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Automating the synthesis of decision procedures in a constructive metatheory

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Abstract

We present an approach to the automatic construction of decision procedures, via a detailed example in propositional logic. The approach adapts the methods of proof‐planning and the heuristics for induction to a new domain, that of metatheoretic procedures. This approach starts by providing an alternative characterisation of validity; the proofs of the correctness and completeness of this characterisation, and the existence of a decision procedure, are then amenable to automation in the way we describe. In this paper we identify a set of principled extensions to the heuristics for induction needed to tackle the proof obligations arising in the new problem domain and discuss their integration within the clam‐Oyster system.

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Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Telematica, Università di Genova, Viale Causa 13, 16145, Genova, Italy

    Alessandro Armando

  2. Department of Artificial Intelligence, University of Edinburgh, 80 South Bridge, Edinburgh, EH1 1HN, Scotland, UK

    Jason Gallagher, Alan Smaill & Alan Bundy

Authors
  1. Alessandro Armando
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  2. Jason Gallagher
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  3. Alan Smaill
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  4. Alan Bundy
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Armando, A., Gallagher, J., Smaill, A. et al. Automating the synthesis of decision procedures in a constructive metatheory. Annals of Mathematics and Artificial Intelligence 22, 259–279 (1998). https://doi.org/10.1023/A:1018943603394

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