Neuropsychologia 42 (2004) 926–938 Inductive reasoning and implicit memory: evidence from intact and impaired memory systems Luisa Girelli a,∗ , Carlo Semenza b , Margarete Delazer c a Dipartimento di Psicologia, Università degli studi di Milano-Bicocca, Edifico U6, Piazza dell’ Ateneo Nuovo 1, Milan 20126, Italy b Dipartimento di Psicologia, Università degli studi di Trieste, Trieste, Italy c Universitätsklinik für Neurologie Innsbruck, Innsbruck, Italy Received 31 May 2002; received in revised form 25 November 2003; accepted 28 November 2003 Abstract In this study, we modified a classic problem solving task, number series completion, in order to explore the contribution of implicit memory to inductive reasoning. Participants were required to complete number series sharing the same underlying algorithm (e.g., +2), differing in both constituent elements (e.g., 2 4 6 8 versus 5 7 9 11) and correct answers (e.g., 10 versus 13). In Experiment 1, reliable priming effects emerged, whether primes and targets were separated by four or ten fillers. Experiment 2 provided direct evidence that the observed facilitation arises at central stages of problem solving, namely the identification of the algorithm and its subsequent extrapolation. The observation of analogous priming effects in a severely amnesic patient strongly supports the hypothesis that the facilitation in number series completion was largely determined by implicit memory processes. These findings demonstrate that the influence of implicit processes extends to higher level cognitive domain such as induction reasoning. © 2003 Elsevier Ltd. All rights reserved. Keywords: Number series; Arithmetic reasoning; Amnesia; Priming 1. Introduction Inductive reasoning, defined as the process of inferring a general rule by inspection of specific instances, is regarded to be a critical constituent of human intelligence (Spearman, 1923; Thurstone, 1938). Research by cognitive psychol- ogists demonstrated that inductive reasoning is essential in problem solving, in the development of expertise and in learning (Bisanz, Bisanz, & Korpan, 1994; Pellegrino & Glaser, 1982). In particular, rule induction has been shown to underlie a variety of activities such as concept formation (Simon & Lea, 1974), reading comprehension (Greeno, 1978), and effective instruction (Norman, Genter, & Stevens, 1976). Typical examples of inductive reasoning tasks are series completion problems that require noting similar relation- ships across instances (Holzman, Pellegrino, & Glaser, 1983; Kotovsky & Simon, 1973; Simon & Kotovsky, 1963). In the completion of letter or number series, such as A C E G or 2 4 8 16, a general rule, which defines the relations among the constituent elements, has to be identified and subsequently ∗ Corresponding author. Tel.: +39-02-6448-6722; fax: +39-02-6448-6706. E-mail address: luisa.girelli@unimib.it (L. Girelli). applied to continue the series. Letter series and number se- ries offer the opportunity to create a universe of items and to determine item difficulty on an a priori basis (Quereshi & Seitz, 1993); moreover, they seem rather sensitive indices of problem solving abilities (Holzman et al., 1983). For this reason, tasks of series completion gained wide application in both educational and psychological assessments (Langdon & Warrington, 1995; Thorndike, Hagen, & Sattler, 1986). Solution of series completion problems is a complex pro- cess and elaborate theoretical frameworks have been pro- posed to model the cognitive steps involved (Holzman et al., 1983; Kotovsky & Simon, 1973; Simon & Kotovsky, 1963). Overall, four basic components of series completion are de- picted by cognitive models. The first component, relations detection, requires the subject to scan the series and to ad- vance hypotheses about the way in which one element of the series is related to the adjacent one. Relations between elements may be simple or complex, they may involve a single arithmetic operation (such as addition or subtraction) or more than one operation (such as multiplication and sub- traction). The second component is the discovery of peri- odicity. The period length of a series defines the number of elements that completes one cycle: simple series have a pe- riod length of 1 (such as 2 5 8 11—rule +3), where the same relation applies to each following element, more complex 0028-3932/$ – see front matter © 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.neuropsychologia.2003.11.016