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A Sequent Calculus for 3-Dimensional Space

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Advances in Artificial Intelligence – SBIA 2010 (SBIA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6404))

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Abstract

A central issue for spatial reasoning in practice is to formalize reasoning about 3-dimensional space. In this paper, a spatial logic called 3-dimensional spatial logic (3SL), which can appropriately represent the 3-Cartesian product ω 3 of the set ω of natural numbers, is introduced as a Gentzen-type sequent calculus. 3SL is an extension and generalization of the linear-time temporal logic LTL in which the time domain is ω. The completeness and cut-elimination theorems for 3SL are proved.

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References

  1. Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, Formal Models and Semantics (B), pp. 995–1072. Elsevier, MIT Press (1990)

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Author information

Authors and Affiliations

  1. Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishi Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Norihiro Kamide

Authors
  1. Norihiro Kamide
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Editor information

Editors and Affiliations

  1. FURG, Centro de Ciências Computacionais, Universidade Federal do Rio Grande, Av. Itália, km 8 – Campus Carreiros, 96.201-900, Rio Grande, RS, Brazil

    Antônio Carlos da Rocha Costa

  2. UFRGS, Instituto de Informática, Universidade Federal do Rio Grande do Sul, Av. Bento Conçalves 9.500, 91501-970, Porto Alegre, RS, Brazil

    Rosa Maria Vicari

  3. Departamento de Ciência da Computação, Centro Universitário da FEI, Av. Humberto A. C. Branco 3972, 09850-901, São Bernardo do Campo, SP, Brazil

    Flavio Tonidandel

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Kamide, N. (2010). A Sequent Calculus for 3-Dimensional Space. In: da Rocha Costa, A.C., Vicari, R.M., Tonidandel, F. (eds) Advances in Artificial Intelligence – SBIA 2010. SBIA 2010. Lecture Notes in Computer Science(), vol 6404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16138-4_27

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  • DOI: https://doi.org/10.1007/978-3-642-16138-4_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16137-7

  • Online ISBN: 978-3-642-16138-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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