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Mexican International Conference on Artificial Intelligence

MICAI 2005: MICAI 2005: Advances in Artificial Intelligence pp 119–131Cite as

Deductive Systems’ Representation and an Incompleteness Result in the Situation Calculus

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3789))

Abstract

It is shown in this paper a way of representing deductive systems using the situation calculus. The situation calculus is a family of first order languages with induction that allows the specification of evolving worlds and reasoning about them and has found a number of applications in AI. A method for the representation of formulae and of proofs is presented in which the induction axiom on states is used to represent structural induction on formulae and proofs. This paper’s formalizations are relevant for the purpose of meta reasoning and of automated or manual deduction in the context of situation calculus specifications. An example proof is given for the fact that no deductive system is complete for arbitrary situation calculus specifications (an expectable result).

This research was supported by project 201.093.0041-1.0 of the Dirección de Investigación, University of Concepción.

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Author information

Authors and Affiliations

  1. Departamento de Ingeniería Informática y Ciencia de la Computación, Facultad de Ingeniería, University of Concepción, Chile

    Pablo Sáez

Authors
  1. Pablo Sáez
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Editor information

Editors and Affiliations

  1. National Polytechnic Institute, Center for Computing Research, 07738, Mexico City, México

    Alexander Gelbukh

  2. Technológico de Monterrey (ITESM), Campus Ciudad de México (CCM), Calle del Puente 222, Col. Ejudos de Huipulco, 14360 DF, Tlalpan, Mexico

    Álvaro de Albornoz

  3. Center for Intelligent Systems, Tecnológico de Monterrey, Campus Monterrey, 64849, Monterrey, N.L., Mexico

    Hugo Terashima-Marín

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© 2005 Springer-Verlag Berlin Heidelberg

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Sáez, P. (2005). Deductive Systems’ Representation and an Incompleteness Result in the Situation Calculus. In: Gelbukh, A., de Albornoz, Á., Terashima-Marín, H. (eds) MICAI 2005: Advances in Artificial Intelligence. MICAI 2005. Lecture Notes in Computer Science(), vol 3789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11579427_13

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  • DOI: https://doi.org/10.1007/11579427_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29896-0

  • Online ISBN: 978-3-540-31653-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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