Papers

1982-1985

1982-1985

2009-2012

2007-2008

2003-2006

1999-2002

1995-1998

1989-1993

1986-1987

1982-1985

1977-1981

1962-1975

In experimental investigations related to Kelly’s theory of constructs, it was

found that subjects on the average choose a positive over a negative pole with

the probability 0.62. In this paper, it is shown that the choice of this constant

can be mathematically explained with the algebraic model of ethical cognition.

The analysis of the Boolean model of ethical cognition has demonstrated that

a law similar to the principle of complementarity is realized in the model:

‘interference of feelings’ is incompatible with the correct registration of inner

intentions. The entire class of the possible algebraic model is investigated, and

it is shown that if we postulate the existence in the human psyche of the

principle of complementarity and of analogues of parallel and sequential

locations of physical devices, then as a consequence we obtain the Boolean

model.

A brief description of an algebraic model of ethical cognition based on an

exponential representation of Boolean function is given in this paper. This

model allows us to connect the behavior of an individual with the structure of

his inner world. Unexpectedly, we found that the classical idealized experiment

on the interference of the electrons from two sleets can be simulated with the

help of the same model. Thus, we succeeded in establishing connection

between the phenomenon of cognition and the quantum phenomenon by

looking at quantum mechanics through a psychologist’s eyes.

Any finite graph (non directed, no loops) can be coupled with its comple-

mentary graph producing what we term a completed graph. This paper

studies completed graphs in the context of a structural concept called

stratification that is motivated by theoretical work in social psychology and

sociology. A completed graph is stratified in case its node (vertex) set can be

divided into two nonempty subsets with exactly one of the two types of ties

holding between every pair of nodes from distinct sets. A completed graph is

totally stratified in case every one of its nontrivial completed subgraphs is

stratified. The first part of the paper relates the concept of stratification to

the familiar graph property of connectedness. In particular, a completed graph

is totally stratified if and only if it does not have a four point completed

subgraph that is connected in both the original graph relation and its comple-

mentary relation. Using the concept of stratification, completed graphs can be

decomposed uniquely into taxonomic structures, that is nested sets of

partitions. An algorithm for the decomposition based on the work with the

concept of stratification is developed. The relationship between the notion of

stratification and the ideas in balance theory is examined, and stratification is

viewed as a generalization of Davis’ notion of clustering. It turns out that the

concepts of clique, status, and structural equivalence used throughout the

social network literature can be defined in an interesting way for completed

graphs. Cliques are sets of nodes with similar internal links and statuses are

sets of nodes with similar external links. Structurally equivalent sets are both

cliques and statuses. The concepts of status and structural equivalence are

closely related to the decomposition algorithm. In particular, for any totally

stratified completed graph, the set of all statuses and the set of all maximal

structurally equivalent sets can be generated by mathematical operations

performed on the taxonomic decomposition of the completed graph. Finally

some of our results are informally related to the block-modeling approach to

analyzing social network data discussed in several previous Journal of

Mathematical Psychology articles.

1982-1985

2009-2012

2007-2008

2003-2006

1999-2002

1995-1998

1989-1993

1986-1987

1982-1985

1977-1981

1962-1975

1982-1985