Declarative Bias for Structural Domains

We present a formal solution to the problem of situation identification in learning of structural concepts. Structural concepts are characterized by the interrelationships and attributes of their parts, rather than by just their own direct attributes. Our solution extends the declarative approach to bias of (Russell and Grosof, 1987) by formalizing the beliefs about relevancy in a more complex form that expresses the preservation of properties under mappings, using second-order logic to express the existence of isomorphisms. Concept learning, including prediction, analogical inference and single-instance generalization, then emerges as deduction from such isomorphic determinations plus instance data. Situation Identification and Declarative Bias One of the main tasks faced by a learning agent is the situation-identification problem: to identify the aspects of its empirical experience that are relevant to learning a goal concept (Charniak and McDermott, 1985; Bundy et al., 1985). Such relevancy constraints constitute an important part of the bias the agent needs to focus its hypothesis formation. Without a suitably condensed intermediate description language, an agent learning to classify 100x100-binary-pixel visual scenes, for example, would confront a hypothesis space of size 2 10000 . Declarative Bias (Russell and Grosof, 1987, 1989; Grosof and Russell, 1989; Russell, 1989) is an approach that enables a learning agent to autonomously derive these relevancies in a goal-directed manner from its background beliefs. Determinations are a form of axiom that express relevancy and can be used to represent appropriate description languages for instances. For example: {Make(x, u) ∧Model(x, v)} ≻ CarV alue(x, z) def ≡ ∀x1x2uvz.Make(x1, u) ∧Make(x2, u) ∧Model(x1, v) ∧Model(x2, v) ⇒ {CarV alue(x1, z) ≡ CarV alue(x2, z)} Concept learning, including prediction, analogical inference and single-instance generalization, then emerges as deduction from such determinations plus instance data. An inference engine called IDL that performs this kind of reasoning, including a form of chaining among determinations, has been implemented on top of the MRS theorem prover (Genesereth, 1983) by Lise Getoor (Getoor, 1989). More generally, default determinations and other defeasible beliefs can be used to perform inference in a non-monotonic logical system, enabling the system to make inductive leaps and to shift bias when observations contradict the original bias (Grosof and Russell, 1989).