451 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Generalising weighted model counting

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    Given a formula in propositional or (finite-domain) first-order logic and some non-negative weights, weighted model counting (WMC) is a function problem that asks to compute the sum of the weights of the models of the formula. Originally used as a flexible way of performing probabilistic inference on graphical models, WMC has found many applications across artificial intelligence (AI), machine learning, and other domains. Areas of AI that rely on WMC include explainable AI, neural-symbolic AI, probabilistic programming, and statistical relational AI. WMC also has applications in bioinformatics, data mining, natural language processing, prognostics, and robotics. In this work, we are interested in revisiting the foundations of WMC and considering generalisations of some of the key definitions in the interest of conceptual clarity and practical efficiency. We begin by developing a measure-theoretic perspective on WMC, which suggests a new and more general way of defining the weights of an instance. This new representation can be as succinct as standard WMC but can also expand as needed to represent less-structured probability distributions. We demonstrate the performance benefits of the new format by developing a novel WMC encoding for Bayesian networks. We then show how existing WMC encodings for Bayesian networks can be transformed into this more general format and what conditions ensure that the transformation is correct (i.e., preserves the answer). Combining the strengths of the more flexible representation with the tricks used in existing encodings yields further efficiency improvements in Bayesian network probabilistic inference. Next, we turn our attention to the first-order setting. Here, we argue that the capabilities of practical model counting algorithms are severely limited by their inability to perform arbitrary recursive computations. To enable arbitrary recursion, we relax the restrictions that typically accompany domain recursion and generalise circuits (used to express a solution to a model counting problem) to graphs that are allowed to have cycles. These improvements enable us to find efficient solutions to counting fundamental structures such as injections and bijections that were previously unsolvable by any available algorithm. The second strand of this work is concerned with synthetic data generation. Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm’s superiority over another. However, benchmarks are often limited and fail to reveal differences among the algorithms. First, we show how random instances of probabilistic logic programs (that typically use WMC algorithms for inference) can be generated using constraint programming. We also introduce a new constraint to control the independence structure of the underlying probability distribution and provide a combinatorial argument for the correctness of the constraint model. This model allows us to, for the first time, experimentally investigate inference algorithms on more than just a handful of instances. Second, we introduce a random model for WMC instances with a parameter that influences primal treewidth—the parameter most commonly used to characterise the difficulty of an instance. We show that the easy-hard-easy pattern with respect to clause density is different for algorithms based on dynamic programming and algebraic decision diagrams than for all other solvers. We also demonstrate that all WMC algorithms scale exponentially with respect to primal treewidth, although at differing rates

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Through and beyond classicality: analyticity, embeddings, infinity

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    Structural proof theory deals with formal representation of proofs and with the investigation of their properties. This thesis provides an analysis of various non-classical logical systems using proof-theoretic methods. The approach consists in the formulation of analytic calculi for these logics which are then used in order to study their metalogical properties. A specific attention is devoted to studying the connections between classical and non-classical reasoning. In particular, the use of analytic sequent calculi allows one to regain desirable structural properties which are lost in non-classical contexts. In this sense, proof-theoretic versions of embeddings between non-classical logics - both finitary and infinitary - prove to be a useful tool insofar as they build a bridge between different logical regions

    Data Management for Dynamic Multimedia Analytics and Retrieval

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    Multimedia data in its various manifestations poses a unique challenge from a data storage and data management perspective, especially if search, analysis and analytics in large data corpora is considered. The inherently unstructured nature of the data itself and the curse of dimensionality that afflicts the representations we typically work with in its stead are cause for a broad range of issues that require sophisticated solutions at different levels. This has given rise to a huge corpus of research that puts focus on techniques that allow for effective and efficient multimedia search and exploration. Many of these contributions have led to an array of purpose-built, multimedia search systems. However, recent progress in multimedia analytics and interactive multimedia retrieval, has demonstrated that several of the assumptions usually made for such multimedia search workloads do not hold once a session has a human user in the loop. Firstly, many of the required query operations cannot be expressed by mere similarity search and since the concrete requirement cannot always be anticipated, one needs a flexible and adaptable data management and query framework. Secondly, the widespread notion of staticity of data collections does not hold if one considers analytics workloads, whose purpose is to produce and store new insights and information. And finally, it is impossible even for an expert user to specify exactly how a data management system should produce and arrive at the desired outcomes of the potentially many different queries. Guided by these shortcomings and motivated by the fact that similar questions have once been answered for structured data in classical database research, this Thesis presents three contributions that seek to mitigate the aforementioned issues. We present a query model that generalises the notion of proximity-based query operations and formalises the connection between those queries and high-dimensional indexing. We complement this by a cost-model that makes the often implicit trade-off between query execution speed and results quality transparent to the system and the user. And we describe a model for the transactional and durable maintenance of high-dimensional index structures. All contributions are implemented in the open-source multimedia database system Cottontail DB, on top of which we present an evaluation that demonstrates the effectiveness of the proposed models. We conclude by discussing avenues for future research in the quest for converging the fields of databases on the one hand and (interactive) multimedia retrieval and analytics on the other

    Meta-ontology fault detection

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    Ontology engineering is the field, within knowledge representation, concerned with using logic-based formalisms to represent knowledge, typically moderately sized knowledge bases called ontologies. How to best develop, use and maintain these ontologies has produced relatively large bodies of both formal, theoretical and methodological research. One subfield of ontology engineering is ontology debugging, and is concerned with preventing, detecting and repairing errors (or more generally pitfalls, bad practices or faults) in ontologies. Due to the logical nature of ontologies and, in particular, entailment, these faults are often both hard to prevent and detect and have far reaching consequences. This makes ontology debugging one of the principal challenges to more widespread adoption of ontologies in applications. Moreover, another important subfield in ontology engineering is that of ontology alignment: combining multiple ontologies to produce more powerful results than the simple sum of the parts. Ontology alignment further increases the issues, difficulties and challenges of ontology debugging by introducing, propagating and exacerbating faults in ontologies. A relevant aspect of the field of ontology debugging is that, due to the challenges and difficulties, research within it is usually notably constrained in its scope, focusing on particular aspects of the problem or on the application to only certain subdomains or under specific methodologies. Similarly, the approaches are often ad hoc and only related to other approaches at a conceptual level. There are no well established and widely used formalisms, definitions or benchmarks that form a foundation of the field of ontology debugging. In this thesis, I tackle the problem of ontology debugging from a more abstract than usual point of view, looking at existing literature in the field and attempting to extract common ideas and specially focussing on formulating them in a common language and under a common approach. Meta-ontology fault detection is a framework for detecting faults in ontologies that utilizes semantic fault patterns to express schematic entailments that typically indicate faults in a systematic way. The formalism that I developed to represent these patterns is called existential second-order query logic (abbreviated as ESQ logic). I further reformulated a large proportion of the ideas present in some of the existing research pieces into this framework and as patterns in ESQ logic, providing a pattern catalogue. Most of the work during my PhD has been spent in designing and implementing an algorithm to effectively automatically detect arbitrary ESQ patterns in arbitrary ontologies. The result is what we call minimal commitment resolution for ESQ logic, an extension of first-order resolution, drawing on important ideas from higher-order unification and implementing a novel approach to unification problems using dependency graphs. I have proven important theoretical properties about this algorithm such as its soundness, its termination (in a certain sense and under certain conditions) and its fairness or completeness in the enumeration of infinite spaces of solutions. Moreover, I have produced an implementation of minimal commitment resolution for ESQ logic in Haskell that has passed all unit tests and produces non-trivial results on small examples. However, attempts to apply this algorithm to examples of a more realistic size have proven unsuccessful, with computation times that exceed our tolerance levels. In this thesis, I have provided both details of the challenges faced in this regard, as well as other successful forms of qualitative evaluation of the meta-ontology fault detection approach, and discussions about both what I believe are the main causes of the computational feasibility problems, ideas on how to overcome them, and also ideas on other directions of future work that could use the results in the thesis to contribute to the production of foundational formalisms, ideas and approaches to ontology debugging that can properly combine existing constrained research. It is unclear to me whether minimal commitment resolution for ESQ logic can, in its current shape, be implemented efficiently or not, but I believe that, at the very least, the theoretical and conceptual underpinnings that I have presented in this thesis will be useful to produce more foundational results in the field

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic

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    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
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