Rules in relevant logic — II: Formula representation

This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A ₁ .A ₂ . ... .A _n B, the conjunctive form,A ₁&A ₂ & ...A _n B, the combined conjunctive and iterated form, enthymematic version of these three forms, and the classical implicational form,A ₁&A ₂& ...A _n B. The concept of general enthymeme is introduced and the Deduction Theorem is shown to apply for rules essentially derived using Modus Ponens and Adjunction only, with logics containing either (A B)&(B C) .A C orA B .B C .A C.I acknowledge help from anonymous referees for guidance in preparing Part II, and especially for the suggestion that Theorem 9 could be expanded to fully contraction-less logics.     

Book reviews

The Popularization of Medicine 1650–1850 Roy Porter (ed.), 1992 London, Routledge pp. x + 296, £50 (hardback) ISBN 0415 07217 4

Quantum Mechanics: An Empiricist View Bas Van Fraassen, 1991 Clarendon Press, Oxford pp. 558, £17.50 (paperback), ISBN 019 8239807     

Punished and Nonpunished Responding in A Multiple Schedule in Humans: A Brief Report

Four male subjects responded on a multiple schedule in which responding was maintained by a random interval 20-sec (RI20) schedule of point presentation. Responding was suppressed in alternating components by an added variable ratio 30 (VR30) schedule of point subtractions. Each component was accompanied by distinctive stimulus lights. Subjects were exposed to the multiple schedule from the initial session. Two subjects experienced four 50-min sessions daily (Experiment 1) and the other two subjects participated in one 50-min session daily (Experiment 2). Once responding in the punished components had stabilized, responding in the nonpunished components continued to increase across sessions. Nonpunished responding did not stabilize even after as many as 36 sessions. These results are discussed in the context of previous studies using animals which employed multiple schedules with punished and nonpunished response contingencies.

     

The predictive validity of teacher nominations: A five-year followup of at-risk youth

The purpose of this study was to examine the predictive validity of a teacher nomination procedure for identifying at- risk children. Two hundred and twenty-five children were nominated by their teachers as well- adjusted (n= 75), socially withdrawn (n=76), or socially aggressive (n=74) during the fourth grade. Five years later, 198 of these children (88%) were located and their adjustment evaluated. Significant differences among the nominated children were found on a variety of measures, including academic grades, sociometric status, and social behavior. In addition, differences in school dropout and delinquent offenses were noted. Results are discussed in terms of the validity of teacher nomination procedures and their utility in identifying at- risk youth.     

Retraction of Ross and LoLordo findings concerning blocking in serial feature-positive discriminations.

Findings concerning the effectiveness of stimuli from various conditioning procedures in blocking conditioned excitation and occasion-setting functions of an added stimulus in a serial feature-postive discrimination training procedure (LoLordo & Ross, 1987; Ross & LoLordo, 1986, 1987) are retracted. Videotapes on which the published data were based were rescored by 2-5 people, most of whom were uninformed about group memberships of the subjects. In no case did the rescoring confirm any of the orginal findings of blocking. Possible factors contributing to the discrepancies are discussed. The experiments should be repeated with feature stimuli that are less similar to each other and with several scorers, at least one of whom is unaware of the group assignment of the subjects.