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The Logic System of Concept Graphs with Negation
And Its Relationship to Predicate Logic
Taschenbuch von Frithjof Dau
Sprache: Englisch

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Beschreibung
The aim of contextual logic is to provide a formal theory of elementary logic, which is based on the doctrines of concepts, judgements, and conclusions. Concepts are mathematized using Formal Concept Analysis (FCA), while an approach to the formalization of judgements and conclusions is conceptual graphs, based on Peirce's existential graphs. Combining FCA and a mathematization of conceptual graphs yields so-called concept graphs, which offer a formal and diagrammatic theory of elementary logic.
Expressing negation in contextual logic is a difficult task. Based on the author's dissertation, this book shows how negation on the level of judgements can be implemented. To do so, cuts (syntactical devices used to express negation) are added to concept graphs. As we can express relations between objects, conjunction and negation in judgements, and existential quantification, the author demonstrates that concept graphs with cuts have the expressive power of first-order predicate logic. While doing so, the author distinguishes between syntax and semantics, and provides a sound and complete calculus for concept graphs with cuts. The author's treatment is mathematically thorough and consistent, and the book gives the necessary background on existential and conceptual graphs.
The aim of contextual logic is to provide a formal theory of elementary logic, which is based on the doctrines of concepts, judgements, and conclusions. Concepts are mathematized using Formal Concept Analysis (FCA), while an approach to the formalization of judgements and conclusions is conceptual graphs, based on Peirce's existential graphs. Combining FCA and a mathematization of conceptual graphs yields so-called concept graphs, which offer a formal and diagrammatic theory of elementary logic.
Expressing negation in contextual logic is a difficult task. Based on the author's dissertation, this book shows how negation on the level of judgements can be implemented. To do so, cuts (syntactical devices used to express negation) are added to concept graphs. As we can express relations between objects, conjunction and negation in judgements, and existential quantification, the author demonstrates that concept graphs with cuts have the expressive power of first-order predicate logic. While doing so, the author distinguishes between syntax and semantics, and provides a sound and complete calculus for concept graphs with cuts. The author's treatment is mathematically thorough and consistent, and the book gives the necessary background on existential and conceptual graphs.
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
Start.- 1 Introduction.- 2 Basic Definitions.- Alpha.- 3 Overview for Alpha.- 4 Semantics for Nonexistential Concept Graphs.- 5 Calculus for Nonexistential Concept Graphs.- 6 Soundness and Completeness.- Beta.- 7 Overview for Beta.- 8 First Order Logic.- 9 Semantics for Existential Concept Graphs.- 10 Calculus for Existential Concept Graphs.- 11 Syntactical Equivalence to FOL.- 12 Summary of Beta.- 13 Concept Graphs without Cuts.- 14 Design Decisions.
Details
Erscheinungsjahr: 2003
Genre: Informatik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 232
Reihe: Lecture Notes in Computer Science
Inhalt: xii
216 S.
ISBN-13: 9783540206071
ISBN-10: 3540206078
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Dau, Frithjof
Auflage: 2003
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Lecture Notes in Computer Science
Maße: 235 x 155 x 13 mm
Von/Mit: Frithjof Dau
Erscheinungsdatum: 24.11.2003
Gewicht: 0,359 kg
preigu-id: 102480532
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
Start.- 1 Introduction.- 2 Basic Definitions.- Alpha.- 3 Overview for Alpha.- 4 Semantics for Nonexistential Concept Graphs.- 5 Calculus for Nonexistential Concept Graphs.- 6 Soundness and Completeness.- Beta.- 7 Overview for Beta.- 8 First Order Logic.- 9 Semantics for Existential Concept Graphs.- 10 Calculus for Existential Concept Graphs.- 11 Syntactical Equivalence to FOL.- 12 Summary of Beta.- 13 Concept Graphs without Cuts.- 14 Design Decisions.
Details
Erscheinungsjahr: 2003
Genre: Informatik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 232
Reihe: Lecture Notes in Computer Science
Inhalt: xii
216 S.
ISBN-13: 9783540206071
ISBN-10: 3540206078
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Dau, Frithjof
Auflage: 2003
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Lecture Notes in Computer Science
Maße: 235 x 155 x 13 mm
Von/Mit: Frithjof Dau
Erscheinungsdatum: 24.11.2003
Gewicht: 0,359 kg
preigu-id: 102480532
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