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Título : Analysis and Synthesis of Logics : How to Cut and Paste Reasoning Systems Tipo de documento: documento electrónico Autores: Walter Carnielli ; SpringerLink (Online service) ; Marcelo Coniglio ; Dov M. Gabbay ; Paula Gouveia ; Sernadas, Cristina Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2008 Colección: Applied Logic Series, ISSN 1386-2790 num. 35 Número de páginas: XVI, 602 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-6782-2 Idioma : Inglés (eng) Palabras clave: Mathematics Logic Mathematical logic and Foundations Formal Languages Clasificación: 51 Matemáticas Resumen: Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature (for instance, two Hilbert calculi or a Hilbert calculus and a tableau calculus). The important issue of preservation of properties is extensively addressed. For instance, sufficient conditions are provided for a combined logic to be sound and complete when the original component logics are known to be sound and complete. The book brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). It also provides examples of potential applications in emergent fields like security protocols, quantum computing, networks and argumentation theory, besides discussing more classical applications like software specification, knowledge representation, computational linguistics and modular automated reasoning. This monograph will be of interest to researchers and graduate students in mathematical logic, theory of computation and philosophical logic with no previous knowledge of the subject of combining and decomposing logics, but with a working knowledge of first-order logic. The book will also be relevant for people involved in research projects where logic is used as a tool and the need for working with several logics at the same time is mandatory (for instance, temporal, epistemic and probabilistic logics) Nota de contenido: Introductory overview -- Splicing logics: Syntactic fibring -- Splicing logics: Semantic fibring -- Heterogeneous fibring -- Fibring non-truth functional logics -- Fibring first-order logics -- Fibring higher-order logics -- Modulated fibring -- Splitting logics -- New trends: Network fibring -- Summing-up and outlook En línea: http://dx.doi.org/10.1007/978-1-4020-6782-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34289 Analysis and Synthesis of Logics : How to Cut and Paste Reasoning Systems [documento electrónico] / Walter Carnielli ; SpringerLink (Online service) ; Marcelo Coniglio ; Dov M. Gabbay ; Paula Gouveia ; Sernadas, Cristina . - Dordrecht : Springer Netherlands, 2008 . - XVI, 602 p : online resource. - (Applied Logic Series, ISSN 1386-2790; 35) .
ISBN : 978-1-4020-6782-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Logic Mathematical logic and Foundations Formal Languages Clasificación: 51 Matemáticas Resumen: Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature (for instance, two Hilbert calculi or a Hilbert calculus and a tableau calculus). The important issue of preservation of properties is extensively addressed. For instance, sufficient conditions are provided for a combined logic to be sound and complete when the original component logics are known to be sound and complete. The book brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). It also provides examples of potential applications in emergent fields like security protocols, quantum computing, networks and argumentation theory, besides discussing more classical applications like software specification, knowledge representation, computational linguistics and modular automated reasoning. This monograph will be of interest to researchers and graduate students in mathematical logic, theory of computation and philosophical logic with no previous knowledge of the subject of combining and decomposing logics, but with a working knowledge of first-order logic. The book will also be relevant for people involved in research projects where logic is used as a tool and the need for working with several logics at the same time is mandatory (for instance, temporal, epistemic and probabilistic logics) Nota de contenido: Introductory overview -- Splicing logics: Syntactic fibring -- Splicing logics: Semantic fibring -- Heterogeneous fibring -- Fibring non-truth functional logics -- Fibring first-order logics -- Fibring higher-order logics -- Modulated fibring -- Splitting logics -- New trends: Network fibring -- Summing-up and outlook En línea: http://dx.doi.org/10.1007/978-1-4020-6782-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34289 Ejemplares
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Título : Hybrid Logic and its Proof-Theory Tipo de documento: documento electrónico Autores: Torben Braüner ; SpringerLink (Online service) Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2011 Colección: Applied Logic Series, ISSN 1386-2790 num. 37 Número de páginas: XIII, 231 p Il.: online resource ISBN/ISSN/DL: 978-94-007-0002-4 Idioma : Inglés (eng) Palabras clave: Philosophy Logic Mathematical logic and Formal Languages Foundations Clasificación: 51 Matemáticas Resumen: This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic) Nota de contenido: Preface, -- 1 Introduction to Hybrid Logic -- 2 Proof-Theory of Propositional Hybrid Logic -- 3 Tableaus and Decision Procedures for Hybrid Logic -- 4 Comparison to Seligman’s Natural Deduction System -- 5 Functional Completeness for a Hybrid Logic -- 6 First-Order Hybrid -- 7 Intensional First-Order Hybrid Logic -- 8 Intuitionistic Hybrid Logic -- 9 Labelled Versus Internalized Natural Deduction -- 10 Why does the Proof-Theory of Hybrid Logic Behave soWell? - References -- Index En línea: http://dx.doi.org/10.1007/978-94-007-0002-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33485 Hybrid Logic and its Proof-Theory [documento electrónico] / Torben Braüner ; SpringerLink (Online service) . - Dordrecht : Springer Netherlands, 2011 . - XIII, 231 p : online resource. - (Applied Logic Series, ISSN 1386-2790; 37) .
ISBN : 978-94-007-0002-4
Idioma : Inglés (eng)
Palabras clave: Philosophy Logic Mathematical logic and Formal Languages Foundations Clasificación: 51 Matemáticas Resumen: This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic) Nota de contenido: Preface, -- 1 Introduction to Hybrid Logic -- 2 Proof-Theory of Propositional Hybrid Logic -- 3 Tableaus and Decision Procedures for Hybrid Logic -- 4 Comparison to Seligman’s Natural Deduction System -- 5 Functional Completeness for a Hybrid Logic -- 6 First-Order Hybrid -- 7 Intensional First-Order Hybrid Logic -- 8 Intuitionistic Hybrid Logic -- 9 Labelled Versus Internalized Natural Deduction -- 10 Why does the Proof-Theory of Hybrid Logic Behave soWell? - References -- Index En línea: http://dx.doi.org/10.1007/978-94-007-0002-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33485 Ejemplares
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Título : A Modern Perspective on Type Theory : From its Origins until Today Tipo de documento: documento electrónico Autores: Kamareddine, Fairouz ; SpringerLink (Online service) ; Laan, Twan ; Nederpelt, Rob Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2005 Colección: Applied Logic Series, ISSN 1386-2790 num. 29 Número de páginas: XIV, 360 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-2335-4 Idioma : Inglés (eng) Palabras clave: Mathematics Logic Computer science Mathematical logic and Foundations of Computing Clasificación: 51 Matemáticas Resumen: `Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-application of functions was at the heart of Russell's paradox. This led Russell to introduce type theory in order to avoid the paradox. Since, the twentieth century has seen an amazing number of theories concerned with types and functions and many applications. Progress in computer science also meant more and more emphasis on the use of logic, types and functions to study the syntax, semantics, design and implementation of programming languages and theorem provers, and the correctness of proofs and programs. The authors of this book have themselves been leading the way by providing various extensions of type theory which have been shown to bring many advantages. This book gathers much of their influential work and is highly recommended for anyone interested in type theory. The main emphasis is on: - Types: from Russell to Ramsey, to Church, to the modern Pure Type Systems and some of their extensions. - Functions: from Frege, to Russell to Church, to Automath and the use of functions in mathematics, programming languages and theorem provers. - The role of types in logic: Kripke's notion of truth, the evolution and role of the propositions as types concept and its use in logical frameworks. - The role of types in computation: extensions of type theories which can better model proof checkers and programming languages are given. The first part of the book is historical, yet at the same time, places historical systems (like Russell's RTT) in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms), but at the same time, places another historical system (the proof checker Automath) in the modern setting. The third part uses this bridging in the first two parts between historical and modern systems to propose new systems that bring more advantages together. This book has much to offer to mathematicians, logicians and to computer scientists in general. It will have considerable influence for many years to come.' - Henk Barendregt Nota de contenido: The Evolution of Type Theory until the 1940s -- Prehistory -- Type theory in Principia Mathematica -- Deramification -- Propositions as Types, Pure Type Systems, AUTOMATH -- Propositions as Types and Pure Type Systems -- The pre-PAT RTT and STT in PAT-style -- A Correspondence between RTT and the system Nuprl -- Automath -- Extensions of Pure Type Systems -- Pure Type Systems with definitions -- The Barendregt cube with parameters -- Pure Type Systems with parameters and definitions En línea: http://dx.doi.org/10.1007/1-4020-2335-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35201 A Modern Perspective on Type Theory : From its Origins until Today [documento electrónico] / Kamareddine, Fairouz ; SpringerLink (Online service) ; Laan, Twan ; Nederpelt, Rob . - Dordrecht : Springer Netherlands, 2005 . - XIV, 360 p : online resource. - (Applied Logic Series, ISSN 1386-2790; 29) .
ISBN : 978-1-4020-2335-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Logic Computer science Mathematical logic and Foundations of Computing Clasificación: 51 Matemáticas Resumen: `Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-application of functions was at the heart of Russell's paradox. This led Russell to introduce type theory in order to avoid the paradox. Since, the twentieth century has seen an amazing number of theories concerned with types and functions and many applications. Progress in computer science also meant more and more emphasis on the use of logic, types and functions to study the syntax, semantics, design and implementation of programming languages and theorem provers, and the correctness of proofs and programs. The authors of this book have themselves been leading the way by providing various extensions of type theory which have been shown to bring many advantages. This book gathers much of their influential work and is highly recommended for anyone interested in type theory. The main emphasis is on: - Types: from Russell to Ramsey, to Church, to the modern Pure Type Systems and some of their extensions. - Functions: from Frege, to Russell to Church, to Automath and the use of functions in mathematics, programming languages and theorem provers. - The role of types in logic: Kripke's notion of truth, the evolution and role of the propositions as types concept and its use in logical frameworks. - The role of types in computation: extensions of type theories which can better model proof checkers and programming languages are given. The first part of the book is historical, yet at the same time, places historical systems (like Russell's RTT) in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms), but at the same time, places another historical system (the proof checker Automath) in the modern setting. The third part uses this bridging in the first two parts between historical and modern systems to propose new systems that bring more advantages together. This book has much to offer to mathematicians, logicians and to computer scientists in general. It will have considerable influence for many years to come.' - Henk Barendregt Nota de contenido: The Evolution of Type Theory until the 1940s -- Prehistory -- Type theory in Principia Mathematica -- Deramification -- Propositions as Types, Pure Type Systems, AUTOMATH -- Propositions as Types and Pure Type Systems -- The pre-PAT RTT and STT in PAT-style -- A Correspondence between RTT and the system Nuprl -- Automath -- Extensions of Pure Type Systems -- Pure Type Systems with definitions -- The Barendregt cube with parameters -- Pure Type Systems with parameters and definitions En línea: http://dx.doi.org/10.1007/1-4020-2335-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35201 Ejemplares
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Título : Proof Theory for Fuzzy Logics Tipo de documento: documento electrónico Autores: Metcalfe, George ; SpringerLink (Online service) ; Olivetti, Nicola ; Dov M. Gabbay Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2009 Colección: Applied Logic Series, ISSN 1386-2790 num. 36 Número de páginas: VIII, 276 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-9409-5 Idioma : Inglés (eng) Palabras clave: Mathematics Logic Artificial intelligence Algebra Ordered algebraic structures Mathematical logic and Foundations Mathematics, general Intelligence (incl. Robotics) Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations Nota de contenido: The Semantic Basis -- Hilbert Systems -- Gentzen Systems -- Syntactic Eliminations -- Fundamental Logics -- Uniformity and Efficiency -- First-Order Logics -- Further Topics En línea: http://dx.doi.org/10.1007/978-1-4020-9409-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33960 Proof Theory for Fuzzy Logics [documento electrónico] / Metcalfe, George ; SpringerLink (Online service) ; Olivetti, Nicola ; Dov M. Gabbay . - Dordrecht : Springer Netherlands, 2009 . - VIII, 276 p : online resource. - (Applied Logic Series, ISSN 1386-2790; 36) .
ISBN : 978-1-4020-9409-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Logic Artificial intelligence Algebra Ordered algebraic structures Mathematical logic and Foundations Mathematics, general Intelligence (incl. Robotics) Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations Nota de contenido: The Semantic Basis -- Hilbert Systems -- Gentzen Systems -- Syntactic Eliminations -- Fundamental Logics -- Uniformity and Efficiency -- First-Order Logics -- Further Topics En línea: http://dx.doi.org/10.1007/978-1-4020-9409-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33960 Ejemplares
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Título : Reasoning Robots : The Art and Science of Programming Robotic Agents Tipo de documento: documento electrónico Autores: Thielscher, Michael ; SpringerLink (Online service) Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2005 Colección: Applied Logic Series, ISSN 1386-2790 num. 33 Número de páginas: XIV, 328 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-3069-7 Idioma : Inglés (eng) Palabras clave: Philosophy Computer programming Artificial intelligence of Technology Programming Techniques Intelligence (incl. Robotics) Clasificación: 51 Matemáticas Resumen: The book provides an in-depth and uniform treatment of a mathematical model for reasoning robotic agents. The book also contains an introduction to a programming method and system based on this model. The mathematical model, known as the "Fluent Calculus,'' describes how to use classical first-order logic to set up symbolic models of dynamic worlds and to represent knowledge of actions and their effects. Robotic agents use this knowledge and their reasoning facilities to make decisions when following high-level, long-term strategies. The book covers the issues of reasoning about sensor input, acting under incomplete knowledge and uncertainty, planning, intelligent troubleshooting, and many other topics. The mathematical model is supplemented by a programming method which allows readers to design their own reasoning robotic agents. The usage of this method, called "FLUX,'' is illustrated by many example programs. The book includes the details of an implementation of FLUX using the standard programming language PROLOG, which allows readers to re-implement or to modify and extend the generic system. The design of autonomous agents, including robots, is one of the most exciting and challenging goals of Artificial Intelligence. Reasoning robotic agents constitute a link between knowledge representation and reasoning on the one hand, and agent programming and robot control on the other. The book provides a uniform mathematical model for the problem-driven, top-down design of rational agents, which use reasoning for decision making, planning, and troubleshooting. The implementation of the mathematical model by a general PROLOG program allows readers to practice the design of reasoning robotic agents. Since all implementation details are given, the generic system can be easily modified and extended Nota de contenido: Special Fluent Calculus -- Special FLUX -- General Fluent Calculus -- General FLUX -- Knowledge Programming -- Planning -- Nondeterminism -- Imprecision* -- Indirect Effects: Ramification Problem* -- Troubleshooting: Qualification Problem -- Robotics En línea: http://dx.doi.org/10.1007/1-4020-3069-X Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35207 Reasoning Robots : The Art and Science of Programming Robotic Agents [documento electrónico] / Thielscher, Michael ; SpringerLink (Online service) . - Dordrecht : Springer Netherlands, 2005 . - XIV, 328 p : online resource. - (Applied Logic Series, ISSN 1386-2790; 33) .
ISBN : 978-1-4020-3069-7
Idioma : Inglés (eng)
Palabras clave: Philosophy Computer programming Artificial intelligence of Technology Programming Techniques Intelligence (incl. Robotics) Clasificación: 51 Matemáticas Resumen: The book provides an in-depth and uniform treatment of a mathematical model for reasoning robotic agents. The book also contains an introduction to a programming method and system based on this model. The mathematical model, known as the "Fluent Calculus,'' describes how to use classical first-order logic to set up symbolic models of dynamic worlds and to represent knowledge of actions and their effects. Robotic agents use this knowledge and their reasoning facilities to make decisions when following high-level, long-term strategies. The book covers the issues of reasoning about sensor input, acting under incomplete knowledge and uncertainty, planning, intelligent troubleshooting, and many other topics. The mathematical model is supplemented by a programming method which allows readers to design their own reasoning robotic agents. The usage of this method, called "FLUX,'' is illustrated by many example programs. The book includes the details of an implementation of FLUX using the standard programming language PROLOG, which allows readers to re-implement or to modify and extend the generic system. The design of autonomous agents, including robots, is one of the most exciting and challenging goals of Artificial Intelligence. Reasoning robotic agents constitute a link between knowledge representation and reasoning on the one hand, and agent programming and robot control on the other. The book provides a uniform mathematical model for the problem-driven, top-down design of rational agents, which use reasoning for decision making, planning, and troubleshooting. The implementation of the mathematical model by a general PROLOG program allows readers to practice the design of reasoning robotic agents. Since all implementation details are given, the generic system can be easily modified and extended Nota de contenido: Special Fluent Calculus -- Special FLUX -- General Fluent Calculus -- General FLUX -- Knowledge Programming -- Planning -- Nondeterminism -- Imprecision* -- Indirect Effects: Ramification Problem* -- Troubleshooting: Qualification Problem -- Robotics En línea: http://dx.doi.org/10.1007/1-4020-3069-X Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35207 Ejemplares
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