16 research outputs found

    Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic

    Get PDF
    This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL , in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established

    Conflict-driven learning in AI planning state-space search

    Get PDF
    Many combinatorial computation problems in computer science can be cast as a reachability problem in an implicitly described, potentially huge, graph: the state space. State-space search is a versatile and widespread method to solve such reachability problems, but it requires some form of guidance to prevent exploring that combinatorial space exhaustively. Conflict-driven learning is an indispensable search ingredient for solving constraint satisfaction problems (most prominently, Boolean satisfiability). It guides search towards solutions by identifying conflicts during the search, i.e., search branches not leading to any solution, learning from them knowledge to avoid similar conflicts in the remainder of the search. This thesis adapts the conflict-driven learning methodology to more general classes of reachability problems. Specifically, our work is placed in AI planning. We consider goal-reachability objectives in classical planning and in planning under uncertainty. The canonical form of "conflicts" in this context are dead-end states, i.e., states from which the desired goal property cannot be reached. We pioneer methods for learning sound and generalizable dead-end knowledge from conflicts encountered during forward state-space search. This embraces the following core contributions: When acting under uncertainty, the presence of dead-end states may make it impossible to satisfy the goal property with absolute certainty. The natural planning objective then is MaxProb, maximizing the probability of reaching the goal. However, algorithms for MaxProb probabilistic planning are severely underexplored. We close this gap by developing a large design space of probabilistic state-space search methods, contributing new search algorithms, admissible state-space reduction techniques, and goal-probability bounds suitable for heuristic state-space search. We systematically explore this design space through an extensive empirical evaluation. The key to our conflict-driven learning algorithm adaptation are unsolvability detectors, i.e., goal-reachability overapproximations. We design three complementary families of such unsolvability detectors, building upon known techniques: critical-path heuristics, linear-programming-based heuristics, and dead-end traps. We develop search methods to identify conflicts in deterministic and probabilistic state spaces, and we develop suitable refinement methods for the different unsolvability detectors so to recognize these states. Arranged in a depth-first search, our techniques approach the elegance of conflict-driven learning in constraint satisfaction, featuring the ability to learn to refute search subtrees, and intelligent backjumping to the root cause of a conflict. We provide a comprehensive experimental evaluation, demonstrating that the proposed techniques yield state-of-the-art performance for finding plans for solvable classical planning tasks, proving classical planning tasks unsolvable, and solving MaxProb in probabilistic planning, on benchmarks where dead-end states abound.Viele kombinatorisch komplexe Berechnungsprobleme in der Informatik lassen sich als Erreichbarkeitsprobleme in einem implizit dargestellten, potenziell riesigen, Graphen - dem Zustandsraum - verstehen. Die Zustandsraumsuche ist eine weit verbreitete Methode, um solche Erreichbarkeitsprobleme zu lösen. Die Effizienz dieser Methode hĂ€ngt aber maßgeblich von der Verwendung strikter Suchkontrollmechanismen ab. Das konfliktgesteuerte Lernen ist eine essenzielle Suchkomponente fĂŒr das Lösen von Constraint-Satisfaction-Problemen (wie dem ErfĂŒllbarkeitsproblem der Aussagenlogik), welches von Konflikten, also Fehlern in der Suche, neue Kontrollregeln lernt, die Ă€hnliche Konflikte zukĂŒnftig vermeiden. In dieser Arbeit erweitern wir die zugrundeliegende Methodik auf Zielerreichbarkeitsfragen, wie sie im klassischen und probabilistischen Planen, einem Teilbereich der KĂŒnstlichen Intelligenz, auftauchen. Die kanonische Form von „Konflikten“ in diesem Kontext sind sog. Sackgassen, ZustĂ€nde, von denen aus die Zielbedingung nicht erreicht werden kann. Wir prĂ€sentieren Methoden, die es ermöglichen, wĂ€hrend der Zustandsraumsuche von solchen Konflikten korrektes und verallgemeinerbares Wissen ĂŒber Sackgassen zu erlernen. Unsere Arbeit umfasst folgende BeitrĂ€ge: Wenn der Effekt des Handelns mit Unsicherheiten behaftet ist, dann kann die Existenz von Sackgassen dazu fĂŒhren, dass die Zielbedingung nicht unter allen UmstĂ€nden erfĂŒllt werden kann. Die naheliegendste Planungsbedingung in diesem Fall ist MaxProb, das Maximieren der Wahrscheinlichkeit, dass die Zielbedingung erreicht wird. Planungsalgorithmen fĂŒr MaxProb sind jedoch wenig erforscht. Um diese LĂŒcke zu schließen, erstellen wir einen umfangreichen Bausatz fĂŒr Suchmethoden in probabilistischen ZustandsrĂ€umen, und entwickeln dabei neue Suchalgorithmen, Zustandsraumreduktionsmethoden, und AbschĂ€tzungen der Zielerreichbarkeitswahrscheinlichkeit, wie sie fĂŒr heuristische Suchalgorithmen gebraucht werden. Wir explorieren den resultierenden Gestaltungsraum systematisch in einer breit angelegten empirischen Studie. Die Grundlage unserer Adaption des konfliktgesteuerten Lernens bilden Unerreichbarkeitsdetektoren. Wir konzipieren drei Familien solcher Detektoren basierend auf bereits bekannten Techniken: Kritische-Pfad Heuristiken, Heuristiken basierend auf linearer Optimierung, und Sackgassen-Fallen. Wir entwickeln Suchmethoden, um Konflikte in deterministischen und probabilistischen ZustandsrĂ€umen zu erkennen, sowie Methoden, um die verschiedenen Unerreichbarkeitsdetektoren basierend auf den erkannten Konflikten zu verfeinern. Instanziiert als Tiefensuche weisen unsere Techniken Ă€hnliche Eigenschaften auf wie das konfliktgesteuerte Lernen fĂŒr Constraint-Satisfaction-Problemen. Wir evaluieren die entwickelten Methoden empirisch, und zeigen dabei, dass das konfliktgesteuerte Lernen unter gewissen Voraussetzungen zu signifikanten Suchreduktionen beim Finden von PlĂ€nen in lösbaren klassischen Planungsproblemen, Beweisen der Unlösbarkeit von klassischen Planungsproblemen, und Lösen von MaxProb im probabilistischen Planen, fĂŒhren kann

    A Machine Learning Approach for Optimizing Heuristic Decision-making in OWL Reasoners

    Get PDF
    Description Logics (DLs) are formalisms for representing knowledge bases of application domains. TheWeb Ontology Language (OWL) is a syntactic variant of a very expressive description logic. OWL reasoners can infer implied information from OWL ontologies. The performance of OWL reasoners can be severely affected by situations that require decision-making over many alternatives. Such a non-deterministic behavior is often controlled by heuristics that are based on insufficient information. This thesis proposes a novel OWL reasoning approach that applies machine learning (ML) to implement pragmatic and optimal decision-making strategies in such situations. Disjunctions occurring in ontologies are one source of non deterministic actions in reasoners. We propose two ML-based approaches to reduce the non-determinism caused by dealing with disjunctions. The first approach is restricted to propositional description logic while the second one can deal with standard description logic. The first approach builds a logistic regression classifier that chooses a proper branching heuristic for an input ontology. Branching heuristics are first developed to help Propositional Satisfiability (SAT) based solvers with making decisions about which branch to pick in each branching level. The second approach is the developed version of the first approach. An SVM (Support Vector Machine) classier is designed to select an appropriate expansion-ordering heuristic for an input ontology. The built-in heuristics are designed for expansion ordering of satisfiability testing in OWL reasoners. They determine the order for branches in search trees. Both of the above approaches speed up our ML-based reasoner by up to two orders of magnitude in comparison to the non-ML reasoner. Another source of non-deterministic actions is the order in which tableau rules should be applied. On average, our ML-based approach that is an SVM classifier achieves a speedup of two orders of magnitude when compared to the most expensive rule ordering of the non-ML reasoner

    Fuzzy Description Logics with General Concept Inclusions

    Get PDF
    Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by HĂĄjek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived

    Towards Next Generation Sequential and Parallel SAT Solvers

    Get PDF
    This thesis focuses on improving the SAT solving technology. The improvements focus on two major subjects: sequential SAT solving and parallel SAT solving. To better understand sequential SAT algorithms, the abstract reduction system Generic CDCL is introduced. With Generic CDCL, the soundness of solving techniques can be modeled. Next, the conflict driven clause learning algorithm is extended with the three techniques local look-ahead, local probing and all UIP learning that allow more global reasoning during search. These techniques improve the performance of the sequential SAT solver Riss. Then, the formula simplification techniques bounded variable addition, covered literal elimination and an advanced cardinality constraint extraction are introduced. By using these techniques, the reasoning of the overall SAT solving tool chain becomes stronger than plain resolution. When using these three techniques in the formula simplification tool Coprocessor before using Riss to solve a formula, the performance can be improved further. Due to the increasing number of cores in CPUs, the scalable parallel SAT solving approach iterative partitioning has been implemented in Pcasso for the multi-core architecture. Related work on parallel SAT solving has been studied to extract main ideas that can improve Pcasso. Besides parallel formula simplification with bounded variable elimination, the major extension is the extended clause sharing level based clause tagging, which builds the basis for conflict driven node killing. The latter allows to better identify unsatisfiable search space partitions. Another improvement is to combine scattering and look-ahead as a superior search space partitioning function. In combination with Coprocessor, the introduced extensions increase the performance of the parallel solver Pcasso. The implemented system turns out to be scalable for the multi-core architecture. Hence iterative partitioning is interesting for future parallel SAT solvers. The implemented solvers participated in international SAT competitions. In 2013 and 2014 Pcasso showed a good performance. Riss in combination with Copro- cessor won several first, second and third prices, including two Kurt-Gödel-Medals. Hence, the introduced algorithms improved modern SAT solving technology

    Engineering an Advanced Location-Based Augmented Reality Engine for Smart Mobile Devices

    Get PDF
    Daily business routines more and more require to access information systems in a mobile manner, while preserving a desktop-like feeling at the same time. The goal of this work is to outline the engineering process of a sophisticated mobile service running on a smartphone. More precisely, we show how to develop the core of a location-based augmented reality engine for the iPhone 4S based on the operating system iOS 5.1 (or higher). We denote this engine as AREA. In particular, we develop concepts for coping with limited resources on a mobile device, while providing a smooth user augmented reality experience at the same time. We further present and develop a suitable application architecture in this context, which easily allows integrating augmented reality with a wide range of applications

    Implementation methodology for using concurrent and collaborative approaches for theorem provers, with case studies of SAT and LCF style provers

    Get PDF
    Theorem provers are faced with the challenges of size and complexity, fueled by the increasing range of applications. The use of concurrent/ distributed programming paradigms to engineer better theorem provers merits serious investigation, as it provides: more processing power and opportunities for implementing novel approaches to address theorem proving tasks hitherto infeasible in a sequential setting. Investigation of these opportunities for two diverse theorem prover settings with an emphasis on desirable implementation criteria is the core focus of this thesis. Concurrent programming is notoriously error prone, hard to debug and evaluate. Thus, implementation approaches which promote easy prototyping, portability, incremental development and effective isolation of design and implementation can greatly aid the enterprise of experimentation with the application of concurrent techniques to address specific theorem proving tasks. In this thesis, we have explored one such approach by using Alice ML, a functional programming language with support for concurrency and distribution, to implement the prototypes and have used programming abstractions to encapsulate the implementations of the concurrent techniques used. The utility of this approach is illustrated via proof-of-concept prototypes of concurrent systems for two diverse case studies of theorem proving: the propositional satisfiability problem (SAT) and LCF style (first-order) theorem proving, addressing some previously unexplored parallelisation opportunities for each, as follows:. SAT: We have developed a novel hybrid approach for SAT and implemented a prototype for the same: DPLL-Stalmarck. It uses two complementary algorithms for SAT, DPLL and Stalmarck’s. The two solvers run asynchronously and dynamic information exchange is used for co-operative solving. Interaction of the solvers has been encapsulated as a programming abstraction. Compared to the standalone DPLL solver, DPLL-Stalmarck shows significant performance gains for two of the three problem classes considered and comparable behaviour otherwise. As an exploratory research effort, we have developed a novel algorithm, Concurrent Stalmarck, by applying concurrent techniques to the Stalmarck algorithm. A proof-of-concept prototype for the same has been implemented. Implementation of the saturation technique of the Stalmarck algorithm in a parallel setting, as implemented in Concurrent Stalmarck, has been encapsulated as a programming abstraction. LCF: Provision of programmable concurrent primitives enables customisation of concurrent techniques to specific theorem proving scenarios. In this case study, we have developed a multilayered approach to support programmable, sound extensions for an LCF prover: use programming abstractions to implement the concurrent techniques; use these to develop novel tacticals (control structures to apply tactics), incorporating concurrent techniques; and use these to develop novel proof search procedures. This approach has been implemented in a prototypical LCF style first-order prover, using Alice ML. New tacticals developed are: fastest-first; distributed composition; crossTalk: a novel tactic which uses dynamic, collaborative information exchange to handle unification across multiple sub-goals, with shared meta-variables; a new tactic, performing simultaneous proof-refutation attempts on propositional (sub- )goals, by invoking an external SAT solver (SAT case study), as a counter-example finder. Examples of concrete theorem proving scenarios are provided, demonstrating the utility of these extensions. Synthesis of a variety of automatic proof search procedures has been demonstrated, illustrating the scope of programmability and customisation, enabled by our multilayered approach

    Extended caching, backjumping and merging for expressive description logics

    No full text
    With this contribution we push the boundary of some known optimisations such as caching to the very expressive Description Logic SROIQ. The developed method is based on a sophisticated dependency management and a precise unsatisfiability caching technique, which further enables better informed tableau backtracking and more efficient pruning. Additionally, we optimise the handling of cardinality restrictions, by introducing a strategy called pool-based merging. We empirically evaluate the proposed optimisations within the novel reasoning system Konclude and show that the proposed optimisations indeed result in significant performance improvements

    Dealing with Variability in Process-aware Information Systems: Language Requirements, Features, and Existing Proposals

    Get PDF
    The increasing adoption of Process-aware Information Systems (PAISs), together with the variability of Business Processes (BPs) across different application contexts, has resulted in large process model repositories with collections of related process model variants. To reduce both costs and occurrence of errors, the explicit management of variability throughout the BP lifecycle becomes crucial. In literature, several proposals dealing with BP variability have been proposed. However, the lack of a method for their systematic comparison makes it difficult to select the most appropriate one meeting current needs best. To close this gap, this work presents an evaluation framework that allows analyzing and comparing the variability support provided by existing proposals developed in the context of BP variability. The framework encompasses a set of language requirements as well as a set of variability support features. While language requirements allow assessing the expressiveness required to explicitly represent variability of different process perspectives, variability support features reflect the tool support required to properly cover such expressiveness. Our evaluation framework has been derived based on an in-depth analysis of several large real-world process scenarios, an extensive literature review, and an analysis of existing PAISs. In this vein, the framework helps to understand BP variability along the BP lifecycle. In addition, it supports PAISs engineers in deciding, which of the existing BP variability proposals meets best their needs

    Reasoning Algebraically with Description Logics

    Get PDF
    Semantic Web applications based on the Web Ontology Language (OWL) often require the use of numbers in class descriptions for expressing cardinality restrictions on properties or even classes. Some of these cardinalities are specified explicitly, but quite a few are entailed and need to be discovered by reasoning procedures. Due to the Description Logic (DL) foundation of OWL, those reasoning services are offered by DL reasoners. Existing DL reasoners employ reasoning procedures that are arithmetically uninformed and substitute arithmetic reasoning by "don't know" non-determinism in order to cover all possible cases. This lack of information about arithmetic problems dramatically degrades the performance of DL reasoners in many cases, especially with ontologies relying on the use of Nominals and Qualied Cardinality Restrictions. The contribution of this thesis is twofold: on the theoretical level, it presents algebraïżœic reasoning with DL (ReAl DL) using a sound, complete, and terminating reasoning procedure for the DL SHOQ. ReAl DL combines tableau reasoning procedures with algebraic methods, namely Integer Programming, to ensure arithmetically better informed reasoning. SHOQ extends the standard DL ALC with transitive roles, role hierarchies, qualified cardinality restrictions (QCRs), and nominals, and forms an expressive subset of OWL. Although the proposed algebraic tableau is double exponential in the worst case, it deals with cardinalities with an additional level of information and properties that make the calculus amenable and well suited for optimizations. In order for ReAl DL to have a practical merit, suited optimizations are proposed towards achieving an efficient reasoning approach that addresses the sources of complexity related to nominals and QCRs. On the practical level, a running prototype reasoner (HARD) is implemented based on the proposed calculus and optimizations. HARD is used to evaluate the practical merit of ReAl DL, as well as the effectiveness of the proposed optimizations. Experimental results based on real world and synthetic ontologies show that ReAl DL outperforms existing reasoning approaches in handling the interactions between nominals and QCRs. ReAl DL also comes with some interesting features such as the ability to handle ontologies with cyclic descriptions without adopting special blocking strategies. ReAl DL can form a basis to provide more efficient reasoning support for ontologies using nominals or QCRs
    corecore