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AN APPROACH TO FORMAL PSYCHIATRY HOWARD T. HERMANN, M.D.,* and JOHN CHRISTOPHER KOTELLY] The following essay, condensed from a forthcoming book, lacks full annotation and clinical illustrations. In cursory form, it presents the essence of an approach. The infinite, permutative nuances of the clinic should, in principle, be derivable from such an idealized schema. However, as can readily be seen in the treatment of affects, the system is not fully developed. This is no compendium ofpsychopathology; rather, it is an attempt to construct a formal language (and, therefore, theory) for psychiatry. Section I develops the formal expressions. It uses a variation ofthe language ofmodel theory [i]. Context and metaphoric identification are formally defined and their central role introduced. From this base, we construct a value theory whose explicit inclusion ofa context operator relaxes some ofthe constraints ofcurrent value theory. In SectionII, after a phenomenological treatment ofinduction and evocation ofmodels, we outline application ofthe language to "mental regulatory mechanisms." Emotions, or "affects," are then developed in Section III; and finally, in Section IV, a formal schema for pathology ("psychiatry") is presented, with some sample classifications. Ifour work stimulates efforts to devise a more objective representation of psychiatric phenomena so that students of behavior can talk to each other objectively, it will have served its purpose. For readers unfamiliar with the mathematics of Section I, we suggest a quick initial pass and a more detailed reading on completion of the article. * Associate in Psychiatry, Harvard Medical School, McLean Hospital, Belmont, Massachusetts. ? Present address, NASA, Electronic Research Center, Computer Research Laboratory, Cambridge , Massachusetts. We wish to acknowledge the editorial collaboration ofConstance Botvin and the secretarial assistance of Donna Dickinson. The Bezalel Foundation, Inc., supported the cost of publication. 272 Howard T. Hermann andJohn Christopher Kotelly · Approach to Formal Psychiatry Perspectives in Biology and Medicine · Winter 1967 In the following work, we shall be concerned with a fundamental aspect of biological systems, namely, the plasticity that allows them to mold themselves to the ever changing relationships of nature. This is particularly exemplified by the central nervous system. We believe that one can best describe and analyze this plasticity by a language of model formation. "Models" need in no way be similar to their causes, the "real thing." They arise from the interaction or coupling between "real things" (including other models) and a modeling system. They need only obey the rule oflawfully correlating themselves in such a way that they express all differences and relations of "real things." We propose a formal definition of models in which all these correlative aspects are represented. We shall develop the representations so as to be useful in describing human mental functions. I. The Formal System A model is an ordered set (B, X, h, h*, B*, Xf), denoted by Mod(B, X, h), to be read "B models X relative to h," where (?) X is the set being modeled, (2) B is the modeling set, and (3) h is a map from X to B, written xKb, or, equivalently, h:X —> B, where h is called the filter and h*:X* —> Bf. A map is defined as a relation between two sets, where elements ofthe first set are given correspondencies to those in the second set. X* is the set ofall mappings ofX into X, that is, the set ofall possible changes that can be made within the set, X. Similarly, B* is the set of all mappings of B into B. Each is closed under a single-valued, binary, associative operation , 0, with a unit element [respectively, Id(X*) and Id(B*)], where Id equals, by definition, identity. B* and X* satisfy the conditions of a semigroup , and h*:X* —> B* is a homomorphism. Definition: Given two models, MOd(B1, X, ht) and Mod(B2, X, h2), the "sum" ofthe two models is denoted by Mod(B„ X, k), Mod(B2, X, h2) à MOd(B1 T B2, X, hi T h2). From the definition of model, it can be proven that the sum oftwo models, Mod(Bz T B2, X, K @ h2), is also a model. A. Composition of Models Given two models, Mod(B, X, h) and Mod(B', B, h'), where h:X —» B...

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