Sequent-systems and groupoid models. I

The purpose of this paper is to connect the proof theory and the model theory of a family of propositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related toBCK algebras, and, finally, Johansson's and Heyting's logic. First, sequent-systems are given for these logics, and cut-elimination results are proved. In these sequent-systems the rules for the logical operations are never changed: all changes are made in the structural rules. Next, Hubert-style formulations are given for these logics, and algebraic completeness results are demonstrated with respect to residuated lattice-ordered groupoids. Finally, model structures related to relevant model structures (of Urquhart, Fine, Routley, Meyer, and Maksimova) are given for our logics. These model structures are based on groupoids parallel to the sequent-systems. This paper lays the ground for a kind of correspondence theory for axioms of logics with implication weaker than Heyting's, a correspondence theory analogous to the correspondence theory for modal axioms of normal modal logics.The first part of the paper, which follows, contains the first two sections, which deal with sequent-systems and Hubert-formulations. The second part, due to appear in the next issue of this journal, will contain the third section, which deals with groupoid models.     

An evaluation of the Garren-Edwards diet and behavior modification program

This study evaluated the efficacy of the Garren-Edwards Behavior Modification Program, which uses the Garren-Edwards Gastric Bubble as an adjunct to treatment. Group therapy sessions were conducted with 23 morbidly obese subjects for 6 months on a biweekly basis. Each therapy session used a five-stage problem-solving sequence designed to facilitate adaptive behavioral alternatives. In evaluating weight change, a multivariate analysis of variance was conducted along with two preplanned orthogonal comparisons. Patients lost significant amounts of weight between initial to 3-month (p<.0001) and 3- to 6-month intervals (p<0001). A similar treatment effect was noted in an additional sample of 24 morbidly obese subjects following 3 months of treatment (p<0005). The findings support the value of longer goal-oriented programs in promoting continued weight loss. Implications for treatment process and therapist interventions prompted by this new format are discussed.