurately. Furthermore, we propose a framework for constructing human-comprehensible explanations for candidate facts from both KG and text. Extracted explanations are used to insure the validity of KG facts. Finally, to facilitate KG exploration, we introduce a method that combines KG embeddings with rule mining to compute informative entity clusters with explanations.Wissensgraphen haben viele Anwendungen in verschiedenen Bereichen, beispielsweise im Finanz- und Gesundheitswesen. Wissensgraphen sind jedoch unvollständig und enthalten auch ungültige Daten. Hohe Abdeckung und Korrektheit erfordern neue Methoden zur Wissensgraph-Erweiterung und Wissensgraph-Validierung. Beide Aufgaben zusammen werden als Wissensgraph-Verfeinerung bezeichnet. Ein wichtiger Aspekt dabei ist die Erklärbarkeit und Verständlichkeit von Wissensgraphinhalten für Nutzer. In Anwendungen ist darüber hinaus die nutzerseitige Exploration von Wissensgraphen von besonderer Bedeutung. Suchen und Navigieren im Graph hilft dem Anwender, die Wissensinhalte und ihre Limitationen besser zu verstehen. Aufgrund der riesigen Menge an vorhandenen Entitäten und Fakten ist die Wissensgraphen-Exploration eine Herausforderung. Taxonomische Typsystem helfen dabei, sind jedoch für tiefergehende Exploration nicht ausreichend. Diese Dissertation adressiert die Herausforderungen der Wissensgraph-Verfeinerung und der Wissensgraph-Exploration durch algorithmische Inferenz über dem Wissensgraph. Sie erweitert logisches Schlussfolgern und kombiniert es mit anderen Methoden, insbesondere mit neuronalen Wissensgraph-Einbettungen und mit Text-Mining. Diese neuen Methoden liefern Ausgaben mit Erklärungen für Nutzer. Die Dissertation umfasst folgende Beiträge: Insbesondere leistet die Dissertation folgende Beiträge: • Zur Wissensgraph-Erweiterung präsentieren wir ExRuL, eine Methode zur Revision von Horn-Regeln durch Hinzufügen von Ausnahmebedingungen zum Rumpf der Regeln. Die erweiterten Regeln können neue Fakten inferieren und somit Lücken im Wissensgraphen schließen. Experimente mit großen Wissensgraphen zeigen, dass diese Methode Fehler in abgeleiteten Fakten erheblich reduziert und nutzerfreundliche Erklärungen liefert. • Mit RuLES stellen wir eine Methode zum Lernen von Regeln vor, die auf probabilistischen Repräsentationen für fehlende Fakten basiert. Das Verfahren erweitert iterativ die aus einem Wissensgraphen induzierten Regeln, indem es neuronale Wissensgraph-Einbettungen mit Informationen aus Textkorpora kombiniert. Bei der Regelgenerierung werden neue Metriken für die Regelqualität verwendet. Experimente zeigen, dass RuLES die Qualität der gelernten Regeln und ihrer Vorhersagen erheblich verbessert. • Zur Unterstützung der Wissensgraph-Validierung wird ExFaKT vorgestellt, ein Framework zur Konstruktion von Erklärungen für Faktkandidaten. Die Methode transformiert Kandidaten mit Hilfe von Regeln in eine Menge von Aussagen, die leichter zu finden und zu validieren oder widerlegen sind. Die Ausgabe von ExFaKT ist eine Menge semantischer Evidenzen für Faktkandidaten, die aus Textkorpora und dem Wissensgraph extrahiert werden. Experimente zeigen, dass die Transformationen die Ausbeute und Qualität der entdeckten Erklärungen deutlich verbessert. Die generierten unterstützen Erklärungen unterstütze sowohl die manuelle Wissensgraph- Validierung durch Kuratoren als auch die automatische Validierung. • Zur Unterstützung der Wissensgraph-Exploration wird ExCut vorgestellt, eine Methode zur Erzeugung von informativen Entitäts-Clustern mit Erklärungen unter Verwendung von Wissensgraph-Einbettungen und automatisch induzierten Regeln. Eine Cluster-Erklärung besteht aus einer Kombination von Relationen zwischen den Entitäten, die den Cluster identifizieren. ExCut verbessert gleichzeitig die Cluster- Qualität und die Cluster-Erklärbarkeit durch iteratives Verschränken des Lernens von Einbettungen und Regeln. Experimente zeigen, dass ExCut Cluster von hoher Qualität berechnet und dass die Cluster-Erklärungen für Nutzer informativ sind

Proceedings of the 11th Workshop on Nonmonotonic Reasoning

These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series is to bring together active researchers in the broad area of nonmonotonic reasoning, including belief revision, reasoning about actions, planning, logic programming, argumentation, causality, probabilistic and possibilistic approaches to KR, and other related topics. As part of the program of the 11th workshop, we have assessed the status of the field and discussed issues such as: Significant recent achievements in the theory and automation of NMR; Critical short and long term goals for NMR; Emerging new research directions in NMR; Practical applications of NMR; Significance of NMR to knowledge representation and AI in general