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Since the NCGIA [NCGIA, 1989] research initiative 2 Language of Spatial Relations [Mark et al., 1989] and the meeting in Las Navas [Mark and Frank, 1991] we have argued that analyzing the ways humans think about space is fundamental for other - more abstract - kinds of reasoning. I found a most surprising connection recently in an article by Steedman, in which he argues: Thus it [λ-calculus] is a theory that makes language look as if it has been built on a pre-existing system for planning action in the world, and thereby seem less unique as a cognitive faculty than is usually assumed. (2002, , p. 4) and the language faculty in its syntactic aspect is directly hung onto a more primitive set of prelinguistic operations including these combinators, originally developed for motor planning (p. 5). Some background to the argument: Planning an optimal path in space is a well established, basic human abil- ity which requires the construction of network knowledge of the environment, combined from multiple trips. Planning an optimal sequence of actions can be computed with the same methods, representing the actions in a State - Tran- sition - Diagram, which is structurally equivalent to a street network. I have discovered recently, that planning actions and executing actions can be seen in a category and in the corresponding co-category [Asperti and Longo, 1991]. In robotics, the planning but also the recognition of plans of others is very impor- tant. Geib and Steedman [2007] show the structural similarity in the processes used for plan recognition and natural language processing. Producing an ex- planation for a plan is the same operation as parsing a sentence. This then connects to the initial quote above, which establishes a direct link between the planning of an optimal spatial path and human language, based on a categorical (λ-calculus) argument that these abilities all use the same fundamental process. Developmental arguments demonstrate that the spatial ability is primal and the other are hung onto these. The insight I gain from the connection between path planning, action plan- ning and human language production is rst, the correspondences: • path/action planning sentence production, • plan recognition sentence parsing, • location/state concept expressed in sentence, • target location/state concept to communicate, • starting location/state current context of conversation. The correspondences point out that language production is always based on the current context and whether a produced sentence is felicitous (or not) depends on the context (as can be seen in linguistic discussions, for example, Moens and Steedman, 1987). The correspondence further indicates that locations in space correspond to concepts (typically complex concepts expressing situations) and we need a representation of concepts and context; here I am looking at the representation by Aerts and Gabora [2005a,b], and compare it with a lattice scheme based on distinctions [Frank, 2006]. The second important insight found in this and other papers by Steedman, but also extensively argued by Carpenter [1997], is the advantage of using λ- calculus over rst order predicate logic: unlike rst-order logic, we can in ad- dition provide a term corresponding to the meaning of the verb phrase (p. 39).

References

Diederik Aerts and Liane Gabora. A theory of concepts and their combinations i: The structure of the sets of contexts and properties. Kybernetes, 34:167 191,2005a.

Diederik Aerts and Liane Gabora. A theory of concepts and their combinations ii: A hilbert space representation. Kybernetes, 34:0402205, 2005b.

Andrea Asperti and Giuseppe Longo. Categories, Types and Structures - An Introduction to Category Theory for the Working Computer Scientist. Foundations of Computing. The MIT Press, 1 edition, 1991. Bob Carpenter. Type-Logical Semantics. MIT, 1997.

Andrew U. Frank. Distinctions produce a taxonomic lattice: Are these the units of mentalese? In Brandon Bennett and Christiane Fellbaum, editors, ISBN 1-58603-685-8. Formal Ontology in Information Systems, pages 27 38, Amsterdam, 2006. IOS Press.

C.W. Geib and M. Steedman. On natural language processing and plan recognition. In Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI), pages 1612 1617, 2007.

Cognitive and Linguistic Aspects NATO ASI Series D. Kluwer Academic David M. Mark and Andrew U. Frank, editors. of Geographic Space, volume 63 of Publishers, 1991.

David M. Mark, Andrew U. Frank, Max J. Egenhofer, Scott M. Freundschuh, Matthew McGranaghan, and R. Michael White. Languages of spatial relations: Initiative two specialist meeting report. Technical report, 1989. 3 Proceedings of the 25th annual meeting on Association for Computational Linguistics, M. Moens and M. Steedman. Temporal ontology in natural language. In pages 1 7. Association for Computational Linguistics, 1987.

NCGIA. The u.s. national center for geographic information and analysis: An overview of the agenda for research and education. IJGIS, 2(3):117 136, 1989. Proceedings of the 24th Annual Meeting of the Cognitive Science Society, pages 834 839, 2002. M. Steedman. Formalizing a ordance. In

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