By Alan Blackwell, Kim Marriott, Atsushi Shimojima

Even though diagrammatic representations were a function of human com- nication from early background, fresh advances in printing and digital media technologyhaveintroducedincreasinglysophisticatedvisualrepresentationsinto everydaylife. we have to enhance our realizing of the function of diagramsand sketches in verbal exchange, cognition, artistic idea, and problem-solving. those matters have prompted a surge of curiosity within the learn of diagrammatic notations, specifically in educational disciplines facing cognition, compu- tion, and conversation. We think that the research of diagrammatic verbal exchange is healthier pursued as an interdisciplinary activity. The Diagrams convention sequence used to be introduced to help a global study group with this universal objective. After winning conferences in Edinburgh (2000) and Georgia (2002), Diagrams 2004 was once the 3rd occasion within the sequence. The Diagramsseries draws a largenumber of researchersfrom nearly all academic?elds who arestudying the character of d- grammatic representations, their use in human verbal exchange, and cognitive or computationalmechanismsforprocessingdiagrams.Bycombiningseveralearlier workshop and symposium sequence that have been held within the US and Europe - R- soning with Diagrammatic Representations (DR), US; considering with Diagrams (TWD), Europe; and idea of visible Languages (TVL), Europe - Diagrams has emerged as an enormous overseas convention in this subject.

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1 Results The results were straightforward. Figure 3 shows the mean number of preferences for the conditions. A chi-square test for independence revealed that the sentence 28 Csaba Veres and Gittan Mansson Fig. 2. A standard n-ary relation and the new notation Fig. 3. Total number of preferences for each sentence type type and notation were not independent in determining preference. -adj. 23, 3 Conclusion Subjects tended to prefer the new notation in the complement-adjunct condition. Our explanation is that this is due to a difference in the conceptual representation of the situations described.

An alphabet is a triple of disjoint sets such that 7 is a finite set whose elements are called object names, is a finite ordered set with a greatest element whose elements are called concept names, and is a family of finite ordered sets (for an whose elements are called relation names. be a special name which is called identity. On we define an order such that but all elements of are incomparable. is the greatest element Definition 4 (Query Graphs with Cuts). , ‘objects’. This letter will recur when we define formal contexts where we have a set G of objects.

1 now allows us to do inductive definitions and proofs as well. Of course the preceding lemma is not surprising: It had to be expected. But as the results, which are clear from a naive understanding of concept graphs, can be proven, the lemma indicates that Def. 1 and the definition of are ‘correct’ mathematization of the underlying structure of query graphs with cuts. The following figure provides a simple example for the last definitions. In the first two lines, a relational graph with cuts is defined (of course, are disjoint sets with and .