Automating the synthesis of decision procedures in a constructive metatheory

  • Authors:

  • Alessandro Armando;Jason Gallagher;Alan Smaill;Alan Bundy

  • Affiliations:

  • Dipartimento di Informatica, Sistemistica e Telematica, Università di Genova, Viale Causa 13, 16145 Genova, Italy E-mail: armando@dist.unige.it;Department of Artificial Intelligence, University of Edinburgh, 80 South Bridge, Edinburgh EH1 1HN, Scotland, UK E-mail: {jason,smaill,bundy}@aisb.ed.ac.uk;Department of Artificial Intelligence, University of Edinburgh, 80 South Bridge, Edinburgh EH1 1HN, Scotland, UK E-mail: {jason,smaill,bundy}@aisb.ed.ac.uk;Department of Artificial Intelligence, University of Edinburgh, 80 South Bridge, Edinburgh EH1 1HN, Scotland, UK E-mail: {jason,smaill,bundy}@aisb.ed.ac.uk

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 1998

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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.