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“Logic”, as understood in this volume, is the set of knowledge at the basis of man’s reasoning faculties: understanding, analysing, arguing. The text presents a review of topics which are useful to strengthen the skills related to reasoning faculties through a brief introduction to the theoretical aspects and exercises intended to assess the understanding. The volume is divided into parts, which are organised in teaching units. The parts and units are presented in such a way that, following the thread in the order in which they are proposed, we move from one topic to the next, acquiring the prerequisites necessary for to what comes after. The text therefore lends itself to a “systematic” use, aimed at an extensive study. However, nothing prevents the reader from adapting the material to other needs, choosing only a few topics that they consider useful to integrate their knowledge, to do a “review” or to further practice on already known topics.

Philosophy: logic --- Occupational & industrial psychology --- Teaching of specific groups & persons with special educational needs --- Mathematical foundations --- Philosophy of science

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web intelligence --- system modelling --- data mining --- machine learning --- mathematical foundations of computational intelligence --- Computational intelligence --- Computational intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer. Automation --- Computer Science

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This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.

Philosophy of mathematics --- History of mathematics --- Mathematical foundations --- Lorenzen on Constructive Mathematics --- Application to Constructive Measure Theory --- Lorenzeṇ’s Work on Lattice-groups and Divisibility Theory --- Krull’s Fundamentalsatz for Integral Domains --- Modern Set Theory and Lorenzen’s Critique of Actual Infinity --- Grundlagenforschung --- Lorenzen’s Consistency Proof and Hilbert’s Larger Programme --- Lorenzen's Dialogue Game --- Game Semantics for Substructural Logics --- Constructive Examination of a Russell-style Ramified Type Theory --- Operative Justification of Logic and Mathematics --- Lorenzen on Proof-theoretic Semantics --- Lorenzen on Databank Management --- Lorenzen on Stochastics --- Russell-style Ramified Type Theory --- Lorenzen and Erlangen School of Methodical Constructivism --- Mathematics --- Mathematics. --- History. --- Mathematical logic. --- Philosophy of Mathematics. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Philosophy. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Math --- Science --- Logic of mathematics --- Mathematics, Logic of

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This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Mathematical logic. --- Computer science—Mathematics. --- Programming languages (Electronic computers). --- Computer programming. --- Artificial intelligence. --- Computer logic. --- Computer organization. --- Mathematical Logic and Foundations. --- Discrete Mathematics in Computer Science. --- Programming Languages, Compilers, Interpreters. --- Programming Techniques. --- Logic in AI. --- Computer Systems Organization and Communication Networks. --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Electronic data processing --- Languages, Artificial --- Organization, Computer --- Electronic digital computers --- Computer science logic --- Logic, Symbolic and mathematical --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Computers --- Electronic computer programming --- Programming (Electronic computers) --- Coding theory --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Programming --- Mathematical Logic and Foundations --- Discrete Mathematics in Computer Science --- Programming Languages, Compilers, Interpreters --- Programming Techniques --- Logic in AI --- Computer Systems Organization and Communication Networks --- categorical models and logics --- language theory, automata, and games --- modal, spatial, and temporal logics --- type theory and proof theory --- concurrency theory and process calculi --- rewriting theory --- semantics of programming languages --- program analysis, correctness, transformation, and verification --- logics of programming --- software specification and refinement --- emerging models of computation --- logical aspects of computational complexity --- models of software security --- logical foundations of data bases --- mathematics --- artificial intellegence --- formal logic --- linguistics --- Mathematical foundations --- Discrete mathematics --- Maths for computer scientists --- Programming & scripting languages: general --- Compilers & interpreters --- Computer programming / software engineering --- Artificial intelligence --- Computer networking & communications --- Discrete mathematics. --- Compilers (Computer programs). --- Logic programming. --- Computer engineering. --- Computer networks. --- Compilers and Interpreters. --- Computer Engineering and Networks. --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Computer programming --- Compiling programs (Computer programs) --- Computer programs --- Programming software --- Systems software --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Distributed processing --- Design and construction