Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.

Philosophy. --- Logic. --- Mathematical Logic and Foundations. --- Logics and Meanings of Programs. --- Philosophy (General). --- Logic design. --- Logic, Symbolic and mathematical. --- Logique --- Structure logique --- Logique symbolique et mathématique --- Philosophy --- Philosophy & Religion --- Logic --- Mental philosophy --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Design, Logic --- Design of logic systems --- Computer logic. --- Mathematical logic. --- Humanities --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Digital electronics --- Electronic circuit design --- Logic circuits --- Machine theory --- Switching theory --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology --- Computer science logic --- Logic, Symbolic and mathematical

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is the first comprehensive introduction to Display Logic in the context of generalized Gentzen calculi. After reviewing several standard and non-standard sequent-style proof systems for modal logics, the author carefully motivates and develops Display Logic, an important refinement of Gentzen's sequent calculus devised by N. Belnap. A general strong cut-elimination theorem is proved that covers a large class of display sequent calculi. Moreover, a proof-theoretic semantics of the modal operators is developed. Proof-theoretic characterizations are also obtained for the logical operations of systems associated with Tarskian structured consequence relations. These systems include constructive logics with strong negation. Using the embedding of intuitionistic logic in S4, display calculi are presented for certain subintuitionistic logics that may be used as monotonic base systems for semantics-based non-monotonic reasoning. Eventually, a first-order display calculus is defined. Its modal extension is general enough to avoid the provability of both the Barcan formula and its converse.

Modality (Logic) --- Modal logic --- Logic --- Nonclassical mathematical logic --- Bisimulation --- Modality (Logic). --- Logic. --- Artificial intelligence. --- Mathematical logic. --- Artificial Intelligence. --- Mathematical Logic and Foundations. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology --- LOGIQUE GENERALE --- LOGIQUE MODALE

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.

Mathematical logic --- Logic --- Computer science --- Computer. Automation --- computers --- programmeren (informatica) --- wiskunde --- logica

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Artificial intelligence. --- Reasoning. --- Logic, Symbolic and mathematical. --- Knowledge, Theory of. --- Philosophy --- Intelligence artificielle --- Raisonnement --- Logique symbolique et mathématique --- Théorie de la connaissance --- Philosophie --- Data processing. --- Informatique --- Artificial intelligence --- Logique symbolique et mathématique --- Théorie de la connaissance --- Logique mathématique --- Philosophy - Data processing. --- Logique --- Knowledge representation

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Philosophy --- Mathematical logic --- Logic --- filosofie --- wiskunde --- logica