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The book provides a self-contained mathematical introduction to linear optimization for  undergraduate students of Mathematics. This book is equally suitable for Science,  Engineering, and Economics students who are interested in gaining a deeper understanding of the mathematical aspects of the subject. The linear optimization problem is analyzed from different perspectives: topological, algebraic, geometrical, logical, and algorithmic. Nevertheless, no previous knowledge of these subjects is required. The essential details are always provided in a special section at the end of each chapter. The technical material is illustrated with multiple examples, problems with fully-worked solutions, and a range of proposed exercises. In Chapter 1, several formulations of the linear optimization problem are presented and related concerning admissible vectors and optimizers. Then, sufficient conditions for the existence of optimizers based on topological techniques are discussed in Chapter 2. The main objective of Chapter 3 is to provide a way for deciding whether or not an admissible vector is an optimizer, relying on Farkas' Lemma. In Chapter 4, linear algebra is used for computing optimizers via basic admissible vectors. A geometrical characterization of these vectors is the goal of Chapter 5. Duality is discussed in Chapter 6, giving yet a new technique for finding optimizers. An introduction to computational complexity is presented in Chapter 7 with the aim to analyze the efficiency of linear optimization algorithms. The complexity of a brute-force algorithm is shown not to be polynomial. Chapter 8 is targeted at the Simplex Algorithm. It includes the proof of its soundness and completeness and an explanation on its non-polynomial complexity. Finally, Chapter 9 concentrates on the integer optimization problem with an emphasis on totally unimodularity. An algorithm based on the Branch and Bound Technique is analyzed.

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are open access, and available via the College Publications website. This Journal is open access, and available in both printed and electronic formats. It is published by College Publications, on behalf of IfCoLog (www.ifcolog.net).

Logic is-arguably-all about proving, but proofs can be "costly," often impossibly so, and today most are delegated to (partly) automatic provers, namely by so-called SAT solvers, software based on the (Boolean) satisfiability problem, or SAT. This is the dual of the (Boolean) validity problem, or VAL, at the core of the conception of the digital computer via Hilbert's Entscheidungsproblem and the Universal Turing Machine. While these problems-VAL significantly less so than SAT-feature in introductory logic textbooks aimed at computer science students, they are largely or wholly absent from textbooks targeting a mathematical or philosophical studentship. Formal logic: Classic problems and proofs corrects this-in our view-misguided state of affairs by providing the basics of formal classical logic from the central viewpoint of a formal, or computer, language that distinguishes itself from the other formal or computer languages by its ability to preserve truth, thus potentially providing solutions to decision problems formulated in terms of VAL and/or SAT. This fundamental aspect of classical logic, truth-preservation, is elaborated on from three main formal semantics, to wit, Tarskian, Herbrand, and algebraic (Boolean) semantics, which, in turn, via the adequateness results for the standard first-order logic, underlie the main proof systems of direct and indirect, or refutation, proofs, associated to VAL and SAT, respectively.Not focusing on the history of classical logic, this book nevertheless provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is thus an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational.

This book is a collection of papers related to a workshop organized in Geneva in January 2017, part of a big event celebrating the centenary of Ferdinand de Saussure's famous "Cours de Linguistique Générale" (CLG). The topic of this workshop was THE FIRST PRINCIPLE stated in the second section of the first part of the CLG entitled: THE ABITRARINESS OF THE SIGN. Discussions are developed according to the three perspectives presented in the call for papers: (1) The details of the formulation of this principle in the CLG, its proper place (cf. the following sentence of section 2: "No one disputes the principle of the arbitrariness of the sign but it is often easier to discover a truth than to assign it its proper place"). Discussions about the question of arbitrariness of the sign in works by Saussure before the CLG are also welcome. (2) How the arbitrariness of the sign has been formulated and stressed before the CLG by other people than Saussure, in particular, but not exclusively, by people of the second part of the 19th century. Three important names: Boole, Peirce, Bréal. (3) The import and value of this principle and the criticisms it received after the publication of the CLG. Special focus will be given on the opposition between arbitrary sign and symbol (as characterized in the CLG: "the symbol is never arbitrary; it is not empty, for there is the rudiment of a natural bond between the signifier and the signified") in the context of mathematical and logical languages (visual reasoning), traffic signs and pictograms (cf. Neurath's Isotype), typefaces (cf. the work of Adrian Frutiger).

Cet ouvrage propose une analyse épistémologique des modèles scientifiques et de leurs modes d'application, centrée sur la définition et l'identification des objets théoriques. La question des idéalisations en science y est traitée en examinant la portée des connaissances pouvant être tirées de modèles scientifiques idéalisés, et les conditions selon lesquelles elles peuvent concerner certains aspects du monde actuel. En discutant différentes approches courantes de cette question en philosophie des sciences, comme certaines formes de réalisme, de fictionnalisme, ou encore de structuralisme, cet ouvrage développe une épistémologie modale définissant notamment l'identité des propriétés et des relations scientifiques dans une perspective causale et nomologique

Languages, machines, and classical computation is a new undergraduate course book on the conjoined subjects of Formal Languages and Automata & Computability and Complexity. By new, we mean more than its recent publication: It is (more) clearly structured around the Chomsky hierarchy, which acts as its backbone; It has an overall algorithmic approach, with many central algorithms thoroughly and clearly described in a step-by-step manner; No programming language or software plays any role whatsoever in it, guaranteeing thus the (mathematical) generality of the diverse contents; It is to some extent a return to the original textbook approaches of the late 1970's / early 1980's, now often-wrongly-seen as too hard for an undergraduate audience; and, Last but not least, it takes into consideration the fact, largely or wholly ignored by other course books on the aforementioned subjects, that to speak of computation today turns out to be an extremely equivocal business, as many other forms of computation have developed outside what we can call the Turing-von Neumann paradigm.A vast selection of exercises is a crucial component to this course book, with exercises ranging from simple tasks to research projects and explorations of creative skills.All the mathematical topics necessary to the satisfactory grasping of the contents discussed are provided in an introductory chapter, making of this a largely self-contained course book.The present second edition corrects addenda and errata, has both improved and new figures, an additional algorithm, and redesigned exercises.

Is it possible to conceive two perfectly identical objects? Is identity even possible withoutindividuality? How would a perfectly symmetrical universe be? The current philosophical debate on identity, and in particular on the necessity of the Leibniz's principle of the identity of indiscernibles, is complex and multi-faceted. Recent works have indicated that the problem becomes increasingly complex if we apply it to mathematical objects. Is it possible to speak of 'identity' for numbers? How can we identify numbers?Drawing on philosophical accounts on identity and individuality in contemporary metaphysics (analytic and continental), this book explores a new path. The author argues that an identity without individuality is possible. By means of a critique of the idea of the identity of indiscernibles, the book formulates the concept of 'manifold identity', through the concept of 'iteration'. Iteration is a specific transgression of the identity of indiscernibles arising from the collision of two forms of identity: qualitative identity and numerical identity. Nonetheless, a pair of perfectly identical objects is still a paradox, a contradiction.The first thesis of the book is that iteration is a paraconsistent and dialethetical logical structure, which allows for true contradiction. The author applies recent works in non-standard logic and dialetheism (Priest, Routley, Berto) to illustrate how we can make sense of the idea that objects can be perfectly identical but discernible.The second thesis of the book is that iteration is the basis of enumerability and computability. A 'computable object' is an object constructed on the basis of an iterative logic. It is possible to re-interpret all the primary concepts of computability theory through the logic of iteration.

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are open access, and available via the College Publications website. This Journal is open access, and available in both printed and electronic formats. It is published by College Publications, on behalf of IfCoLog (www.ifcolog.net).

Does the Chinese academic discourse on human rights differ from the official one as put forward by the Chinese government? How do Chinese legal theories justify the attribution of human rights and their protection through the law in the context of an authoritarian state? Do Chinese academic theorisations on rights and the law have any capacity to influence the wider public debate in China despite the ideological constraints and censorship imposed on academics by the party in power? In order to answer these questions, this book explores the theories of law and rights by contemporary Chinese legal scholars, paying particular attention to their views on the rule of law and the explanation of rights. It investigates the ways in which legal scholars have made use of arguments from the rediscovered Chinese traditional jurisprudence, the liberal tradition, and the Marxist-Leninist-Maoist canon.

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are open access, and available via the College Publications website. This Journal is open access, and available in both printed and electronic formats. It is published by College Publications, on behalf of IfCoLog (www.ifcolog.net).

Justification logics are closely related to modal logics and can be viewed as a refinement of the latter with machinery for justification manipulation. Justifications are represented directly in the language by terms, which can be interpreted as formal proofs in a deductive system, evidence for knowledge, winning strategy in a game, etc. This more expressive language proved beneficial in both proof theory and epistemology and helped investigate problems ranging from a classical provability semantics for intuitionistic logic to the logical omniscience problem.Justification logic is a new and fast evolving field that offers unexpected new approaches and insights into old problems. Its position at the junction of mathematics, philosophy, and computer science makes it of interest to a wide audience.This book provides a rigorous introduction to justification logic. It covers the basic constructions of justification logic as well as epistemic models and provability semantics. Further it includes chapters on decidability and complexity of justification logics as well as a chapter on self-referentiality. It also contains detailed historic remarks on the subject.

This book provides an introduction to several mathematical topics of importance in Computer Science but often considered to be outside the scope of traditional Discrete Methods courses. It offers basic treatments of Calculus, Complex Numbers, Statistics, and Linear Algebra with a particular emphasis on Spectral Methods.The presentation is intended for students with minimal mathematical background. Its principal aim being to emphasize the significant applications in modern CS for which some awareness of these fields is essential, e.g. Machine Learning, Data Science, Computational Game Theory, and Optimization. The focus is, therefore, directed towards applications in CS rather than detailed mathematical exposition.About the author: Paul Dunne is a Professor of CS at the University of Liverpool where he has worked since 1985. He studied CS at the University of Edinburgh (1977-1981) and completed his PhD research at Warwick University (1981-1984). In his time at Liverpool he has had experience in teaching all levels of undergraduate from first year through to Honours year presenting courses on Computability and Complexity Theory, Algorithms, Operating Systems, and the topic of the present book. He has published research in a range of fields from Boolean Function complexity, phase transition phenomena, AI and Law, complexity in multiagent systems, and has recently been most active in the area of models of Computational Argument.

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2018, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This volume represents a homage to Cristina Burani. She dedicated her research activity mainly to the cognitive processes underlying single word recognition and reading, by exploring both the morpho-lexical and the sublexical variables involved. The contributions to this volume reflect the broad range of interests that have characterised Cristina's scientific life. Cristina Burani is Research Director at the ISTC (Institute of Cognitive Sciences and Technologies), CNR (National Research Council) in Rome. This volume arises from the scientific meeting held in June 2019 to honour her formal retirement. The program dealt with the main topics of Cristina Burani's scientific career, central to Italian Psycholinguistics. During her career, Cristina oriented, inspired and collaborated with many researchers and established the field of Psycholinguistics as an active research area in Italy. This book expresses the admiration and the acknowledgment of her influence on Italian research.

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are open access, and available via the College Publications website. This Journal is open access, and available in both printed and electronic formats. It is published by College Publications, on behalf of IfCoLog (www.ifcolog.net).