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Proof Theory

Author : Katalin Bimbo
ISBN : 9781466564688
Genre : Mathematics
File Size : 33.66 MB
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Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics. The book is suitable for a wide audience and can be used in advanced undergraduate or graduate courses. Computer scientists will discover intriguing connections between sequent calculi and resolution as well as between sequent calculi and typed systems. Those interested in the constructive approach will find formalizations of intuitionistic logic and two calculi for linear logic. Mathematicians and philosophers will welcome the treatment of a range of variations on calculi for classical logic. Philosophical logicians will be interested in the calculi for relevance logics while linguists will appreciate the detailed presentation of Lambek calculi and their extensions.
Category: Mathematics

Logic Language Information And Computation

Author : Lawrence S. Moss
ISBN : 9783662576694
Genre : Mathematics
File Size : 68.19 MB
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Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 25th Workshop on Logic, Language, Information and Communication, WoLLIC 2018, held inBogota, Colombia, in July 2018. The 16 full papers together with 3 short papers and 3 invited talks presented were fully reviewed and selected from 30 submissions. The vision for the conference is to provide an annual forum which is large enough to provide meaningful interactions between logic and the sciences related to information and computation.
Category: Mathematics

Basic Proof Theory

Author : A. S. Troelstra
ISBN : 0521779111
Genre : Computers
File Size : 52.42 MB
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Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.
Category: Computers

Automated Reasoning With Analytic Tableaux And Related Methods

Author : Renate A. Schmidt
ISBN : 9783319669021
Genre : Computers
File Size : 39.72 MB
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This book contains the proceedings of the 26th International Conference on Automated Reasoning with Analytics Tableaux and Related Methods, TABLEAUX 2017, held in Brasília, Bazil, in September 2017. The 19 contributed papers presented in this volume were carefully reviewed and selected from 27 submissions.They are organized in topical sections named: Sequent systems; tableaux; transitive closure and cyclic proofs; formalization and complexity. Also included are papers of three invited speakers.
Category: Computers

Handbook Of Discrete And Combinatorial Mathematics

Author : Kenneth H. Rosen
ISBN : 9781351644051
Genre : Mathematics
File Size : 86.13 MB
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Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.
Category: Mathematics

A Proof Theory For Description Logics

Author : Alexandre Rademaker
ISBN : 9781447140023
Genre : Mathematics
File Size : 45.5 MB
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Description Logics (DLs) is a family of formalisms used to represent knowledge of a domain. They are equipped with a formal logic-based semantics. Knowledge representation systems based on description logics provide various inference capabilities that deduce implicit knowledge from the explicitly represented knowledge. A Proof Theory for Description Logics introduces Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ). Cut-elimination and Normalization are proved for the calculi. The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes.
Category: Mathematics

Combinatory Logic

Author : Katalin Bimbó
ISBN : 9781439800003
Genre : Computers
File Size : 65.17 MB
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Combinatory logic is one of the most versatile areas within logic that is tied to parts of philosophical, mathematical, and computational logic. Functioning as a comprehensive source for current developments of combinatory logic, this book is the only one of its kind to cover results of the last four decades. Using a reader-friendly style, the author presents the most up-to-date research studies. She includes an introduction to combinatory logic before progressing to its central theorems and proofs. The text makes intelligent and well-researched connections between combinatory logic and lambda calculi and presents models and applications to illustrate these connections.
Category: Computers

Type Theory And Formal Proof

Author : Rob Nederpelt
ISBN : 9781316061084
Genre : Computers
File Size : 59.37 MB
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Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. The authors begin with untyped lambda calculus and proceed to several fundamental type systems, including the well-known and powerful Calculus of Constructions. The book also covers the essence of proof checking and proof development, and the use of dependent type theory to formalise mathematics. The only prerequisite is a basic knowledge of undergraduate mathematics. Carefully chosen examples illustrate the theory throughout. Each chapter ends with a summary of the content, some historical context, suggestions for further reading and a selection of exercises to help readers familiarise themselves with the material.
Category: Computers

Lambda Calculus With Types

Author : Henk Barendregt
ISBN : 9780521766142
Genre : Mathematics
File Size : 34.37 MB
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This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.
Category: Mathematics

Automated Reasoning

Author : Nicola Olivetti
ISBN : 9783319402291
Genre : Mathematics
File Size : 76.21 MB
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This book constitutes the refereed proceedings of the 8th International Joint Conference on Automated Reasoning, IJCAR 2016, held in Coimbra, Portugal, in June/July 2016. IJCAR 2014 was a merger of three leading events in automated reasoning, namely CADE (International Conference on Automated Deduction), FroCoS (International Symposium on Frontiers of Combining Systems) and TABLEAUX (International Conference on Automated Reasoning with Analytic Tableaux and Related Methods). The 26 revised full research papers and 9 system descriptions presented together with 4 invited talks were carefully reviewed and selected from 79 submissions. The papers have been organized in topical sections on satisfiability of Boolean formulas, satisfiability modulo theory, rewriting, arithmetic reasoning and mechanizing mathematics, first-order logic and proof theory, first-order theorem proving, higher-order theorem proving, modal and temporal logics, non-classical logics, and verification.
Category: Mathematics