#
Bidirectional Named Sets as Structural Models of Interpersonal Communication^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Named Sets and Fundamental Triads

**X**= (X, f, I), in which X and N are two objects and f is a correspondence (e.g., a binary relation) between X and I. With respect to

**X**, X is called the support of

**X**, N is called the component of names (reflector) or set of names of

**X**, and f is called the naming correspondence (reflection) of

**X**. Note that here, f is not necessarily a mapping or a function.

**D**= (X, f, Y), in which the naming relation f goes in two directions.

**Proposition 1.**

- (a) The sequential composition of basic named sets is a basic named set.
- (b) The sequential composition of bidirectional named sets is a bidirectional named set.
- (c) The sequential composition of cyclic named sets is a cyclic named set.

- The direct component X = (X, f, Z)
- The inverse component Y = (Z, g, X)

**Proposition**

**2**.

**X**≬

**Y**= (X, f, I) ≬ (Y, g, J) = (X ∪ J, f ∪ g

^{−1}, I ∪ Y)

^{o}of Y, i.e.,

^{o}

_{o}q

_{o}, J) where r

_{o}= r ∩ (X × (I ∩ Y)) and q

_{o}= q ∩ ((I ∩ Y) × J).

**Example**

**1**

**Example**

**2**

**X**⊕

**Y**= (X, f, I) ⊕ (Y, g, J) = (X ∪ J, f ∪ g, I ∪ Y)

**X**©

**Y**= (X, r, Y) © (Y, q, X) = (X, r∘q, X)

**X**,

**Y**]

## 3. Interpersonal Communication

- -
- Communication space, e.g., a channel or a system of channels, is the medium, in which communication goes and which allows sending messages from the sender to the receiver
- -
- A system of messages, e.g., one message, where a message is the object sent (transmitted)
- -
- A context consists of conditions (environment) in which communication goes

- -
- The physical component of a message, e.g., electrical signals or piece of paper with some text.
- -
- The structural component of a message, e.g., text or picture
- -
- The mental component of a message, e.g., the meaning of a text

- -
- Individual contexts
- -
- Group contexts
- -
- General contexts

- -
- The physical component of a context, e.g., conditions, in which information is sent and received
- -
- The structural component of a context, e.g., language of the message
- -
- The mental component of a context, e.g., knowledge of the sender and receiver

- -
- The starting message m
_{0}is the first message in communication. - -
- The concluding message m
_{f}is the last message in communication. - -
- A feedback message is an outcoming message caused by some incoming message.
- -
- A direct feedback message is an outcoming message caused by the previous incoming message.
- -
- An initializing message is a message that is not a feedback message.

- -
- Communication is linear if it consists of a single communication thread.
- -
- Communication is branching if it contains, at least, one communication multithread.
- -
- The most general is concurrent communication.

## Conflicts of Interest

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Burgin, M.
Bidirectional Named Sets as Structural Models of Interpersonal Communication. *Proceedings* **2017**, *1*, 58.
https://doi.org/10.3390/IS4SI-2017-03916

**AMA Style**

Burgin M.
Bidirectional Named Sets as Structural Models of Interpersonal Communication. *Proceedings*. 2017; 1(3):58.
https://doi.org/10.3390/IS4SI-2017-03916

**Chicago/Turabian Style**

Burgin, Mark.
2017. "Bidirectional Named Sets as Structural Models of Interpersonal Communication" *Proceedings* 1, no. 3: 58.
https://doi.org/10.3390/IS4SI-2017-03916