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Completeness of indexed ε-calculus

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Abstract.

Epsilon terms indexed by contexts were used by K. von Heusinger to represent definite and indefinite noun phrases as well as some other constructs of natural language. We provide a language and a complete first order system allowing to formalize basic aspects of this representation. The main axiom says that for any finite collection S 1,…,S k of distinct definable sets and elements a 1,…,a k of these sets there exists a choice function assigning a i to S i for all i≤k. We prove soundness and completeness theorems for this system S ε i fin.

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Authors and Affiliations

  1. Department of Philosophy, Stanford University, Stanford, California, USA

    G.E. Mints & Darko Sarenac

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  1. G.E. Mints
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  2. Darko Sarenac
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Correspondence to G.E. Mints.

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Mathematics Subject Classification (2000): 03B10, 03B65

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Mints, G., Sarenac, D. Completeness of indexed ε-calculus. Arch. Math. Logic 42, 617–625 (2003). https://doi.org/10.1007/s00153-003-0170-6

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  • DOI: https://doi.org/10.1007/s00153-003-0170-6

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