949 research outputs found

    Cyclic proof systems for modal fixpoint logics

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    This thesis is about cyclic and ill-founded proof systems for modal fixpoint logics, with and without explicit fixpoint quantifiers.Cyclic and ill-founded proof-theory allow proofs with infinite branches or paths, as long as they satisfy some correctness conditions ensuring the validity of the conclusion. In this dissertation we design a few cyclic and ill-founded systems: a cyclic one for the weak Grzegorczyk modal logic K4Grz, based on our explanation of the phenomenon of cyclic companionship; and ill-founded and cyclic ones for the full computation tree logic CTL* and the intuitionistic linear-time temporal logic iLTL. All systems are cut-free, and the cyclic ones for K4Grz and iLTL have fully finitary correctness conditions.Lastly, we use a cyclic system for the modal mu-calculus to obtain a proof of the uniform interpolation property for the logic which differs from the original, automata-based one

    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

    Bounded Model Checking for Asynchronous Hyperproperties

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    Many types of attacks on confidentiality stem from the nondeterministic nature of the environment that computer programs operate in (e.g., schedulers and asynchronous communication channels). In this paper, we focus on verification of confidentiality in nondeterministic environments by reasoning about asynchronous hyperproperties. First, we generalize the temporal logic A-HLTL to allow nested trajectory quantification, where a trajectory determines how different execution traces may advance and stutter. We propose a bounded model checking algorithm for A-HLTL based on QBF-solving for a fragment of the generalized A-HLTL and evaluate it by various case studies on concurrent programs, scheduling attacks, compiler optimization, speculative execution, and cache timing attacks. We also rigorously analyze the complexity of model checking for different fragments of A-HLTL.Comment: 34 page

    A Symbolic Language for Interpreting Decision Trees

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    The recent development of formal explainable AI has disputed the folklore claim that "decision trees are readily interpretable models", showing different interpretability queries that are computationally hard on decision trees, as well as proposing different methods to deal with them in practice. Nonetheless, no single explainability query or score works as a "silver bullet" that is appropriate for every context and end-user. This naturally suggests the possibility of "interpretability languages" in which a wide variety of queries can be expressed, giving control to the end-user to tailor queries to their particular needs. In this context, our work presents ExplainDT, a symbolic language for interpreting decision trees. ExplainDT is rooted in a carefully constructed fragment of first-ordered logic that we call StratiFOILed. StratiFOILed balances expressiveness and complexity of evaluation, allowing for the computation of many post-hoc explanations--both local (e.g., abductive and contrastive explanations) and global ones (e.g., feature relevancy)--while remaining in the Boolean Hierarchy over NP. Furthermore, StratiFOILed queries can be written as a Boolean combination of NP-problems, thus allowing us to evaluate them in practice with a constant number of calls to a SAT solver. On the theoretical side, our main contribution is an in-depth analysis of the expressiveness and complexity of StratiFOILed, while on the practical side, we provide an optimized implementation for encoding StratiFOILed queries as propositional formulas, together with an experimental study on its efficiency

    Logics and Algorithms for Hyperproperties

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    System requirements related to concepts like information flow, knowledge, and robustness cannot be judged in terms of individual system executions, but rather require an analysis of the relationship between multiple executions. Such requirements belong to the class of hyperproperties, which generalize classic trace properties to properties of sets of traces. During the past decade, a range of new specification logics has been introduced with the goal of providing a unified theory for reasoning about hyperproperties. This paper gives an overview on the current landscape of logics for the specification of hyperproperties and on algorithms for satisfiability checking, model checking, monitoring, and synthesis

    Formulaic sequences in Early Modern English: A corpus-assisted historical pragmatic study

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    This doctoral project identifies formulaic sequences (hereinafter FS and the plural form FSs) in Early Modern English (hereinafter EModE) and intends to investigate the functions they serve in communication and different text types, namely EModE dialogues and letters. Main contributions of the study include, firstly, the study provides solid arguments and further evidence that FSs are constructions in the Construction Grammar instead of exceptions in the traditional grammar-dictionary model. Within this theoreticall framework, I proposed a new working definition of FSs that is inclusive, descriptive, and methodologically neutral. The study also argues that there are fundamental differences between FSs and lexical bundles (LBs), although the latter often treated as an alternative term of FSs or sub-groups of FSs. Nevertheless, after a thorogh review of the characteristics of the two mult-word units, the study argues that despite of the differences, LBs can be upgrated to FSs as long as they fulfill certail sematic, syntactic, and pragmatic criteria. THis forms the fundation of the methodology design of the study. Secondly, the study enhanced the corpus-assisted approach to the identification of FSs, esp. in EModE texts. The approach consists of three steps: preparation, identification, and generalisation. The identification step was further conducted within two phases: automatic generation of LBs for a corpus and manual identification of FSs from LBs. Specifically, in the preparation step, the dissertation critically discussed how spelling variation in EModE texts shall be dealt with in investigations on FSs. I designed a series of criteria for the two-phase identification of FSs. For one thing, I disagree with previous research that two-word LBs shall be excluded from examination by arguing that many of them are formulaic and cannot be captured from longer LBs and the workload of processing the massive number of two-word LBs is actually manageable. For another, the study contributes an easy-to-follow flow chart demonstrating the procedure of the manual identification of FSs from LBs and listing the criteria that guide the decision-making process. Thirdly, the study provides systematic and comprehensive accounts of FSs in EModE dialogues and letters, esp. how their forms are conventionally mapped to their functions. Data analysis were conducted from aspects such as degree of fixedness, grammatical structures, distribution across function categories, multi-functional FSs, genre-specific FSs, etc. General findings suggest that EModE dialogues and letters actually have many similarities regarding the form and function of FSs and general trends of distribution across function categories. However, outstanding differences between the two text types can be observed too. From the perspective of form, the distinction lies in word choice in realisations of certain FSs. From the perspective of meaning/function, the distinction lies in the kinds of functions that need FSs the most or the least and common function combinations. More importantly, the study observed two types of relationships among FSs themselves and the discourse, including horizonal networks and vertical networks, which reflects the complexity of FSs and their identity as constructions. Specifically, three types of horizontal networks of FSs are embedding, attaching, and joining. A pair of new concepts is proposed to describe the vertical networks: superordinate FSs and subordinate FSs. As a result of the vertical networks, three types of functional diviation are observed: function extension, shifting, and specification

    Uncertainty in runtime verification : a survey

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    Runtime Verification can be defined as a collection of formal methods for studying the dynamic evaluation of execution traces against formal specifications. Aside from creating a monitor from specifications and building algorithms for the evaluation of the trace, the process of gathering events and making them available for the monitor and the communication between the system under analysis and the monitor are critical and important steps in the runtime verification process. In many situations and for a variety of reasons, the event trace could be incomplete or could contain imprecise events. When a missing or ambiguous event is detected, the monitor may be unable to deliver a sound verdict. In this survey, we review the literature dealing with the problem of monitoring with incomplete traces. We list the different causes of uncertainty that have been identified, and analyze their effect on the monitoring process. We identify and compare the different methods that have been proposed to perform monitoring on such traces, highlighting the advantages and drawbacks of each method

    PolĂ­tica lingĂĽĂ­stica en Luxemburgo y en la Comunidad germanĂłfona de BĂ©lgica: IdeologĂ­as lingĂĽĂ­sticas

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    The language policy discourses of Luxembourg and the German-speaking Community of Belgium (GC) exhibit fundamental differences, yet interesting similarities that so far have not been subject to a discourse analysis from a mixed framework of linguistic anthropology and discourse linguistics (Diskurslinguistik). On the basis of a corpus consisting of current language policy texts and semi-structured interviews with key actors involved in current policy design and implementation, this research aims to answer the question regarding the interplay of ideology and discourse in the design and implementation of the language policy of Luxembourg and the GC. The bulk of the analysis is made up of three layers for each case. Starting point of the analysis is a historical overview that identifies ideologies and language policy discourses that emerged, predominated, and transformed from the 19th century until the 21st century in each case. The second layer is a discourse analysis of current language policy texts with a focus on the ideologies informing current discourses about Luxembourgish in Luxembourg and German in the GC. Finally, the third layer is a discourse analysis of interview extracts with equal focus on ideologies. Through a combined thematic and discourse analysis based on the social semiotics of language, this research provides a description of the discursive patterns of the linguistic structure of passages of each text and interview with the aim of linking these patterns to the identified ideologies that inform the policy discourses. It was found that the connecting node between Luxembourg and the GC lies in the tension between the two themes of standardization and multilingualism. It is shown that standardization and multilingualism are thematic centers from which discourses about language, identity, and nation emanate in these two cases. Through the combination of the historical overview and the meticulous analysis of discursive patterns identified in the linguistic structure of language policy texts and interview extracts, it is not only shown how ideology informs current language policy discourses in Luxembourg and the GC, but also why language policy discourses transform or sediment through time

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum
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