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We study the model-checking problem for first- and monadic second-order logic on finite relational structures. The problem of verifying whether a formula of these logics is true on a given structure is considered intractable in general, but it does become tractable on interesting classes of structures, such as on classes whose Gaifman graphs have bounded treewidth. In this article, we continue this line of research and study model-checking for first- and monadic second-order logic in the presence of an ordering on the input structure. We do so in two settings: the general ordered case, where the input structures are equipped with a fixed order or successor relation, and the order-invariant case, where the formulas may resort to an ordering, but their truth must be independent of the particular choice of order. In the first setting we show very strong intractability results for most interesting classes of structures. In contrast, in the order-invariant case we obtain tractability results for order-invariant monadic second-order formulas on the same classes of graphs as in the unordered case. For first-order logic, we obtain tractability of successor-invariant formulas on classes whose Gaifman graphs have bounded expansion. Furthermore, we show that model-checking for order-invariant first-order formulas is tractable on coloured posets of bounded width. ; European Research Council (ERC) 648527 CE-ITI European Associated Laboratory "Structures in Combinatorics" (LEA STRUCO) P202/12/G061 National Science Centre of Poland UMO-2015/19/P/ST6/03998 European Union (EU) 665778 CONICYT, PIA/Concurso Apoyo a Centros Cientificos y Tecnologicos de Excelencia con Financiamiento Basal AFB170001 ERCCZ LL-1201

AbstractNew closure theorems for shock models in reliability theory are presented. If the number of shocks to failure and the times between the arrivals of shocks have probability distributions of phase type, then so has the time to failure. PH‐distributions are highly versatile and may be used to model many qualitative features of practical interest. They are also well‐suited for algorithmic implementation. The computational aspects of our results are discussed in some detail.

Artificial Intelligence and algorithms are increasingly able to replace human workers in cognitively sophisticated tasks, including ones related to justice. Many governments and international organizations are discussing policies related to the application of algorithmic judges in courts. In this paper, we investigate the public perceptions of algorithmic judges. Across two experiments (N = 1,822), and an internal meta-analysis (N = 3,039), our results show that even though court users acknowledge several advantages of algorithms (i.e., cost and speed), they trust human judges more and have greater intentions to go to the court when a human (vs. an algorithmic) judge adjudicates. Additionally, we demonstrate that the extent that individuals trust algorithmic and human judges depends on the nature of the case: trust for algorithmic judges is especially low when legal cases involve emotional complexities (vs. technically complex or uncomplicated cases).

Intro -- Preface -- Contents -- About the Author -- Part I Foundations -- 1 Introduction to Stochastic Optimisation -- 1.1 Introduction -- 1.2 Conventional Optimisation Methods -- 1.3 Modern Stochastic Methods -- 1.3.1 Heuristics -- 1.3.2 Meta-Heuristics -- 1.3.3 No Free Lunch Theorems -- 1.3.4 Evolutionary Algorithms (EAs) -- 1.3.5 Swarm Intelligence (SI) -- 1.3.6 Socio-inspired Algorithms -- 1.3.7 Physics Inspired Algorithms -- 1.3.8 Hyper-Heuristics -- 1.4 Summary -- References -- 2 Introduction to Culture -- 2.1 Introduction -- 2.2 What is the Culture? -- 2.3 Characteristic Features of Culture -- 2.4 Cultural Learning in Humans and Animals -- 2.5 Cultural Evolution -- 2.6 Social Learning Biases -- 2.7 Who Can Change Cultural Variants? -- 2.8 Summary -- References -- 3 Cultural Algorithms (CAs) -- 3.1 Introduction -- 3.2 Overall Framework -- 3.3 Population Space -- 3.4 Belief Space -- 3.4.1 Situational Knowledge -- 3.4.2 Normative Knowledge -- 3.4.3 History Knowledge -- 3.4.4 Topographical Knowledge -- 3.4.5 Domain Knowledge -- 3.5 Communication Protocols -- 3.5.1 Acceptance Function -- 3.5.2 Influence Function -- 3.6 Cultural Adjustment -- 3.7 Algorithmic Steps -- 3.8 Illustrative Example -- 3.9 Summary -- References -- Part II Application of Cultural Algorithms -- 4 Applications of Cultural Algorithms in Engineering -- 4.1 Introduction -- 4.2 Civil Engineering -- 4.2.1 Transportation Engineering -- 4.2.2 Structural Engineering -- 4.2.3 Environmental Engineering -- 4.2.4 Urban Engineering -- 4.2.5 Water Engineering -- 4.3 Mechanical Engineering -- 4.3.1 Damage Detection -- 4.3.2 Optimum Design -- 4.3.3 Composite Structures -- 4.3.4 Optimal Vibration Control -- 4.3.5 Vehicle Safety -- 4.3.6 Flight Control -- 4.3.7 Gas Turbine Operation -- 4.3.8 Renewable Energy -- 4.4 Chemical Engineering -- 4.4.1 Penicillin Production.

Algorithms decide who sees which ad. – Logos: Meta; Screenshot: Meta Ad Library; Montage: netzpolitik.orgMeta has deployed a new AI system to fix its algorithmic bias problem for housing ads in the US. But it's probably more band-aid than AI fairness solution. Gaps in Meta's compliance report make it difficult to verify if the system is working as intended, which may preview what's to come from more Big Tech compliance reporting in the EU.

I Duality Theory -- Ascent Ray Theorems and Some Applications -- Semi-Infinite Programming Duality: How Special Is It? -- A Saddle Value Characterization of Fan's Equilibrium Points -- Duality in Semi-Infinite Linear Programming -- On the Role of Duality in the Theory of Moments -- Existence Theorems in Semi-Infinite Programs -- II Algorithmic Developments -- An Algorithm for a Continuous Version of the Assignment Problem -- Numerical Estimation of Optima by Use of Duality Inequalities -- Globalization of Locally Convergent Algorithms for Nonlinear Optimization Problems with Constraints -- A Three-Phase Algorithm for Semi-Infinite Programs -- A Review of Numerical Methods for Semi-Infinite Optimization -- An Algorithm for Minimizing Polyhedral Convex Functions -- Numerical Experiments with Globally Convergent Methods for Semi-Infinite Programming Problems -- III Problem Analysis and Modeling -- On the Partial Construction of the Semi-Infinite Banzhaf Polyhedron -- Semi-Infinite and Fuzzy Set Programming -- Semi-Infinite Optimization in Engineering Design -- A Moment Inequality and Monotonicity of an Algorithm -- IV Optimality Conditions and Variational Principles -- Second Order Conditions in Nonlinear Nonsmooth Problems of Semi-Infinite Programming -- On Stochastic Control Problems with Impulse Cost Vanishing -- Dual Variational Principles in Mechanics and Physics -- Authors, Participants, and Affiliations -- Referees -- Table of Contents of the Book of Abstracts.

Intro -- 1 Shakespeare`s tertium non datur -- 1.1 Author`s note -- 1.2 On the state of science -- 1.3 To be, or not to be? -- 1.4 Meta linguistic mathematics -- 1.5 Existential Term Logic -- 1.5.1 The First Axiom of Contradictio in Existentia -- 1.5.2 The Second Axiom of Contradictio in Existentia -- 1.5.3 The Third Axiom of Contradictio in Existentia -- 1.5.4 The Fourth Axiom of Contradictio in Existentia -- 1.5.5 The Fifth Axiom of Contradictio in Existentia or Gödel`s Hamlet -- 1.5.6 The Sixth Axiom of Contradictio in Existentia or the broken crosses -- 1.5.7 The rise of the Phoenix: Transformatio Capitalis and Temperatio Entis -- 1.6 Under the spell of the Ultimus Moriturorum -- 2 Abbasidien Trumen or the deconstruction of reality -- 2.1 Showtime -- 2.2 Meta coding, ever so clever -- 2.3 Mind the gap -- 2.4 Set director Sir Isaac Newton -- 2.5 Truman economist Léon Walras -- 3 Exchange, price and money -- 3.1 The meta arithmetic locality functions -- 3.2 The basic exchange function -- 3.3 The basic price function -- 3.4 Why money matters in microeconomic theory -- 3.5 The microeconomic exchange model -- 3.6 The Six Arithmetic Incompleteness Theorems -- 3.7 Labour and property rights -- 3.7.1 Why labour has no price -- 3.7.2 Reenthroning Locke The Elder -- 3.8 "Bank book credit" -- 3.8.1 The exchange of claims -- 3.8.2 "Bank interest" -- 3.8.3 The Circuit Multiplier -- 3.9 New corporate finance -- 3.9.1 Cashflow based bills of exchange -- 3.9.2 Red Bonds as non-legal tender -- 3.9.3 Red Bonds in online exchange communities -- 3.9.4 Red Bonds comparative cost of capital analysis -- 4 Colour Capital markets -- 4.1 The Colour Capital stock market -- 4.2 The Colour Capital fixed income market -- 4.3 The future of money capital -- Formulary -- Bibliography.

AbstractRecent progress in large language models has led to applications that can (at least) simulate possession of full moral agency due to their capacity to report context-sensitive moral assessments in open-domain conversations. However, automating moral decision-making faces several methodological as well as ethical challenges. They arise in the fields of bias mitigation, missing ground truth for moral "correctness", effects of bounded ethicality in machines, changes in moral norms over time, risks of using morally informed AI systems as actual advice, as well as societal implications an increasing importance of algorithmic moral decision-making would have. This paper comments on all these challenges and provides critical considerations for future research on full artificial moral agency. Importantly, some of the adduced challenges can be met by more careful technology design, but others necessarily require engagement with core problems of meta-ethics.

In his proof of the first incompleteness theorem, Kurt Gödel provided a method of showing the truth of specific arithmetical statements on the condition that all the axioms of a certain formal theory of arithmetic are true. Furthermore, the statement whose truth is shown in this way cannot be proved in the theory in question. Thus it may seem that the relation of logical consequence is wider than the relation of derivability by a pre-defined set of rules. The aim of this paper is to explore under which assumptions the Gödelian statement can rightly be considered a logical consequence of the axioms of the theory in question. It is argued that this is the case only when the all the theorems of the theory in question are understood as statements of the same kind (and true in the same sense) as statements of arithmetic and statements about provability in the theory, and only if the language of the theory contains logical expressions allowing to include certain predicates of meta-language in the language of the theory.

Socio-political problems are discussed in this article connected with the provision of socio-cultural integrity of the society in modern time of mass digitalization and introduction of the automatic and algorithmic systems. In the content of this article digitalization is considered as a global socio-political project, oriented for substitution traditional bases of identification and organization communities. This project is considered from critical position and is based, that its necessary state – oriented policy, directed for conservation and reproduction the historical memory, socio-cultural dominant of the development the society and also metapolitical and meta-legal foundation for sustainability of the political – legal organization in the 21st century.

The authors speak about the thesis about further convergence of the digital and cultural trends of transformations of socio-political system, when processes of digitalization will acquire more and more socio-cultural particularity of the development.

Part 4: Complex System Modelling and Simulation ; International audience ; The price of copper and its variations represent a very important financial issue for mining companies and for the Chilean government because of its impact on the national economy. The price of commodities such as copper is highly volatile, dynamic and troublous. Due to this, forecasting is very complex. Using publicly data from October 24th of 2013 to August 29th of 2014 a multivaried based model using meta-heuristic optimization techniques is proposed. In particular, we use Genetic Algorithms and Simulated Annealing in order to find the best fitting parameters to forecast the variation on the copper price. A non-parametric test proposed by Timmermann and Pesaran is used to demonstrate the forecasting capacity of the models. Our numerical results show that the Genetic Algorithmic approach has a better performance than Simulated Annealing, being more effective for long range forecasting.

THE CONCEPT OF THE SYSTEM OF LAW IN THE LIGHT OF POLITICAL CONFLICTSThe starting point for the presented text is the general belief in the culture of statutory law assumption made in the study of legal texts, that the law is systemic in character. This view has strongly influenced so far the arguments used in legal disputes. The fundamental question put here is the question whether meta-rules, being a consequence of the thesis on the systemic character of law, may be reasonably in a manner acceptable to the parties applied to such legal disputes, which may be qualified also as political conflicts. The answer is positive, yet under certain condition: "systemic character" trait, raised by analytical theories of law, should be used only in so-called "easy cases", as "hard cases" inevitably belong to a competitive domain of so-termed "political philosophy". This could imply a significant narrowing of the scope of application of some theorems belonging to these trends in the field of analytical legal theory, which have been dominant in the Polish legal thought. This includes mainly claims connected with the so-called "deep structure of legal science", eg. a theorem of rationality of the lawgiver.