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The Logic System of Concept Graphs with Negation: And Its Relationship to Predicate Logic

By (author) Frithjof Dau

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The aim of contextual logic is to provide a formal theory of elementary logic, which is based on the doctrines of concepts,Â judgements, and conclusions. Concepts are mathematized using FormalÂ Concept Analysis (FCA), while an approach to the formalization of judgements andÂ conclusions is conceptual graphs, based on Peirce's existential graphs.Â Combining FCAÂ 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 ofÂ judgements can be implemented. To do so, cuts (syntactical devices used to expressÂ 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 authorÂ distinguishes between syntax and semantics, and provides a sound and completeÂ calculus for concept graphs with cuts.Â The author's treatment isÂ mathematically thorough and consistent, and the book gives the necessaryÂ background on existential and conceptual graphs.

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