Nested Concept Graphs and Triadic Power Context Families

In this paper, a contextual semantics for nested concept graphs shall be presented, that has especially two aims: We will propose a situation-based semantics that fits with Sowa’s understanding of contexts and draw the connection to formal concept analysis by founding on formal contexts, more precisely triadic power context families. Its basic idea is to understand interpreted nested concept graphs as situation-based judgements in triadic power context families. With it, the logical th eory can be well developed and inferences can be characterized in three ways: By semantical entailment, by means of a standard model and by a sound and complete calculus.

[1]  John F. Sowa,et al.  Peircean Foundations for a Theory of Context , 1997, ICCS.

[2]  M. Mugnier,et al.  Représenter des connaissances et raisonner avec des graphes , 1996 .

[3]  Susanne Prediger,et al.  Kontextuelle Urteilslogik mit Begriffsgraphen: ein Beitrag zur Restrukturierung der mathematischen Logik , 1998 .

[4]  N. Cocchiarella,et al.  Situations and Attitudes. , 1986 .

[5]  Marie-Laure Mugnier,et al.  Nested Graphs: A Graph-based Knowledge Representation Model with FOL Semantics , 1998, KR.

[6]  John F. Sowa,et al.  Conceptual Structures: Fulfilling Peirce's Dream , 1997, Lecture Notes in Computer Science.

[7]  John F. Sowa,et al.  Conceptual Structures: Information Processing in Mind and Machine , 1983 .

[8]  Susanne Prediger,et al.  Simple Concept Graphs: A Logic Approach , 1998, ICCS.

[9]  Rudolf Wille,et al.  The Basic Theorem of triadic concept analysis , 1995 .

[10]  Rudolf Wille.  Triadic Concept Graphs , 1998, ICCS.

[11]  Marie-Laure Mugnier,et al.  Positive Nested Conceptual Graphs , 1997, ICCS.

[12]  William M. Tepfenhart,et al.  Conceptual Structures: Standards and Practices , 1999, Lecture Notes in Computer Science.

[13]  John McCarthy,et al.  Notes on Formalizing Context , 1993, IJCAI.

[14]  Keith Devlin,et al.  Logic and information , 1991 .

[15]  Rudolf Wille,et al.  A Triadic Approach to Formal Concept Analysis , 1995, ICCS.

[16]  Rudolf Wille,et al.  The Lattice of Concept Graphs of a Relationally Scaled Context , 1999, ICCS.

[17]  Rudolf Wille,et al.  Conceptual Graphs and Formal Concept Analysis , 1997, ICCS.