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### Theme description

Both the graphical representation of logical relations (logical geometry) and the visual modelling of reasoning patterns (diagrammatic reasoning) find their origin in the Aristotelian Square of Opposition.

Older proposals by Euler (1768), Venn (1880, 1881), Peirce (1898, 1933), Lewis Carroll (1896) and others regarding the visual modelling of reasoning patterns built on Aristotelian insights and have given rise to a great variety of modern visualisations of reasoning, including Conceptual Graphs (Sowa 1976), Formal Concept Analysis (Priss 2005, 2009) and Conceptual Structures (Sowa 1984).

In modern times, further foundational work on the Square, its internal relations and its graphical representation has led to several modifications of the original representation. First, the Square was extended to a hexagon of logical relations by the addition of two further operators enriching the Aristotelian logic (Blanché 1966, Horn 1989). Then it was, in different ways, either reduced to a few relations (Löbner 1990) or expanded even further into an octagon of logical relations (Wolenski 2008, Seuren 2010), and – from a less cognitively oriented and more strictly geometrical perspective –to polyhedral structures of opposition (Moretti 2009, Smessaert 2009), showing logical relations implicit in the Aristotelian Square. These developments have led to new insights, in particular regarding the position of the Square vis à vis the Hamiltonian triadic and modern Russellian predicate logic. They have also yielded interesting applications in linguistics, AI, modal logic, cognitive science and other related fields.

The purpose of the conference is to provide a forum for a systematic discussion of this field of research, both from a historical and a contemporary point of view. We therefore welcome contributions primarily on the following topics:

- the history and/or theory of logical geometry (relations of opposition, inclusion, duality, diagrammatic reasoning, etc.);
- contemporary applications of logical geometry and of diagrammatic reasoning;
- the psychological and/or linguistic reality of logical relations and geometry.

### Invited Speakers

Sebastian Loebner (Univ. of Düsseldorf, Germany)

Alessio Moretti (Nice, France)

Uta Priss (Ostfalia University of Applied Sciences, Wolfenbuettel, Germany)

### Abstract Guidelines

Abstracts should not exceed two pages, including data, references and diagrams. Abstracts should be typed in at least 11-point font, with one-inch margins (letter-size; 8 ½ by 11 or A4) and a maximum of 50 lines of text per page. Abstracts must be anonymous and submissions are limited to 2 per author, at least one of which is co-authored.

Only electronic submissions will be accepted. Please submit your abstract using the EasyAbs link for LNAT2: http://linguistlist.org/confcustom/LNAT2

### Important dates

First call for papers: July 8, 2011

Second call for papers: August 30, 2011

Abstract submission deadline: October 1, 2011

Notification of acceptance: November 15, 2011

Conference: December 21-22, 2011

### References

Baron, Margaret E. 1969. A Note on the Historical Development of Logic Diagrams: Leibniz, Euler and Venn. The Mathematical Gazette, Vol. 53, No. 384, pp. 113-125.

Blanché, R. (1966) Structures intellectuelles. Essai sur l’organisation systématique des concepts, Vrin, Paris.

Carroll, L. 1896. Symbolic Logic. New York: Dover.

Euler, L., 1768. Lettres à une Princesse d’Allemagne. St. Petersburg.

Euler, L., Brewster, D. & J. Griscom (1768 [1833]), Letters of Euler on different subjects in natural philosophy : addressed to a German princess : with notes and a life of Euler. New York: J. & J. Harper.

Horn, L. R. (1989), A Natural History of Negation, University of Chicago Press, Chicago.

Löbner, S. 1990. Wahr neben Falsch. Duale Operatoren als die Quantoren natürlicher Sprache, Max Niemeyer Verlag,Tübingen.

Moretti, A. 2009. The Geometry of Logical Opposition. PhD Thesis, Université de

Neuchâtel, Switzerland.

Peirce, C.S. 1898. “The Logic of Relatives”, in: Peirce, C.S. (ed. K. Ketner). Reasoning and the Logic of Things. pp. 146–64.

Peirce, C.S. 1933. Collected Papers. Cambridge, MA: Harvard University Press.

Priss, U. 2005. “Linguistic Applications of Formal Concept Analysis”, in: Ganter, Stumme, Wille (eds.), Formal Concept Analysis. Foundations and Applications. Springer Verlag, pp. 149-160.

Priss, U. 2009. “Formal Concept Analysis as a Tool for Linguistic Data Exploration”, in: Hitzler, P. & H. Scharfe (eds.), Conceptual Structures in Practice, Chapman & Hall/CRC studies in informatics series, pp. 177-198.

Seuren, P. A. M. 2010. Language from within: Vol. 2. The logic of language. Oxford: Oxford University Press.

Smessaert, H. 2009. “On the 3D visualization of the logical relations”, Logica Universalis 3: 212-31.

Sowa, J. F. 1976. “Conceptual Graphs for a Data Base Interface”, IBM Journal of Research and Development 20(4), pp. 336–357.

Sowa, J. F. 1984. Conceptual Structures: Information Processing in Mind and Machine. Reading, MA: Addison-Wesley.

Venn, J. 1880. On the Diagrammatic and Mechanical Representation of Propositions and Reasonings. Philosophical Magazine and Journal of Science, Series 5, vol. 10, No. 59, July

Venn, J. 1881. Symbolic Logic. London: MacMillan and Co.

Wolenski, J. 2008. “Applications of Squares of Opposition and Their Generalizations in Philosophical Analysis”, Logica Universalis 2, pp. 13 – 29.