A Proof and Some Representations

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Abstract

Hilbert defined proofs as derivations from axioms via the modus ponens rule and variable instantiation (this definition has a certain parallel to the ‘recognise-act cycle’ in artificial intelligence). A pre-defined set of rules is applied to an initial state until a goal state is reached. Although this definition is very powerful and it can be argued that nothing else is needed, the nature of proof turns out to be much more diverse, for instance, changes in representation are frequently done. We will explore some aspects of this by McCarthy’s ‘mutilated checkerboard’ problem and discuss the tension between the complexity and the power of mechanisms for finding proofs.

Details

Original languageEnglish
Title of host publicationFrom Animals to Robots and Back: Reflections on Hard Problems in the Study of Cognition
Subtitle of host publicationA Collection in Honour of Aaron Sloman
EditorsJeremy L Wyatt, Dean D Petters, David Hogg
Publication statusPublished - 11 Jul 2014

Publication series

NameCognitive Systems Monographs
PublisherSpringer
Volume22
ISSN (Print)1867-4925