1,316 research outputs found

    On the non-efficient PAC learnability of conjunctive queries

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    This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in much of the computational learning theory literature; (ii) we establish a strong negative PAC learnability result that applies to many restricted classes of conjunctive queries (CQs), including acyclic CQs for a wide range of notions of acyclicity; (iii) we show that CQs (and UCQs) are efficiently PAC learnable with membership queries.<p/

    Fragments and frame classes:Towards a uniform proof theory for modal fixed point logics

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    This thesis studies the proof theory of modal fixed point logics. In particular, we construct proof systems for various fragments of the modal mu-calculus, interpreted over various classes of frames. With an emphasis on uniform constructions and general results, we aim to bring the relatively underdeveloped proof theory of modal fixed point logics closer to the well-established proof theory of basic modal logic. We employ two main approaches. First, we seek to generalise existing methods for basic modal logic to accommodate fragments of the modal mu-calculus. We use this approach for obtaining Hilbert-style proof systems. Secondly, we adapt existing proof systems for the modal mu-calculus to various classes of frames. This approach yields proof systems which are non-well-founded, or cyclic.The thesis starts with an introduction and some mathematical preliminaries. In Chapter 3 we give hypersequent calculi for modal logic with the master modality, building on work by Ori Lahav. This is followed by an Intermezzo, where we present an abstract framework for cyclic proofs, in which we give sufficient conditions for establishing the bounded proof property. In Chapter 4 we generalise existing work on Hilbert-style proof systems for PDL to the level of the continuous modal mu-calculus. Chapter 5 contains a novel cyclic proof system for the alternation-free two-way modal mu-calculus. Finally, in Chapter 6, we present a cyclic proof system for Guarded Kleene Algebra with Tests and take a first step towards using it to establish the completeness of an algebraic counterpart

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Advances and Applications of DSmT for Information Fusion. Collected Works, Volume 5

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    This ïŹfth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different ïŹelds of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some theoretical advances on DSmT, dealing mainly with modiïŹed Proportional ConïŹ‚ict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classiïŹers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identiïŹcation of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classiïŹcation. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classiïŹcation, and hybrid techniques mixing deep learning with belief functions as well

    Belief Revision in Expressive Knowledge Representation Formalisms

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    We live in an era of data and information, where an immeasurable amount of discoveries, findings, events, news, and transactions are generated every second. Governments, companies, or individuals have to employ and process all that data for knowledge-based decision-making (i.e. a decision-making process that uses predetermined criteria to measure and ensure the optimal outcome for a specific topic), which then prompt them to view the knowledge as valuable resource. In this knowledge-based view, the capability to create and utilize knowledge is the key source of an organization or individual’s competitive advantage. This dynamic nature of knowledge leads us to the study of belief revision (or belief change), an area which emerged from work in philosophy and then impacted further developments in computer science and artificial intelligence. In belief revision area, the AGM postulates by AlchourrĂłn, GĂ€rdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. In this thesis, two research directions are considered. In the first, by considering the semantic point of view, we generalize K&M’s approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of “base”, such as belief sets, arbitrary or finite sets of sentences, or single sentences. The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain “assignments”: functions mapping belief bases to total — yet not transitive — “preference” relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M’s original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence. The second research direction in this thesis explores two approaches for revising description logic knowledge bases under fixed-domain semantics, namely model-based approach and individual-based approach. In this logical setting, models of the knowledge bases can be enumerated and can be computed to produce the revision result, semantically. We show a characterization of the AGM revision operator for this logic and present a concrete model-based revision approach via distance between interpretations. In addition, by weakening the KB based on certain domain elements, a novel individual-based revision operator is provided as an alternative approach

    Rational verification and checking for Nash and subgame-perfect equilibria in graph games

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    We study two natural problems about rational behaviors in multiplayer non-zero-sum sequential infinite duration games played on graphs: checking problems, that consist in deciding whether a strategy profile, defined by a Mealy machine, is rational; and rational verification, that consists in deciding whether all the rational answers to a given strategy satisfy some specification. We give the complexities of those problems for two major concepts of rationality: Nash equilibria and subgame-perfect equilibria, and for five major classes of payoff functions: parity, mean-payoff, quantitative reachability, energy, and discounted-sum

    Set Semantics for Asynchronous TeamLTL: Expressivity and Complexity

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    We introduce and develop a set-based semantics for asynchronous TeamLTL. We consider two canonical logics in this setting: the extensions of TeamLTL by the Boolean disjunction and by the Boolean negation. We establish fascinating connections between the original semantics based on multisets and the new set-based semantics as well as show one of the first positive complexity theoretic results in the temporal team semantics setting. In particular we show that both logics enjoy normal forms that can be utilised to obtain results related to expressivity and complexity (decidability) of the new logics. We also relate and apply our results to recently defined logics whose asynchronicity is formalized via time evaluation functions
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