Abstract
The open-domain Frame Problem is the problem of determining what features of an open task environment need to be updated following an action. Here we prove that the open-domain Frame Problem is equivalent to the Halting Problem and is therefore undecidable. We discuss two other open-domain problems closely related to the Frame Problem, the system identification problem and the symbol-grounding problem, and show that they are similarly undecidable. We then reformulate the Frame Problem as a quantum decision problem, and show that it is undecidable by any finite quantum computer.
Highlights
The Frame Problem (FP) was introduced by McCarthy and Hayes [1] as the problem of circumscribing the set of axioms that must be deployed in a first-order logic representation of a changing environment
In open domains, including task environments of interest for autonomous robotics, the ordinary world of human experience, or the universe as a whole, the FP raises potentially-deep questions about the representation of causality and change, the representation of unobserved changes, e.g., leading to unanticipated side-effects. Interest in these questions in the broader cognitive science community led to broader formulations of the FP as the problem of circumscribing relevance relations [3,4], a move vigorously resisted by some AI researchers [5,6]
We show that the FP and the Halting Problem (HP) are equivalent: undecidability of one entails undecidability of the other
Summary
The Frame Problem (FP) was introduced by McCarthy and Hayes [1] as the problem of circumscribing the set of axioms that must be deployed in a first-order logic representation of a changing environment. In open domains, including task environments of interest for autonomous robotics, the ordinary world of human experience, or the universe as a whole, the FP raises potentially-deep questions about the representation of causality and change, the representation of unobserved changes, e.g., leading to unanticipated side-effects. Interest in these questions in the broader cognitive science community led to broader formulations of the FP as the problem of circumscribing (generally logical) relevance relations [3,4], a move vigorously resisted by some AI researchers [5,6]. Practical solutions to the FP, in robotics, remain heuristic (e.g., References [17,18,19])
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