Jesse B. Wright

Realization of Events by Logical Nets

In Representation of Events in Nerve Nets and Finite Automata [3], S. C. Kleene obtains a number of interesting results. The most important of these, his analysis and synthesis theorems (theorems 5 and 3), are obscured both by the complexity of his basic concepts and by the nature of the elements used in his nets. In this paper we give a new formulation and new proofs of Kleene’s analysis and synthesis theorems, in which we presuppose no acquaintance with Kleene’s work. We use simpler basic concepts and construct our nets out of more familiar and convenient elements (see section 4). The simplified formulation and proofs should make these important results more widely accessible. Some detailed comments on Kleene’s ideas are made in section 7.

Flooding in vivo as research tool and treatment method for phobias: a preliminary report

LOODING IN VW0 is a method of treating phobias by rapid exposure in real life to the feared object or situation, maintaining maximum tolerable anxiety until it begins to diminish, then continuing closer and closer exposure until the patient or client is comfortable in the situation which was previously feared.‘vZ Informally, flooding in vivo is one of the most ancient of therapeutic methods, i.e., overcoming one’s fears by facing them. Interestingly, one of its first public proposals by a mental health professional came from Freud3 in 1919. writing that the analysis of a phobia could only go so far without insisting that the patient enter the feared situation and struggle with the anxiety in real life. Though he did not use the term “flooding,” Guthrie” published several anecdotal accounts of successful application of the procedure. Systematic research on flooding under its current name was begun in the late 1960’s by Marks and his colleagues at the Maudsley Institute in London.1s2.5,6 These early investigations showed flooding to be safe, effective, and acceptable to patients, in spite of the intense anxiety which it arouses. It may in fact be the most rapid and effective of all available methods for treating phobias.’ While a rapid and efficient method of treating phobias would be a noteworthy advance, this alone would be of limited import, since, from a public health standpoint, phobias are among the lesser problems facing psychiatry. However, the significance of flooding may not be limited to this. Several of its characteristics make it more researchable than almost any other procedure in psychiatry. It is intense, rapid, simple, and tied specifically to a definable and controllable stimulus situation. In psychiatry, clinical events with these properties are rare indeed. Among the phenomena occurring during flooding and offering themselves for systematic investigation, are: (1) anxiety: for experimental analysis by psychological, physiological, and pharmacological approaches; (2) other reactions by patients; (3) psychotherapeutic change: allowing investigation of biological and psychosocial factors effecting its rate, quality, and durability; and (4) therapist behavior and therapist-patient interaction. The generality of findings arising from the study of flooding must of course be evaluated. If, as is often said, all psychotherapeutic methods have a common

The Theory of Proportionality as an Abstraction of Group Theory.

In this paper we present an axiomatic theory denoted by T which is an abstraction of group theory in the sense that projective geometry is an abstraction of affine geometry. Extending to group theory, F. Klein’s idea, that a geometry is determined by its group of automorphisms, we describe T as the theory whose group of automorphisms is generated by the automorphisms and translations of group theory. In axiomatic terms the relationship between the two theories is characterized by the fact that from T we can arrive at group theory by distinguishing an element, i. e., by introducing a name for the group identity. This situation is analogous to that in geometry, where affine geometry is derived from projective geometry by the introduction of a name for the lines at infinity.

Invariants of the Anti-Automorphisms of a Group

The background for this paper is provided by Klein’s work presented in the Erlangerprogram [1], and more recent developments of these ideas as well as their application outside the field of geometry [2; 3; 4; 5; 6].

Sequence generators, graphs, and formal languages*†

A sequence generator is a finite graph, more general than, but akin to, the usual state diagram associated with a finite automaton. The nodes of a sequence generator represent complete states, and each node is labeled with an input and an output state. An element of the behavior of a sequence generator is obtained by taking the input and output states along an infinite path of the graph. Sequence generators may be associated with formulas of the monadic predicate calculus, in which the individual variables range over the times 0, 1, 2, 3, ···, and the predicate variables represent complete states, input states, and output states. An unrestricted singulary recursion is a formula in which the complete state at time τ + 1 is expressed as a truth-function of the complete state at time τ and the input states from times τ + 1 to τ + h . Necessary and sufficient conditions are given for a formula derived from a sequence generator being equivalent to an unrestricted singulary recursion.