Implementation, and Theory. LNAI 954, Springer Verlag, Berlin 1995,

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2 206 References 15. F. Dau: An Embedding of Existential Graphs into Concept Graphs with Negations. To appear in D. Corbett, U: Priss (Eds.): Conceptual Structures: Integration and Interfaces, LNAI, Springer Verlag, Berlin Heidelberg K. Devlin: Logic and Information. Cambridge University Press, U. Friedrichsdorf: Einführung in die klassische und intensionale Logik. Vieweg, B. Ganter, R. Wille: Formale Begriffsanalyse. Mathematische Grundlagen. Springer Verlag, Berlin Heidelberg B. Ganter, R. Wille: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin Heidelberg New York B. Ganter, R. Wille: Contextual Attribute Logic. In: W. Tepfenhart, W. Cyre (Eds.): Conceptual Structures: Standards and Practices. LNAI 1640, Springer Verlag, Berlin New York 1999, B. Groh, R. Wille: Lattices of Triadic Concept Graphs. In: B. Ganter, G. W. Mineau (Eds.): Conceptual Structures: Logical, Linguistic, and Computational Issues. LNAI 1867, Springer Verlag, Berlin New York 2000, E. M. Hammer: Logic and Visual Information. CSLI Publications, Stanford, California, E. M. Hammer: Semantics for Existential Graphs. Journal Philosohpical Logic, Vol. 27, 1998, J. Hintikka: The Game of Language: Studies in Game-Theoretical Semantics and its Applications. D. Reidel, Dordrecht. 25. J. Hintikka: The Place of C S. Peirce in the History of Logical Theory. In: Brunning and Forster (1997), T. Jech: Set Theory. Academic Press G. N. Kerdiles: Saying it with Pictures: A Logical Landscape of Conceptual Graphs. ILLC Dissertation Series, DS J. Klinger: Simple Semiconcept Graphs: A Boolean Logic Approach. In: H. S. Delugach, G. Stumme (Eds.): Conceptual Structures: Broadening the Base. LNAI 2120, Springer Verlag, Berlin Heidelberg 2001, J. Klinger: Semiconcept Graphs: Syntax and Semantics. Diplomarbeit, FB Mathematik, TU Darmstadt J. Klinger: Semiconcept Graphs with Variables. To appear in D. Corbett, U: Priss (Eds.): Conceptual Structures: Integration and Interfaces, LNAI, Springer Verlag, Berlin Heidelberg L. Kreiser, S. Gottwald, W. Stelzer: Nichtklassische Logik. Akademie Verlag Berlin, A. Levy: Basic Set Theory. Springer Verlag D. Lukose, R. Kremer: Knowledge Engineering: Knowledge Representation. kremer/courses/cg/ 34. B. Mates: Elementare Logik. Vandenhoeck & Ruprecht J. McCarthy: Notes on Formalizing Context. In: Proccedings of the IJCAI 1993, E. Mendelson: Introduction to Mathematical Logic. D. Van Nostrand Company, Princeton J. D. Monk: Introduction to Set Theory, McGraw Hill M.-L. Mugnier: Knowledge Representation and Reasonings Based on Graph Homomophism. In: B. Ganter, G. W. Mineau (Eds.): Conceptual Structures: Logical, Linguistic and Computational Issues. LNAI 1867, Springer Verlag, Berlin New York 2000,

3 References K. Oehler: Charles Sanders Peirce. Beck sche Reihe, H. Pape: Charles S. Peirce: Phänomen und Logik der Zeichen. German translation of Peirce s Syllabus of Certain Topics of Logic.. Suhrkamp Verlag Wissenschaft, C. S. Peirce: Reasoning and the Logic of Things. The Cambridge Conferences Lectures of Cambridge, Massachusetts, London, England, Ed. by K. L. Ketner, H. Putnam, Harvard Univ. Press, Cambridge C. S. Peirce, MS 478. Collected Papers, Harvard University Press, Cambrigde, Massachusetts. 43. C. S. Peirce, J. F. Sowa: Existential Graphs: MS 514 by Charles Sanders Peirce with Commentary by John F. Sowa S. Prediger: Kontextuelle Urteilslogik mit Begriffsgraphen. Ein Beitrag zur Restrukturierung der mathematischen Logik. Shaker Verlag S. Prediger: Simple Concept Graphs: A Logic Approach. In: M, -L. Mugnier, M. Chein (Eds.): Conceptual Structures: Theory, Tools and Applications. LNAI 1453, Springer Verlag, Berlin New York 1998, S. Prediger: Mathematische Logik in der Wissensverarbeitung: Historisch- Philosophische Gründe für eine Kontextuelle Logik. Mathe. Semesterberichte 47, S. Prediger: Terminologische Merkmalslogik in der Formalen Begriffsanalyse. In: G. Stumme, R. Wille (Eds.): Begriffliche Wissensverarbeitung: Methoden und Anwendungen. Springer Verlag, Heidelberg, 2000, S. Prediger: Nested Concept Graphs and Triadic Power Context Families: A Situation based Contextual Approach. In: B. Ganter, G. W. Mineau (Eds.): Conceptual Structures: Logical, Linguistic, and Computational Issues. LNAI 1867, Springer Verlag, Berlin New York 2000, S. Prediger, R. Wille: The Lattice of Concept Graphs of a Relationally Scaled Context. In: W. Tepfenhart, W. Cyre (Eds.): Conceptual Structures: Standards and Practices. LNAI 1640, Springer Verlag, Berlin New York 1999, A. Preller, M.-L. Mugnier, M. Chein: A Logic for Nested Graphs. Research Report 95038, LIRMM, Université Montpellier II, W. Rautenberg: Einführung in die mathematische Logik. Vieweg Lehrbuch Mathematik, D. D. Roberts: The Existential Graphs of Charles S. Peirce. Mouton, The Hague, Paris, D. D. Roberts: The Existential Graphs. Computers Math. Appl.., Vol. 23, No. 6 9, 1992, J. Seligman, L. S. Moss: Situation Theory. In: J. van Benthem, A. ter Meulen: Handbook of Logic and Language, Elsevier Science, Amsterdam S. Shin: Reconstituting Beta Graphs into an Efficacious System. In: Journal of Logic, Language and Information, Vol. 8, No. 3, July S. J. Shin: The Iconic Logic of Peirce s Graphs. Bradford Book, Massachusetts, J. R. Shoenfield: Mathematical Logic. Addison Wesley G. Simonet: Two FOL-Semantics for Simple and Nested Conceptual Graphs. In: M, -L. Mugnier, M. Chein (Eds.): Conceptual Structures: Theory, Tools and Applications. LNAI 1453, Springer Verlag, Berlin New York 1998, J. F. Sowa: Conceptual Structures: Information Processing in Mind and Machine. Addison Wesley Publishing Company Reading, 1984.

4 208 References 60. J. F. Sowa: Conceptual Graphs Summary. In: T. E. Nagle, J. A. Nagle, L. L. Gerholz, P. W. Eklund (Eds.): Conceptual Structures: current research and practice, Ellis Horwood, 1992, J. F. Sowa: Syntax, Semantics, and Pragmatics of Contexts. In: G. Ellis, R. Levinson, W. Rich, J. F. Sowa (Eds.): Conceptual Structures: Applications, Implementation, and Theory. LNAI 954, Springer Verlag, Berlin, 1995, See also [66] 62. J. F. Sowa: Logic: Graphical and Algebraic. Manuskript, Croton-on-Hudson J. F. Sowa: Peircean Foundation for a Theory of Context. In: D. Lukose et al. (Hrsg.): Conceptual Structures: Fulfilling Peirce s Dream. LNAI 1257, Springer Verlag, Berlin New York 1997, See also [66] 64. J. F. Sowa: Conceptual Graphs: Draft Proposed American National Standard. In: W. Tepfenhart, W. Cyre (Eds.): Conceptual Structures: Standards and Practices. LNAI 1640, Springer Verlag, Berlin New York 1999, See also [67] 65. J. F. Sowa: Knowledge Representation: Logical, Philosophical, and Computational Foundations. Brooks Cole Publishing Co., Pacific Grove, CA, J. F. Sowa: Semantic Foundations of Contexts. Thispaperisarevisedmergerof[61]and[63]. 67. J. F. Sowa: Conceptual Graphs: Draft Proposed American National Standard. Old version: New version: See also [64] 68. J. Tappe: Simple Concept Graphs with Universal Quantifiers. FB 4 Preprint, TU Darmstadt H. P. Tuschik, H. Wolter: Mathematische Logik kurzgefasst. BI Wissenschaftsverlag, Mannheim Leipzig Wien Zürich, M. Wermelinger: Conceptual Graphs and First-Order Logic. In: G. Ellis, R. Levinson, W. Rich, J. F. Sowa (Eds.): Conceptual Structures: Applications, Implementation, and Theory. LNAI 954, Springer Verlag, Berlin 1995, R. Wille: Concept Lattices and Conceptual Knowledge Systems. In: Computers & Mathematics with Applications. 23 (1992), R. Wille: Plädoyer für eine Philosophische Grundlegung der Begrifflichen Wissensverarbeitung. In: R. Wille, M. Zickwolff (Eds.): Begriffliche Wissensverarbeitung: Grundfragen und Aufgaben. B.I. Wissenschaftsverlag, Mannheim, 1994, R. Wille: Restructuring Mathematical Logic: An Approach Based on Peirce s Pragmatism. In: A. Ursini, P. Agliano (Eds.): Logic and Algebra. Marcel Dekker, New York 1996, R. Wille: Conceptual Structures of Multicontexts. In: P. W. Eklund, G. Ellis, G. Mann (Hrsg.): Conceptual Structures: Knowledge Representation as Interlingua. LNAI 115, Springer Verlag, Berlin Heidelberg New York 1996, R. Wille: Conceptual Graphs and Formal Concept Analysis. In: D. Lukoseetal. (Hrsg.): Conceptual Structures: Fulfilling Peirce s Dream. LNAI 1257, Springer Verlag, Berlin New York 1997,

5 References R. Wille: Triadic Concept Graphs. In: M.-L. Mugnier / M. Chein (Eds.): Conceptual Structures: Theory, Tools and Application. LNAI 1453, Springer Verlag, Berlin Heidelberg R. Wille: Contextual Logic Summary. In: G. Stumme (Ed.): Working with Conceptual Structures. Contributions to ICCS Shaker, Aachen 2000, R. Wille: Boolean Concept Logic. In: B. Ganter, G. W. Mineau (Eds.): Conceptual Structures: Logical, Linguistic, and Computational Issues. LNAI 1867, Springer Verlag, Berlin New York 2000, R. Wille: Boolean Judgement Logic. In: H. S. Delugach, G. Stumme (Eds.): Conceptual Structures: Broadening the Base. LNAI 2120, Springer Verlag, Berlin Heidelberg 2001, R. Wille: Existential Concept Graphs of Power Context Families. To appear in D. Corbett, U: Priss (Eds.): Conceptual Structures: Integration and Interfaces, LNAI, Springer Verlag, Berlin Heidelberg R. Wille: Conceptual Contents as Information Basics for Contextual Judgement Logic. In: A. d. Moor, W. Lex, B. Ganter (Eds.): Conceptual Structures for Knowledge Creation and Communication, LNAI, Springer Verlag, Berlin Heidelberg 2003.

6 Index ( K,λ) M, 103 α, 30, 97 <, 27 E id,31 E nonid,31 E v,26 V G,31 V e,26 C, 30 G, 30 R, 31 A, 30 CG, 31 CG A,31 =, 101 Neg f,87, 26, 127 [c], 27 fi[c], 27. =, 25, 31, 51 = class,94 = endo,95 pos, 165 K, 43 Φ, 12, 15, 18, 41, , 125, 157, 199 Ψ, , 125, 157 Ψ, 138 Ψ, 138 α empty, 100 β, 26 κ, 31 λ, 43 λ C,43 λ G,43 λ R,43, 26, 87 fi, 27 =, 168 = f, 168 = val,88 ν, 25 φ, 14 ρ, 31 θ, 165 θg, 165, 30, 55 ref, 94 v,31 M ( K,λ), 102 B(K), 43 Alpha, 2, 21, 54, Alphabet, 30 Anti-Normal-Form, 61 Area, 3, 26 Atomic, 69 Beta, 2, 21, 54, 202, 203 Calculus, 17, 188 Equivalence Transformations, 52, Existential Concept Graphs, 107 Existential Concept Graphs without Cuts, 165 First Order Logic, 89, 90 Generalization Transformations, 52, 203, 204 Models, 183, Nonexistential Concept Graphs, 45 Peirce-Style, Chein/Mugnier, 14, 19, 169 Concept, 8, 42, 43 Concept Box, 8, 10, 32 Concept Graph with Cuts, 18 20, 31, 30 38, 73

7 212 Index Representation, Concept Graph without Cuts, 42 Concept Name, 8, 30 Conceptual Content, 52 Conceptual Graph, 1, 8 18, 42 Conclusion,7,42 Conjunction, 3, 5, 98 Consistent, 68 Context, 10 12, 15, 18, 26, 29, 51, 74, 203 Negative, 29, 74, 203 Positive, 29, 74, 203 Contextual Logic, 93 Contextual Semantics, 41, 42, 88 Coreference Link, 10, 16, 19, Cut, 25, 32, Representation, 32 Cut Condition, 44, 94 Deduction Theorem, 60 Dominating Nodes, 30, 96, Double Cut, 3, 4, 16, 54 Edge, 25, 32 Representation, 32 Edge Condition, 44, 94 Enclosing, 29, 36 Directly, 29 Evenly, 3, 29, 36 Oddly, 3, 29, 36 Endoporeutic Method, 41, 42, 95, 95 Evaluation Alpha-Graphs, 44 Classical, 94 Endoporeutic, 95 Equivalence, 96 First Order Logic, 88 Existential Graph, 1 8, 10, 21, 33, 41, 68, 95, 102, 202 Alpha, 2 Beta, 4 Calculus, 3, 13, 45, 51, 54, 59, 73, 80, 202, 203 Concept(ual) Graphs, 8, 9, 11 13, 15, 73 Cuts, 2, 18, 20, 25, 191 Gamma, 7 Line of Identity, 4, 10, 12, 33, 73 Scroll, 3, 12, 100 Existential Graphs, VI, VII First Order Logic, 1, 2, 9, 12, 15, 18, 21, 83 89, 94, 101, 202, 203 Formulas, 83 Subormulas, 83 Formal Concept, 43 Extension, 43 Intension, 43 Formal Concept Analysis, 41, 42 Formal Context, 42, 43 Formulas ff-conversion, 86 Subformula Occurences, 85 Substitutions, 85 Variable-Purified, 86 Gamma, 2 Generic Marker, 9, 30, 74, 81, 98 Indexed, 30 Generic Nodes, 31 Hintikka, 41, 42, 93 Identity, 17, 19, 31, 73, 90, 114, 164, 165, Identity Links, 19, 31, 74, 109, 114, Interpretation, 43 Isomorphism, 36, 55 Except Cuts, 37, 116, 201 Judgement, 2, 32, 42, 43, 68 Juxtaposition, 2, 37, 60, 98 Medads, 2 Model Contextual, 43, 70, Relational, 88, Negation, 2, 3, 5, 11, 15, 16, 18, Nesting, 8, 10, 12, 15, 26 Normal Form, 61 Object Name, 30 Peano, 2 Peirce, V VII, 1 4, 8, 11, 13, 15, 18, 25, 42, 45, 59, 68, 93 Power Context Family, 42, 43

8 Index 213 Prediger, 20, 25, 31, 41 43, 82, , , 184, 188, 191, 193 Projections, 164, 169, 188 Proof First Order Logic, 89 Graphs, 51 Proposition, 2, 3 Propositional Logic, 3, 21, 203 Pseudograph, 68 Quantification, 1, 2, 5, 10, 73, 84, 85, 90, 94, 137 Referent, 9, 10, 31 Relation Name, 31 Relation Oval, 32 Relational Graphs with Cuts, 25, Roberts, 1, 2 Scope, 198, 199, 199 Scribing, 2 Sheet of Assertion, 2, 3, 26, 26 Shin, 1 Sowa, 1, 8 19, 190, 191, , 202, 203 Standard Graph, 163, 164, 172 Standard Model, 42, 163, 164, 166 Subgraph, 35, 34 36, 53 Closed, 36, Type, 8 Universal Type, 9, 17, 30 Universe of Discourse, 8, 42, 88 Valuation, 116 First Order Logic, 88 Partial, 94 Total, 94 Variables, 30, 30, 83, 88, 97, 202 Bound Variables, 83 Free Variables, 83 Vertex, 25, 32 Representation, 32 Vertex Condition, 44, 94 Wermelinger, 14, 15, 55 Wille, 19, 20, 25, 31, 41 43, 52, 168