The Semantics and Proof Theory of the Logic of Bunched Implications PDF Download
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Author: David J. Pym
Publisher: Springer Science & Business Media
ISBN: 9401700915
Category : Mathematics
Languages : en
Pages : 323
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Book Description
This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.
Author: David J. Pym
Publisher: Springer Science & Business Media
ISBN: 9401700915
Category : Mathematics
Languages : en
Pages : 323
Get Book Here
Book Description
This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.
Author: A. S. Troelstra
Publisher: Cambridge University Press
ISBN: 9780521779111
Category : Computers
Languages : en
Pages : 436
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Book Description
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.
Author: Stefan Kiefer
Publisher: Springer
ISBN: 9783030719944
Category : Mathematics
Languages : en
Pages : 574
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Book Description
This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems.
Author: Alessandro Giordani
Publisher: Springer Nature
ISBN: 3030534871
Category : Philosophy
Languages : en
Pages : 245
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Book Description
This volume clusters together issues centered upon the variety of types of intensional semantics. Consisting of 10 contributions, the volume is based on papers presented at the Trends in Logic 2019 conference. The various chapters introduce readers to the topic, or apply new types of logical semantics to elucidate subtleties of logical systems and natural language semantics. The book introduces hyperintentional systems that aim at solving some open philosophical problems. Specifically, the first three studies focus on relating semantics, while the following ones discuss fundamental issues related to hyper-intensional semantics or develop hyper-intensional frameworks to address issues in modal, epistemic, deontic and action logic. Authors in this volume present original results on logical systems but also extend beyond this by offering philosophical considerations on the topic as well. This volume will appeal to students and researchers in the field of logic.
Author: Stefan Kiefer
Publisher: Springer Nature
ISBN: 3030719952
Category : Mathematics
Languages : en
Pages : 587
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Book Description
This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems.
Author: Roberto Amadio
Publisher: Springer Science & Business Media
ISBN: 3540784977
Category : Computers
Languages : en
Pages : 519
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Book Description
This book constitutes the refereed proceedings of the 11th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2008, held in Budapest, Hungary, in March/April 2008 as part of ETAPS 2008, the European Joint Conferences on Theory and Practice of Software. The 33 revised full papers presented together with the abstract of 1 invited talk were carefully reviewed and selected from 124 submissions. A broad variety of theories and methods to support analysis, synthesis, transformation and verification of programs and software systems are addressed, including the following topics: algebraic models, automata and language theory, behavioural equivalences, categorical models, computation processes over discrete and continuous data, infinite state systems, computational structures, logics of programs, modal, spatial, and temporal logics, models of concurrent, reactive, distributed, and mobile systems, process algebras and calculi, semantics of programming languages, software specification and refinement, type systems and type theory, fundamentals of security, semi-structured data, program correctness and verification.
Author: Jerzy Marcinkowski
Publisher: Springer Science & Business Media
ISBN: 3540230246
Category : Computers
Languages : en
Pages : 529
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Book Description
This book constitutes the refereed proceedings of the 18th International Workshop on Computer Science Logic, CSL 2004, held as the 13th Annual Conference of the EACSL in Karpacz, Poland, in September 2004. The 33 revised full papers presented together with 5 invited contributions were carefully reviewed and selected from 88 papers submitted. All current aspects of logic in computer science are addressed ranging from mathematical logic and logical foundations to methodological issues and applications of logics in various computing contexts.
Author: Leopoldo Bertossi
Publisher: Springer
ISBN: 3540305971
Category : Computers
Languages : en
Pages : 300
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Book Description
Inconsistency arises in many areas in advanced computing. Often inconsistency is unwanted, for example in the specification for a plan or in sensor fusion in robotics; however, sometimes inconsistency is useful. Whether inconsistency is unwanted or useful, there is a need to develop tolerance to inconsistency in application technologies such as databases, knowledge bases, and software systems. To address this situation, inconsistency tolerance is being built on foundational technologies for identifying and analyzing inconsistency in information, for representing and reasoning with inconsistent information, for resolving inconsistent information, and for merging inconsistent information. The idea for this book arose out of a Dagstuhl Seminar on the topic held in summer 2003. The nine chapters in this first book devoted to the subject of inconsistency tolerance were carefully invited and anonymously reviewed. The book provides an exciting introduction to this new field.
Author: Jean-Yves Girard
Publisher: Springer
ISBN: 3540489592
Category : Computers
Languages : en
Pages : 409
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Book Description
This book constitutes the refereed proceedings of the 4th International Conference on Typed Lambda Calculi and Applications, TLCA'99, held in L'Aquila, Italy in April 1999. The 25 revised full papers presented were carefully reviewed and selected from a total of 50 submissions. Also included are two invited demonstrations. The volume reports research results on various aspects of typed lambda calculi. Among the topics addressed are noncommutative logics, type theory, algebraic data types, logical calculi, abstract data types, and subtyping.
Author: Franz Baader
Publisher: Springer Science & Business Media
ISBN: 3540252363
Category : Computers
Languages : en
Pages : 572
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Book Description
This book constitutes the refereed proceedings of the 11th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2004, held in Montevideo, Uruguay in March 2005. The 33 revised full papers presented together with abstracts of 4 invited papers were carefully reviewed and selected from 77 submissions. The papers address all current issues in logic programming, automated reasoning, and AI logics in particular description logics, fuzzy logic, linear logic, multi-modal logic, proof theory, formal verification, protocol verification, constraint logic programming, programming calculi, theorem proving, etc.
