Reasoning with Negations: The Australian Plan, Negation-as-Failure and Card Selection Tasks (with Francesco Berto)

September 2026

Francesco Berto and Greg Restall, “Reasoning with Negations: The Australian Plan, Negation-as-Failure and Card Selection Tasks”, article to appear in Review of Philosophy and Psychology.

Two kinds of formal semantics for negation can help us understand puzzles in the psychology of reasoning: the Australian Plan semantics, which generalises the account of negation found in frame semantics for intuitionistic logic, relevant and substructural logics; and negation-as-failure, found in logic programming and default logic. We provide a framework where the two kinds of negation coexist, mapping them to the celebrated distinction between System 1 and System 2 thinking. We use the framework to target the phenomenon of Matching Bias: specifically, to explain why reasoners fare differently in card selection tasks, depending on whether the target property is phrased positively or negatively.

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I’m Greg Restall, and this is my personal website. ¶ I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology ¶ I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.

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