Comparative jugdments in transitive inferences

1 Mayor, J., Gonzalez-Marques, J., Sainz, J.S. y Suengas, G. (1988). Comparative judgements in transitive inferences. En Cornoldi, C. (Ed.) Imagery and Cognition. Proceedings of the Second Workshop on Imagery and Cognition. Padua: Universita di Padova

COMPARATIVE JUGMENTS IN TRANSITIVE INFERENCES JUAN MAYOR, JAVIER GONZALEZ-MARQUES, JAVIER S. SAINZ, and AURORA G.SUENGAS DEPARTAMENTO DE PROCESOS COGNITIVOS, UNIVERSIDAD COMPLUTENSE DE MADRID, SPAIN ABSTRACT An experiment on transitive inference was conducted using three-term comparisons as premises. The stimuli presentation size and the modality were manipulated. The other variables (i.e., first and second premises comparatives, first and secand premises terms arder, and question type) define the body of three term series problems that were presented. We confirmed that modality and size of presentation of stimuli affect the processing of the premises rather than the inference process itself. The inference process takes primarily place during the second premise processing time as a consequence of the non-imperative application o¡ a heuristics hierarchy that acts within the framework of a mental model where analogical representations play a dominant rale. Key words:

Transitive inference; comparative judgments; mental models; modality effect; congruency effect; interference effect; truth value effect.

1. INTRODUCTION Recent studies on transitive inference show the difficulties of adjustment of empirical evidence to models predictions. These difficulties have shifted the focus of inference research towards the role of the format and the functional value of the representation (the image in particular), the processing structure (Evans, 1982; Kaufmann, 1988), and the relationship between inference and camparison processes (Richardson, 1983). The most promising framework seems to be that of the functional value of the representations created and manipulated during the inference process. Two types of theories have been proposed in this regard: Mental model theories, and rule theories (Gallatti, Baran & Sabini, 1986). Mental model theories underline the importance of the semantic interpretation, the relationships, and the truth conditions of the premises. These models suggest the existence of a comparison process that governs a model construction that will, in turn, allow to form the conclusion fram the between and within premises relationships. According to rule theories, while doing an inference, subjects proceed by applying logic rules from an abstract and content independent configuration of the premises. A distinction must be made between mere coding processes and inference processes (Mayor, 1979; Ganzalez-Marques, 1979). A review of research on both sentence verification (Clark & Chase, 1972; Carpenter & Just, 1975; Mayor, 1979, 1981; Mayor & Gonzalez-Marques, 1984), and comparative judgments (Paivio, 1975, 1986; Banks, 1977; Banks & Flora, 1977; Marschark & Paivio, 1981; Sainz, Mayor & Ganzalez-Marques, 1988) helps tu specify the cading processes. In sentence verification, a comparison is made between the sentence and some information either presented to the subject or represented in semantic memory. This process is influenced by syntactic, semantic, pragmatic, and. contextual variables. Symbolic distance effects, congruency effects, and context effects, present in comparative judgments tasks, are largely due to task demands. In order to explain both sentence verification and comparative judgment processes, analogical and propositional types af models have been proposed. Both types of models provide a fair but incomplete account of the empirical data. Significant facilitation and interference effects, similar tu those found in priming and Stroop tasks, appear in sentence verification and comparative judgment tasks when the madality, the size of presentation of the stimuli, and the task are manipulated (Mayor, Sainz & Ganzalez-Marques, 1988). These facilitation and interference effects contribute to clarify the structure and functional basis of the processsing that takes place in sentence verification and comparative judgment tasks. Thus, it seems interesting to study the scope of these effects in more complex situations such as transitive inference tasks. When comparative sentences are used as inference premises, it seems reasonable to assume that the modality would affect the codification of the premises (Paivio, 1975). Since the modality affects neither the processes underlying the manipulation of the truth value, nor the use of logic rules, ¡t is less likely that the modality would interact with the processing structure of the inference. The manipulation of the size of presentation of the stimuli in comparative judgments resulted In interference effects that, under some conditions, interacted with the modality effects (Paivio, 1975;

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Mayor, Sainz & Gonzalez-Marques, 1988). Provided that the representation of the size of the stimuli presented is only relevant to working memory, such interference effects would not be expected to affect beyond the codification of the premises into the inference process itse1f. Three main theories (other than Hunter's, 1957) have attempted to account for the results usually obtained in transitive inference tasks: Image theory, linguistic theory, and mixed theory. All theories have predictions about the differential difficulty of various inference problems (see Riviere, 1986), but based on the designs and materials employed, it is difficult to decide which of these theories adjusts better to the empirical evidence (Evans, 1982). Nevertheless, some principles and effects fram these theories deserve to be considered because of their careful analyses both in relation to the coding of the premises and the inference process. According to the original version of the image theory (DeSoto, London & Handel, 1965), subjects successively codify the two premises, and order the premises series in an spatial axis. The ordering of the premise terms follows two principles: (a) The directionality principle states that it is easier to order the terms according to the direction marked by the relational term. than in the opposite direction. (b) The end-anchoring principle states that a premise is easier to order when its end acts as grammtical subject. Huttenlocher (1968) reduces the latter principle to the second premise, and names it the correspondence principle. The linguistic theory (Clark, 1969) assumes that subjects separately codify the two premises as propositions, and afterwards search for information congruent with the question in these propositions. These processes are guided by three principles: (a) The primacy of functional relationships principle states that a propositional semantic representation is created where the deep structure relationships have primary value; (b) the lexical marking principle stresses the functional asymmetry of most bipolar adjectives; and (c) the congruency principle states that sentence information stored can be retrieved anly if its functional relationships are congruent with the question. The mixed model (Sternberg, 1980) integrates the main principles from the two theories described above. First, subjects codify semantically the premises according to Clark's theory (1969), and then organize them in a spatial structure. Afterwards, the two separate premises have to be integrated in a single representation by using the pivot or middle term. If the comparative statement is affirmative, the search for the pivot does not involve any special difficulties. In negative equatives, the difficulties increase and the negation has to be codified. Then, subjects have to search for the response using the pivot; thus, the search is easier if the pivot is in the second premise. 2. EXPERIMENT In order to clarify the role of images, the structure of processing, and some effects frequently discussed in the field, we conducted the current experiment where certain variables were manipulated in a transitive inference task. The inference involved the comparison of animal sizes. In order to test for the modality effect, the terms of the premises were presented either as words ar as pictures. Subjects' instructions oriented them to solve the inferences disregarding reality. Thus, according to our previous research, we would expect the size of presentation of the stimuli (big or small) to facilitate or interfere with the processing of the inference as a function of its congruency or incongruency both with reality (as it is mentally represented), and with the meaning of the premises. Despite these interferences, we expected the reaction times to be controlled by the truth value of the premises [¡.e., True (T) or False (F) as a function of the differential processing complexity of various types af three pairs of terms (TT, TF, FT, and FF). The rationale for this prediction is that subjects in the task (i.e., comparing real animal sizes) manipulate spatial information that forces an analogical type of processing. In order tu study the truth value sistematically, we used 16 pairs of premises that orthogonally combine both the two premise terms as a function of their real size (i.e., big-small or small-big, for each premise), and the comparatives (i.e., bigger ">" or smaller "B, B>C / A>B, C B ¡s the basic premise; A < B is a premise with one comparative transformation; B > A ¡s a premise with one order tranformation; and B < A is a premise with two comparative and order transformatians). The fact is that analogical models allow to consider that A > B and B < A are represented by the same terms and by the same comparative relation between them, but read in one direction (from big to small) or the contrary (from small to big). This does not occur with A < B and B > A premises representations that force in addition to a change of direction, a size change or an order change (see Mc Gonigle & Chalmers, 1987). A different effect seems to appear with the combination of premises: As shown in Figure 4, the combination of type 1 premises (TT) is faster than the rest, and the combination of type 4 premises (FF) is slower than the rest. (4) The manipulation of the modality and the size of presentation does not structurally affect the inference process, consequently it did not produce significant effects in the reaction times obtained and attributable to the inference process itse1f. Pictures do systematically lead to a faster codification of premises than words due to the fact that metric information is manipulated. Nevertheless, pictures do not interact with the variables that define the inference process. The size of presentation of the stimuli does not reach the significance level as isolated variable, but it does interact with other variables (e.g., comparatives, truth value) in the first premise and, occasionally, in total times. Thus, we seem to confirm the existence of some interference effects, but they seem to be lacated at the level of premises processing than at the level of inference process itself (see Paivio, 1975, 1986 for different results). (5) Vhen sentence verification processes and comparative judgments processes are integrated in transitive inferences, results and explicative hypotheses from verification and comparative judgments cannot be directly extrapolated to situations where the two premises variables interact as has been confirmed by the empirical. data. None of the inference theories is unequivocally supported by the present data. This lack of support could be attributed to the assumption that the mental model constructed by the subjects articulates different principles weighted differently from theories predictions. 4. REFERENCES Banks, W. (1977). Encoding and processing af symbolic information in comparative judgments. In G. Bower (Ed. ), The psychology of Learning and Motivation. New York: Academic Press. Banks, W. P., & Flora, J. (1977). Semantic and perceptual processes in symbolic comparisons. Journal of Experimental Psychology: Human Perception and Performance, 3, 278-290. Carpenter, P. A, & Just, M. A. (1975). Sentence comprehension: A psycholinguistic processing model of verification. Psychological Review, 82, 45-73. Clark, H. H. (1969). Linguistic processes ¡n deductive reasoning. Psychological Review, 76, 378-404. Clark, H. H., & Chase, W. (1972). On the process of comparing sentences against pictures. Cognitive Psychology, 3, 472-517. DeSoto, C. B., London, N., & Handel, S. (1965). Social reasoning and spatial paralogic. Journal of Personality and Social Psychology, 2, 513-521 Evans, J. St. B. T. (1982). Psychology af deductive reasoning. London: Routledge & Kegan Paul. Gallotti, K.M., Baron, J., & Sabini, J. P. (1986). Individual differences in syllogistic reasoning: Deduction rules or mental models? 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