Relevant Robinson's arithmetic

In this paper two different formulations of Robinson's arithmetic based on relevant logic are examined. The formulation based on the natural numbers (including zero) is shown to collapse into classical Robinson's arithmetic, whereas the one based on the positive integers (excluding zero) is shown not to similarly collapse. Relations of these two formulations to R. K. Meyer's system R# of relevant Peano arithmetic are examined, and some remarks are made about the role of constant functions (e.g., multiplication by zero) in relevant arithmetic.This paper has been greatly influenced by the (largely unpublished) work of E. K. Meyer (cf. [7]) on relevant arithmetic, and I wish to thank him, and also N. D. Belnap, Jr. and D. Cohen for helpful advice. In fairness to Meyer it must be said that he finds my axioms 13 and 13(1) too strong (they are not theorems of his system R# - cf. §4 below). Meyer tells me be finds vindication for his view in my chief theorem of §2. For myself, I find the insights behind Meyer's work on R# to be both stable and fruitful, and if I now had to make a choice, I would follow Meyer in his rejection of my axioms. However, the systems I explore in this paper themselves have a surprising amount of internal consistency of motivation (cf. §5). Let a hundred formal systems bloom.     

A theorem in 3-valued model theory with connections to number theory,type theory,and relevant logic

Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (non-degenerate) 3-valued counterpart of . Classical sentences that are true in are non-false in . Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic (the proof for number theory was obtained earlier by R. K. Meyer and suggested the present abstract development).     

Coactor's behavior and imitative aggression

After being exposed to either an aggressive or a nonaggressive filmed model, four- and five-year-old boys were tested for imitation while either alone or with a confederate who had also seen the film. The confederate's behavior was either inactive, the same as that in the film, the same as that in the film the child had not seen, novel but of the same category (aggressive or nonaggressive) as that in the film seen, or novel but in the category of the film not seen. These conditions conformed to the dimensions of a 2 × 6 factoral design. According to prediction, the imitation of subjects exposed to the aggressive model was greatest when the confederate's behavior was similar to the model's. No difference in imitation was produced by the confederate's actions if the boy had watched the nonaggressive model. The results were interpreted within the context of social comparison theory.This project was facilitated by the senior author's Margaret Bosshardt Pace and Paul David Pace Research Fellowship.     

THOG: The anatomy of a problem

Summary Three experiments are reported on the attempts to solve a novel hypothetico-deductive problem. Its solution demands both the postulation of hypotheses about its structure and a combinatorial analysis upon the consequences of these hypotheses. The majority of subjects (students) failed to solve the problem because they argued from the properties of stimuli rather than from hypotheses about their conceptual status. The results suggest that a familiarity with the logical structure of the problem and the elicitation of appropriate hypotheses failed to correct this intuitive approach. These findings are discussed in relation to Piaget's theory of formal operations, and (very tentatively) in relation to habitual styles of thought.     

Temporal properties of responding during stimuli that precede response-independent food

Pigeons' keypecks were reinforced with grain on the average of once per minute by schedules that maintained low response rates and by schedules that maintained high response rates. During these schedules, a fixed-duration conditioned stimulus (CS) ranging from 7.5 to 120 sec in duration across conditions terminated with response-independent food. Response rates during the CS were inversely related to CS duration. The rates and the temporal patterns of responding during the shortest CS were similar whether the ongoing schedule maintained high response rates or low response rates. As CS duration increased, the rate and pattern of responding during the CS converged on the rate and pattern of responding maintained by the baseline schedule. These data indicate that changes in responding during stimuli that signal response-independent reinforcement are not homogeneous throughout the CS; that response measures, such as “suppression ratios”, which presume homogeneity may mislead us; and that conditioned suppression and conditioned enhancement may be better talked about in terms of species-specific approach and avoidance than in terms of emotional states.     

Classifying pictures and words: Implications for the dual-coding hypothesis

In deciding that two items come from the same category, subjects were delayed if the items were presented as a word and a picture, as compared with two words or two pictures. Subjects were not delayed if the items were not to be compared. Hence, the delay appears to occur during the retrieval and comparison of know ledge about the items, not during their perceptual analysis. The results suggest that there are two distinct codes involved in the categorization of words and pictures, rather than a single code.