A Fundamental Limitation of Symbol-Argument-Argument Notation As a Model of Human Relational Representations
2004; Wiley; Volume: 26; Issue: 26 Linguagem: Inglês
ISSN
1551-6709
Autores Tópico(s)Action Observation and Synchronization
ResumoA Fundamental Limitation of Symbol-Argument-Argument Notation As a Model of Human Relational Representations Leonidas A. A. Doumas (adoumas@psych.ucla.edu) John E. Hummel (jhummel@psych.ucla.edu) Department of Psychology, University of California, Los Angeles 405 Hilgard Ave. Los Angeles, CA 90095-1563 Abstract the symbols and their arrangement (i.e., role-filler bindings). For example, the expressions chase (Pat, Don) and chase (Don, Pat) mean different things, but Pat, Don, and chase mean the same things in both expressions. Formal symbol systems have this property by assumption: It is given in the definition of the system that symbols retain their meanings across different expressions, and that the meaning of an expression is a function of both its constituent symbols and their arrangement. Physical symbol systems (Newell, 1990)—such as digital computers and human brains—cannot simply “assume” these properties, but instead must actively work to ensure that both are satisfied. The claim that human mental representations are symbolic in this sense is controversial (e.g., Elman et al., 1996), however, relational generalization has proved unattainable for non-symbolic models of cognition, and there is reason to believe it is fundamentally unattainable for such models (see Doumas & Hummel, in press; Halford, Wilson, & Phillips, 1998; Hummel & Holyoak, 2003a; Marcus, 1998). Human mental representations are both structure-sensitive (i.e., symbolic) and semantically rich. Connectionist models have well-known limitations in capturing the structure- sensitivity of mental representations, while traditional symbolic models based on varieties of symbol-argument- argument notation (SAA) have difficulty capturing their semantic richness. We argue that this limitation of SAA is fundamental and cannot be alleviated in the notational format of SAA itself. Finally, we review an approach to human mental representation that captures both its structure- sensitivity and semantic richness. Relational reasoning—reasoning constrained by the relational roles that objects play, rather than just the features of the objects themselves—is ubiquitous in human mental life, and includes analogical inference, schema induction, and the application of explicit rules (Gentner, 1983; Holyoak & Thagard, 1995). In order to support human-like relational thinking, a representational system must meet two general requirements (Hummel & Holyoak, 1997): First, it must represent relations independently of their fillers and simultaneously specify how fillers are bound to relational roles (i.e., it must be a symbol system; Newell, 1990). Second, it must explicitly specify the semantic content of relational roles and their fillers. In this paper, we consider in detail the implications of the latter requirement, with an emphasis on symbol-argument-argument notation (SAA), which includes propositional notation, high-rank tensors, and many varieties of labeled graphs. Human Relational Representations Specify the Semantic Content of Objects and Relational Roles A second important property of human relational representations is that they explicitly specify the semantic content of objects and relational roles (e.g., the lover and beloved roles of love (x, y) or the killer and killed roles of murder (x, y)): We know what it means to be a lover or a killer, and that knowledge is part of our representation of the relation itself (as opposed to being specified in a lookup table, a set of inference rules, or some other external structure). As a result, it is easy to appreciate that the patient (i.e., killed) role of murder (x, y) is like the patient role of manslaughter (x, y), even though the agent roles differ (i.e., the act is intentional in the former case but not the latter); and the agent (i.e., killer) role of murder (x, y) is similar to the agent role of attempted-murder (x, y), even though the patient roles differ. More evidence that we represent the semantics of relational roles explicitly is that we can easily solve mappings that violate the “n-ary” restriction (Hummel & Holyoak, 1997). That is, we can map n-place predicates onto m-place predicates where n ≠ m . For instance, given statements such as taller-than (Abe, Bill), tall (Chad) and short (Dave), it is easy to map Abe to Chad and Bill to Properties of Relational Representations Human Relational Representations are Symbolic Symbolic representations have the property that symbols are invariant with their role in an expression 1 , and the meaning of the expression as a whole is a function of both This is not to say that symbols may not have shades of meaning that vary from one context to another. For example, the symbol “loves” suggests different relations in loves (Mary, John) vs. loves (Mary, Chocolate). However, as noted by Hummel and Holyoak (2003a), this kind of contextual shading must be a function of the system’s knowledge, rather than an inevitable consequence of the way in which it binds relational roles to their fillers.
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