102 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Crisp bi-G\"{o}del modal logic and its paraconsistent expansion

    Full text link
    In this paper, we provide a Hilbert-style axiomatisation for the crisp bi-G\"{o}del modal logic \KbiG. We prove its completeness w.r.t.\ crisp Kripke models where formulas at each state are evaluated over the standard bi-G\"{o}del algebra on [0,1][0,1]. We also consider a paraconsistent expansion of \KbiG with a De Morgan negation ¬\neg which we dub \KGsquare. We devise a Hilbert-style calculus for this logic and, as a~con\-se\-quence of a~conservative translation from \KbiG to \KGsquare, prove its completeness w.r.t.\ crisp Kripke models with two valuations over [0,1][0,1] connected via ¬\neg. For these two logics, we establish that their decidability and validity are PSPACE\mathsf{PSPACE}-complete. We also study the semantical properties of \KbiG and \KGsquare. In particular, we show that Glivenko theorem holds only in finitely branching frames. We also explore the classes of formulas that define the same classes of frames both in K\mathbf{K} (the classical modal logic) and the crisp G\"{o}del modal logic \KG^c. We show that, among others, all Sahlqvist formulas and all formulas ϕ→χ\phi\rightarrow\chi where ϕ\phi and χ\chi are monotone, define the same classes of frames in K\mathbf{K} and \KG^c

    Fuzzy bi-G\"{o}del modal logic and its paraconsistent relatives

    Full text link
    We present the axiomatisation of the fuzzy bi-G\"{o}del modal logic (formulated in the language containing △\triangle and treating the coimplication as a defined connective) and establish its PSpace-completeness. We also consider its paraconsistent relatives defined on fuzzy frames with two valuations e1e_1 and e2e_2 standing for the support of truth and falsity, respectively, and equipped with \emph{two fuzzy relations} R+R^+ and R−R^- used to determine supports of truth and falsity of modal formulas. We establish embeddings of these paraconsistent logics into the fuzzy bi-G\"{o}del modal logic and use them to prove their PSpace-completeness and obtain the characterisation of definable frames

    Non-standard modalities in paraconsistent G\"{o}del logic

    Full text link
    We introduce a paraconsistent expansion of the G\"{o}del logic with a De Morgan negation ¬\neg and modalities ■\blacksquare and ⧫\blacklozenge. We equip it with Kripke semantics on frames with two (possibly fuzzy) relations: R+R^+ and R−R^- (interpreted as the degree of trust in affirmations and denials by a given source) and valuations v1v_1 and v2v_2 (positive and negative support) ranging over [0,1][0,1] and connected via ¬\neg. We motivate the semantics of ■ϕ\blacksquare\phi (resp., ⧫ϕ\blacklozenge\phi) as infima (suprema) of both positive and negative supports of ϕ\phi in R+R^+- and R−R^--accessible states, respectively. We then prove several instructive semantical properties of the logic. Finally, we devise a tableaux system for branching fragment and establish the complexity of satisfiability and validity.Comment: arXiv admin note: text overlap with arXiv:2303.1416

    Towards a logical foundation of randomized computation

    Get PDF
    This dissertation investigates the relations between logic and TCS in the probabilistic setting. It is motivated by two main considerations. On the one hand, since their appearance in the 1960s-1970s, probabilistic models have become increasingly pervasive in several fast-growing areas of CS. On the other, the study and development of (deterministic) computational models has considerably benefitted from the mutual interchanges between logic and CS. Nevertheless, probabilistic computation was only marginally touched by such fruitful interactions. The goal of this thesis is precisely to (start) bring(ing) this gap, by developing logical systems corresponding to specific aspects of randomized computation and, therefore, by generalizing standard achievements to the probabilistic realm. To do so, our key ingredient is the introduction of new, measure-sensitive quantifiers associated with quantitative interpretations. The dissertation is tripartite. In the first part, we focus on the relation between logic and counting complexity classes. We show that, due to our classical counting propositional logic, it is possible to generalize to counting classes, the standard results by Cook and Meyer and Stockmeyer linking propositional logic and the polynomial hierarchy. Indeed, we show that the validity problem for counting-quantified formulae captures the corresponding level in Wagner's hierarchy. In the second part, we consider programming language theory. Type systems for randomized \lambda-calculi, also guaranteeing various forms of termination properties, were introduced in the last decades, but these are not "logically oriented" and no Curry-Howard correspondence is known for them. Following intuitions coming from counting logics, we define the first probabilistic version of the correspondence. Finally, we consider the relationship between arithmetic and computation. We present a quantitative extension of the language of arithmetic able to formalize basic results from probability theory. This language is also our starting point to define randomized bounded theories and, so, to generalize canonical results by Buss

    The Holocaust in Three Generations

    Get PDF
    What form does the dialogue about the family past during the Nazi period take in families of those persecuted by the Nazi regime and in families of Nazi perpetrators and bystanders? What impact does the past of the first generation, and their own way of dealing with it have on the lives of their children and grandchildren?What are the differences between the dialogue about the family past and the Holocaust in families of Nazi perpetrators and in families of Holocaust survivors?This book examines these questions on the basis of selected case studies

    \u27Play the Book Again\u27: Towards a Systems Approach to Game Adaptation

    Get PDF
    Situated at the interstices of game studies, adaptation scholarship, and literary theory, this dissertation puts forth a theoretical framework for effectively analyzing literary game adaptations (that is, playable digital or analog systems that are based upon a work or works of literature) as expressive intertextual systems which facilitate aesthetic experiences. By integrating contemporary game studies with filmic adaptation studies and literary theory, I argue that game adaptations allow us to see how games, adaptations, and indeed all texts can be productively conceived of as Barthesian networks of meaning: collections of interacting formal, narrative, intertextual, and contextual elements from which a user\u27s experience arises. Doing so destabilizes the primacy of concepts that are so often used to justify hierarchical relationships between high art and popular culture, opening up new interpretations of texts which do not lend themselves to analysis via traditional literary or cinematic methodologies. Thinking of adaptations in terms of the systemized relationships between texts, intertexts, and the user rather than as merely derivative copies of a single original also redefines the classically hierarchical relationship between adaptations and their sources that has plagued adaptation studies discourse from its inception. Through my readings of a variety of digital and analog games based on William Shakespeare\u27s Hamlet (Ryan North\u27s gamebook To Be or Not to Be), J.R.R. Tolkien\u27s The Hobbit (Beam Software\u27s Hobbit text-adventure), Jane Austen\u27s Pride and Prejudice (Storybrewers\u27 tabletop roleplaying game Good Society), and Henry David Thoreau\u27s Walden (Tracy Fullerton\u27s contemplative digital walking simulator Walden, a game), I illustrate how thinking of texts as systems affords interpretatively productive play, encouraging users to reinterpret, revise, and remix culture to their own ends

    Automated Reasoning

    Get PDF
    This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

    The Holocaust in Three Generations

    Get PDF
    Victims and Perpetrators What form does the dialogue about the family past during the Nazi period take in families of those persecuted by the Nazi regime and in families of Nazi perpetrators and bystanders? What impact does the past of the first generation, and their own way of dealing with it have on the lives of their children and grandchildren? What are the differences between the dialogue about the family past and the Holocaust in families of Nazi perpetrators and in families of Holocaust survivors? This book examines these questions on the basis of selected case studies
    • …
    corecore