Knowledge Compilation of Logic Programs Using Approximation Fixpoint Theory

To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015 Recent advances in knowledge compilation introduced techniques to compile \emph{positive} logic programs into propositional logic, essentially exploiting the constructive nature of the least fixpoint computation. This approach has several advantages over existing approaches: it maintains logical equivalence, does not require (expensive) loop-breaking preprocessing or the introduction of auxiliary variables, and significantly outperforms existing algorithms. Unfortunately, this technique is limited to \emph{negation-free} programs. In this paper, we show how to extend it to general logic programs under the well-founded semantics. We develop our work in approximation fixpoint theory, an algebraical framework that unifies semantics of different logics. As such, our algebraical results are also applicable to autoepistemic logic, default logic and abstract dialectical frameworks

On cascade products of answer set programs

Describing complex objects by elementary ones is a common strategy in mathematics and science in general. In their seminal 1965 paper, Kenneth Krohn and John Rhodes showed that every finite deterministic automaton can be represented (or "emulated") by a cascade product of very simple automata. This led to an elegant algebraic theory of automata based on finite semigroups (Krohn-Rhodes Theory). Surprisingly, by relating logic programs and automata, we can show in this paper that the Krohn-Rhodes Theory is applicable in Answer Set Programming (ASP). More precisely, we recast the concept of a cascade product to ASP, and prove that every program can be represented by a product of very simple programs, the reset and standard programs. Roughly, this implies that the reset and standard programs are the basic building blocks of ASP with respect to the cascade product. In a broader sense, this paper is a first step towards an algebraic theory of products and networks of nonmonotonic reasoning systems based on Krohn-Rhodes Theory, aiming at important open issues in ASP and AI in general.Comment: Appears in Theory and Practice of Logic Programmin

Derivation methods for hybrid knowledge bases with rules and ontologies

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia InformáticaFirst of all, I would like to thank my advisor, José Júlio Alferes, for his incredible support. Right from the start, during the first semester of this work, when we were 2700 km apart and meeting regularly via Skype, until the end of this dissertation, he was always committed and available for discussions, even when he had lots of other urgent things to do. A really special thanks to Terrance Swift, whom acted as an advisor, helping me a lot in the second implementation, and correcting all XSB’s and CDF’s bugs. This implementation wouldn’t surely have reached such a fruitful end without his support. I would also like to thank all my colleagues and friends at FCT for the great work environment and for not letting me take myself too serious. A special thanks to my colleagues from Dresden for encouraging me to work even when there were so many other interesting things to do as an Erasmus student. I’m indebted to Luís Leal, Bárbara Soares, Jorge Soares and Cecília Calado, who kindly accepted to read a preliminary version of this report and gave me their valuable comments. For giving me working conditions and a partial financial support, I acknowledge the Departamento de Informática of the Faculdade de Ciências e Tecnologias of Universidade Nova de Lisboa. Last, but definitely not least, I would like to thank my parents and all my family for their continuous encouragement and motivation. A special thanks to Bruno for his love, support and patience

Arithmetic and Modularity in Declarative Languages for Knowledge Representation

The past decade has witnessed the development of many important declarative languages for knowledge representation and reasoning such as answer set programming (ASP) languages and languages that extend first-order logic. Also, since these languages depend on background solvers, the recent advancements in the efficiency of solvers has positively affected the usability of such languages. This thesis studies extensions of knowledge representation (KR) languages with arithmetical operators and methods to combine different KR languages. With respect to arithmetic in declarative KR languages, we show that existing KR languages suffer from a huge disparity between their expressiveness and their computational power. Therefore, we develop an ideal KR language that captures the complexity class NP for arithmetical search problems and guarantees universality and efficiency for solving such problems. Moreover, we introduce a framework to language-independently combine modules from different KR languages. We study complexity and expressiveness of our framework and develop algorithms to solve modular systems. We define two semantics for modular systems based on (1) a model-theoretical view and (2) an operational view on modular systems. We prove that our two semantics coincide and also develop mechanisms to approximate answers to modular systems using the operational view. We augment our algorithm these approximation mechanisms to speed up the process of solving modular system. We further generalize our modular framework with supported model semantics that disallows self-justifying models. We show that supported model semantics generalizes our two previous model-theoretical and operational semantics. We compare and contrast the expressiveness of our framework under supported model semantics with another framework for interlinking knowledge bases, i.e., multi-context systems, and prove that supported model semantics generalizes and unifies different semantics of multi-context systems. Motivated by the wide expressiveness of supported models, we also define a new supported equilibrium semantics for multi-context systems and show that supported equilibrium semantics generalizes previous semantics for multi-context systems. Furthermore, we also define supported semantics for propositional programs and show that supported model semnatics generalizes the acclaimed stable model semantics and extends the two celebrated properties of rationality and minimality of intended models beyond the scope of logic programs

Optimizing the computation of overriding

We introduce optimization techniques for reasoning in DLN---a recently introduced family of nonmonotonic description logics whose characterizing features appear well-suited to model the applicative examples naturally arising in biomedical domains and semantic web access control policies. Such optimizations are validated experimentally on large KBs with more than 30K axioms. Speedups exceed 1 order of magnitude. For the first time, response times compatible with real-time reasoning are obtained with nonmonotonic KBs of this size

An executable formal semantics of PHP with applications to program analysis

Nowadays, many important activities in our lives involve the web. However, the software and protocols on which web applications are based were not designed with the appropriate level of security in mind. Many web applications have reached a level of complexity for which testing, code reviews and human inspection are no longer sufficient quality-assurance guarantees. Tools that employ static analysis techniques are needed in order to explore all possible execution paths through an application and guarantee the absence of undesirable behaviours. To make sure that an analysis captures the properties of interest, and to navigate the trade-offs between efficiency and precision, it is necessary to base the design and the development of static analysis tools on a firm understanding of the language to be analysed. When this underlying knowledge is missing or erroneous, tools can’t be trusted no matter what advanced techniques they use to perform their task. In this Thesis, we introduce KPHP, the first executable formal semantics of PHP, one of the most popular languages for server-side web programming. Then, we demonstrate its practical relevance by developing two verification tools, of increasing complexity, on top of it - a simple verifier based on symbolic execution and LTL model checking and a general purpose, fully configurable and extensible static analyser based on Abstract Interpretation. Our LTL-based tool leverages the existing symbolic execution and model checking support offered by K, our semantics framework of choice, and constitutes a first proof-of-concept of the usefulness of our semantics. Our abstract interpreter, on the other hand, represents a more significant and novel contribution to the field of static analysis of dynamic scripting languages (PHP in particular). Although our tool is still a prototype and therefore not well suited for handling large real-world codebases, we demonstrate how our semantics-based, principled approach to the development of verification tools has lead to the design of static analyses that outperform existing tools and approaches, both in terms of supported language features, precision, and breadth of possible applications.Open Acces

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

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