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The Bulletin of Symbolic Logic was established in 1995 by the Association for Symbolic Logic (ASL) to provide a journal of high standards that would be both accessible and of interest to as wide an audience as possible. Its stated purpose is to keep the logic community informed quickly of important developments in all parts of the discipline. The Bulletin of Symbolic Logic primarily publishes two types of papers: articles and communications. Articles present topics of broad interest that should be accessible to a large audience. They can be purely expository, survey, or historical articles, or they may contain, in addition, new ideas or results or new approaches to old ones. Communications are announcements of important new results and ideas. They are expected to include a description of the new work, as well as enough history, background, and explanation to make the significance of the work apparent to a wide audience. Papers in The Bulletin may deal with any aspect of logic, including mathematical or philosophical logic, logic in computer science or linguistics, the history or philosophy of logic, or applications of logic to other fields.

Logic, Symbolic and mathematical --- JEX4 --- Logique symbolique et mathématique --- Logic, Symbolic and mathematical. --- Symbolische logica. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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This collection of papers deal with challenges in disciplines such as complexity theory, games, algorithms and semi group theory and discuss current chellenges in this field

Machine theory. --- Logic, Symbolic and mathematical. --- Computer science --- Computational complexity. --- Mathematics. --- Complexity, Computational --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Mathematics --- Machine theory --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Algorithms --- Logic, Symbolic and mathematical --- Recursive functions --- Robotics

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This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.

Logic --- Philosophy --- Philosophy & Religion --- Philosophy. --- Logic. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Psychology --- Science --- Reasoning --- Thought and thinking --- Mental philosophy --- Humanities --- Methodology --- Logic, Symbolic and mathematical. --- Computer science. --- Informatics --- Proof theory --- Semantics - Mathematical models --- Logic, symbolic and mathematical --- Semantics

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A concise and self-contained introduction to causal inference, increasingly important in data science and machine learning.The mathematization of causality is a relatively recent development, and has become increasingly important in data science and machine learning. This book offers a self-contained and concise introduction to causal models and how to learn them from data. After explaining the need for causal models and discussing some of the principles underlying causal inference, the book teaches readers how to use causal models: how to compute intervention distributions, how to infer causal models from observational and interventional data, and how causal ideas could be exploited for classical machine learning problems. All of these topics are discussed first in terms of two variables and then in the more general multivariate case. The bivariate case turns out to be a particularly hard problem for causal learning because there are no conditional independences as used by classical methods for solving multivariate cases. The authors consider analyzing statistical asymmetries between cause and effect to be highly instructive, and they report on their decade of intensive research into this problem. The book is accessible to readers with a background in machine learning or statistics, and can be used in graduate courses or as a reference for researchers. The text includes code snippets that can be copied and pasted, exercises, and an appendix with a summary of the most important technical concepts.

Mobile & handheld device programming / Apps programming --- Machine learning --- Neural networks & fuzzy systems --- Machine learning. --- Logic, Symbolic and mathematical. --- Inference. --- Computer algorithms. --- Causation. --- Causality --- Cause and effect --- Effect and cause --- Final cause --- Beginning --- God --- Metaphysics --- Philosophy --- Necessity (Philosophy) --- Teleology --- Algorithms --- Ampliative induction --- Induction, Ampliative --- Inference (Logic) --- Reasoning --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Learning, Machine --- Artificial intelligence --- Machine theory

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This book is open access under a CC BY 4.0 license. This book addresses the age-old problem of infinite regresses in epistemology. How can we ever come to know something if knowing requires having good reasons, and reasons can only be good if they are backed by good reasons in turn? The problem has puzzled philosophers ever since antiquity, giving rise to what is often called Agrippa's Trilemma. The current volume approaches the old problem in a provocative and thoroughly contemporary way. Taking seriously the idea that good reasons are typically probabilistic in character, it develops and defends a new solution that challenges venerable philosophical intuitions and explains why they were mistakenly held. Key to the new solution is the phenomenon of fading foundations, according to which distant reasons are less important than those that are nearby. The phenomenon takes the sting out of Agrippa's Trilemma; moreover, since the theory that describes it is general and abstract, it is readily applicable outside epistemology, notably to debates on infinite regresses in metaphysics. The book is a potential game-changer and a must for any advanced student or researcher in the field.

Philosophy. --- Operations research. --- Decision making. --- Epistemology. --- Mathematical logic. --- Physics. --- Statistics. --- Mathematical Logic and Foundations. --- Statistical Theory and Methods. --- History and Philosophical Foundations of Physics. --- Operation Research/Decision Theory. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Epistemology --- Theory of knowledge --- Philosophy --- Psychology --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Mental philosophy --- Humanities --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Decision making --- Genetic epistemology. --- Logic, Symbolic and mathematical. --- Mathematical statistics. --- Operations Research/Decision Theory. --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Developmental psychology --- Knowledge, Theory of --- Statistics . --- epistemic justification --- infinite regress --- epistemology --- ethics --- metaphysics --- philosophy