IA Scholar Query: A Fomalization of the Binary Object-Role Model based on Logic.
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Internet Archive Scholar query results feedeninfo@archive.orgTue, 05 Jul 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440The provably total recursive functions and the MRDP theorem in Basic Arithmetic and its extensions
https://scholar.archive.org/work/dqrf4dnnqjbv3fx34i3oprmthy
We study Basic Arithmetic, BA introduced by W. Ruitenburg. BA is an arithmetical theory based on basic logic which is weaker than intuitionistic logic. We show that the class of the provably total recursive functions of BA is a proper sub-class of the primitive recursive functions. Three extensions of BA, called BA+U, BA_c and EBA are investigated with relation to their provably total recursive functions. It is shown that the provably total recursive functions of these three extensions of BA are exactly the primitive recursive functions. Moreover, among other things, it is shown that the well-known MRDP theorem does not hold in BA, BA+U, BA_c, but holds in EBA.Mohammad Ardeshir, Erfan Khaniki, Mohsen Shahriariwork_dqrf4dnnqjbv3fx34i3oprmthyTue, 05 Jul 2022 00:00:00 GMTModel-Centric Verification of Artificial Intelligence
https://scholar.archive.org/work/njuev4tygvdcpag5ctsdonojcu
This work shows how provable guarantees can be used to supplement probabilistic estimates in the context of Arti?cial Intelligence (AI) systems. Statistical techniques measure the expected performance of a model, but low error rates say nothing about the ways in which errors manifest. Formal veri?cation of model adherence to design speci?cations can yield certi?cates which explicitly detail the operational conditions under which violations occur. These certi?- cates enable developers and users of AI systems to reason about their trained models in contractual terms, eliminating the chance that otherwise easily preventable harm be in icted due to an unforeseen fault leading to model failure. As an illustration of this concept, we present our veri?cation pipeline named Tree Ensemble Accreditor (TEA). TEA leverages our novel Boolean Satis?ability (SAT) formalism for voting tree ensemble models for classi?cation tasks. Our formalism yields disruptive speed gains over related tree ensemble veri?cation techniques. The efficiency of TEA allows us to verify harder speci?cations on models of larger scales than reported in literature. In a radiation safety context, we show how Local Adversarial Robustness (LAR) of trained models on validation data points can be incorporated into the model selection rocess. We explore the relationship between prediction outcome and model robustness, allowing us to yield the de?nition of LAR that best satis?es the engineering desiderata that the model should be robust only when it makes correct predictions. In an algorithmic fairness context, we show how Global Individual Fairness (GIF) can be tested, both in and out of data support. When the model violates the GIF speci?cation, we enumerate all counterexamples to the formula so we may reveal the structure of unfairness that is absorbed by the model during training. In a clinical context, we show how a Safety-Paramount Engineering Constraint (SPEC) can be satis?ed simply by tuning the prediction threshold of the tree ensemble. This facilitate [...]Nicholas Gisolfiwork_njuev4tygvdcpag5ctsdonojcuThu, 19 May 2022 00:00:00 GMTRituals of apparition in the Theban Magical Library
https://scholar.archive.org/work/d2cef6s53zdkrdu5f5d2ailmyu
This thesis examines the evidence for divinatory practices in Roman Egypt, focusing on rituals for questioning deities, and using the so-called "Theban Magical Library" as the core corpus within which this practice is examined. The first chapter examines the evidence for this archive, its publication and reception history, as well as its form and contents, in terms of physical, scribal, linguistic, and ritual features. This analysis is then used to situate the Library within the cultural context of Roman Egypt, and the historical development of Egyptian magical practice. The second and third chapters focus on the "ritual of apparition", setting out a structural approach that focuses on the way in which recurrent features are combined and elaborated into a wide array of individual rituals. Alongside a lexicographical discussion of Greek and Egyptian terms for such rituals, the second chapter discusses the social context within which these practices may have taken place, and sets out a hypothetical cognitive schema within which the rituals may have been understood and experienced as efficacious. The third chapter focuses on the particular components of these rituals, looking at the way in which objects and actions were fitted into larger rituals, and how variations in their employment affected the way in which they "functioned" as parts of the practitioner's ritual technology.Korshi Dosoowork_d2cef6s53zdkrdu5f5d2ailmyuMon, 28 Mar 2022 00:00:00 GMTFreezing, Bounded-Change and Convergent Cellular Automata
https://scholar.archive.org/work/yd2zkpdnsjfcxozwbdgnbsbq64
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes a bounded number of state changes in any orbit, and finally cellular automata where each orbit converges to some fixed point. Many examples studied in the literature fit into these definitions, in particular the works on cristal growth started by S. Ulam in the 60s. The central question addressed here is how the computational power and computational hardness of basic properties is affected by the constraints of convergence, bounded number of change, or local decreasing of states in each cell. By studying various benchmark problems (short-term prediction, long term reachability, limits) and considering various complexity measures and scales (LOGSPACE vs. PTIME, communication complexity, Turing computability and arithmetical hierarchy) we give a rich and nuanced answer: the overall computational complexity of such cellular automata depends on the class considered (among the three above), the dimension, and the precise problem studied. In particular, we show that all settings can achieve universality in the sense of Blondel-Delvenne-K\r{u}rka, although short term predictability varies from NLOGSPACE to P-complete. Besides, the computability of limit configurations starting from computable initial configurations separates bounded-change from convergent cellular automata in dimension~1, but also dimension~1 versus higher dimensions for freezing cellular automata. Another surprising dimension-sensitive result obtained is that nilpotency becomes decidable in dimension~ 1 for all the three classes, while it stays undecidable even for freezing cellular automata in higher dimension.Nicolas Ollinger, Guillaume Theyssierwork_yd2zkpdnsjfcxozwbdgnbsbq64Mon, 31 Jan 2022 00:00:00 GMT