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Circumscription — Applications to Formalizing Common Sense Knowledge

Reference: John McCarthy (1986). “Applications of Circumscription to Formalizing Common Sense Knowledge.” Artificial Intelligence 28(1): 89-116. Source file: mccarthy-applications1986.pdf. Sequel to the 1980 paper; see Circumscription - A Form of Nonmonotonic Reasoning for the original formulation and motivation. URL

Summary

The 1986 sequel that supersedes the technical machinery of McCarthy’s 1980 Circumscription paper. Where the 1980 paper introduced predicate and domain circumscription as rules of conjecture for handling the qualification problem, this paper presents a new, more symmetric version — now called formula circumscription — and shows how it, together with a uniform abnormality predicate ab, can formalise a wide range of common-sense reasoning tasks: is-a hierarchies with exceptions, the unique-names hypothesis, the frame problem (via circumscribing abnormality-of-fluents rather than asserting individual frame axioms), and defeasible defaults.

The central methodological move is to express a typical common-sense rule as “normally, P” — formalised as ∀x. ¬ab(aspect₁(x)) ⊃ P(x) — and then circumscribe ab relative to the known facts, with certain other predicates and functions allowed to vary during the minimisation. Allowing predicates other than the one being minimised to vary was the key technical gap in the 1980 formulation; it is what lets circumscription express the frame problem properly (the ab predicate is circumscribed while the fluent values are varied), and what makes prioritised and parallel circumscriptions possible. Birds-fly/Tweety, blocks-on-blocks, and other benchmark examples are worked out in detail.

Alongside Ascribing Mental Qualities to Machines and First Order Theories of Individual Concepts and Propositions, this is the paper that consolidates McCarthy’s logicist programme for common-sense knowledge into a concrete technical agenda: formalise in sorted first-order logic, add concepts-as-individuals where modality is needed, use circumscription (over ab) to handle defaults and the frame problem, and build large reusable common-sense databases. It is the paper cited in the ACL/agent-communication literature whenever “McCarthy on circumscription” is invoked as a foundation for defeasible agent reasoning.

Key Ideas

  • Formula circumscription generalises predicate circumscription: circumscribe a formula with some predicates and functions allowed to vary.
  • The abnormality predicate ab provides a uniform idiom: “normally P” becomes ¬ab(aspect(x)) ⊃ P(x), and the formalisation is combined with ab being circumscribed.
  • Solves the frame problem via circumscribing ab(aspect, action, fluent, situation) while letting the fluents vary — no more individual frame axioms per (action, fluent) pair.
  • Is-a hierarchies with exceptions: “birds fly except when abnormal”, cancellation of inheritance via ab.
  • Unique-names hypothesis stated and circumscribed in the same framework.
  • Prioritised circumscription briefly explored: minimise one abnormality before another.
  • Supersedes the 1980 paper; references in the literature “to this paper only would better refer to the latter paper in addition or to the latter paper only” (quoting McCarthy on the 1980 paper’s jmc.stanford.edu page).

Connections

Conceptual Contribution

Tags

#foundational #mccarthy #non-monotonic #common-sense #knowledge-representation #circumscription #frame-problem #1986

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