Frithjof Dau (auth.)3540206078, 9783540206071
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.
Table of contents :
Front Matter….Pages –
1 Introduction….Pages 1-23
2 Basic Definitions….Pages 25-38
3 Overview for Alpha….Pages 39-40
4 Semantics for Nonexistential Concept Graphs….Pages 41-44
5 Calculus for Nonexistential Concept Graphs….Pages 45-62
6 Soundness and Completeness….Pages 63-80
7 Overview for Beta….Pages 81-82
8 First Order Logic….Pages 83-91
9 Semantics for Existential Concept Graphs….Pages 93-105
10 Calculus for Existential Concept Graphs….Pages 107-123
11 Syntactical Equivalence to FOL….Pages 125-156
12 Summary of Beta….Pages 157-162
13 Concept Graphs without Cuts….Pages 163-185
14 Design Decisions….Pages 187-204
Back Matter….Pages –
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