# Shared Context Facilitates Lexical Variation in Sign Language Emergence

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## Abstract

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## 1. Introduction

## 2. Model Description

**Purpose**. The purpose of this model is to investigate how shared context affects lexical variation in sign language emergence. As shown in Figure 3, the agent-based model takes the following values as input parameters:

- The number of concepts (n_concepts);
- The number of bits (n_bits): the number of bits (0 or 1) in the culturally salient features and form (i.e., the length of a word);
- The number of agents in the model (n_agents) (i.e., the population size);
- The number of groups (n_groups): agents are assigned to a group, which determines which features of a referent are culturally salient to an agent;
- The initial degree of overlap between the culturally salient features and form (initial_degree_of_overlap) (the parameter simulating iconicity);
- The number of time steps in the model (n_steps).

**Entities, state variables and scales**. The only entity in the model is the agent, which is the entity in the model that represents one individual in the real world. Agents consist of a unique id and a group that they are assigned to during the initialization stage (first stage of the model). Furthermore, each agent has a language representation which is explained in the initialization below. Figure 4 shows an example of an agent.

**Process overview and scheduling**. The set-up of the model is outlined in initialization below. After the initialization phase, each time step consists of the processes outlined in Table 1. For details of these processes, see the Submodels sections. A schematic overview of the order of processes and parameter input is provided in Figure 3.

**Initialization**. For each group (n_groups), a bit vector of length n_bits is generated per concept (n_concepts). Following the example provided in Figure 4, the culturally salient features associated with concept A is 001 and concept B is 000. In the real world, this could be analogous to two concepts, say, pig and butterfly, which have different culturally salient features (dependent on the background of a person), such as wings for a butterfly and pigs rolling in mud or how they are killed in farming. Roughly, the string of 0s and 1s representing the culturally salient features can be thought of as a unique representation of the characteristics of that concept, given the group one is in.

**Submodel Language game**. The language games consist of two agents interacting—a sender and a receiver, simulating a simplified exchange between two individuals. At each time step in the model, all agents take one turn as a sender in the language game. As shown in Figure 5, the language game consists of four steps. First, the sender randomly chooses a concept and produces the corresponding form. In Figure 5, the sender has randomly chosen concept A. In real life, this would be analogous to an individual wanting to communicate about a given concept and producing the corresponding sign or uttering the corresponding word.

**Submodel Collect data**. In the data collection phase of each time step, two calculations are made: the mean degree of iconicity and the mean lexical variability. Calculation examples are demonstrated with the agents in Figure 6.

## 3. Results

#### 3.1. Two Example Runs

- The number of concepts (n_concepts): 10;
- The number of bits (n_bits): 10;
- The number of agents in the model (n_agents): 10;
- The initial degree of overlap between the culturally salient features and form (initial_degree_of_overlap): 0.9;
- The number of steps in the model (n_steps): 2000.

#### 3.1.1. Language Game Results

#### 3.1.2. Lexical Variability and Iconicity

#### 3.2. The Effect of Multiple Groups on Lexical Variation

#### 3.3. The Effect of Population Size on Lexical Variation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Parameter Exploration

#### Appendix A.1. Initial Degree of Iconicity

**Figure A1.**The mean lexical variability over the 2000 model stages for different numbers of groups that agents can be assigned to (n_groups): 1, 5 and 10, while varying the degree of overlap between the form and culturally salient features at the start of the run (initial_degree_of_overlap). The dark line represents the mean and the shaded area represents the standard deviation of the 100 repetitions. With one exception (n_groups = 1 and initial_degree_of_overlap = 1), the higher the initial degree of overlap between form and culturally salient features, the lower the mean lexical variability. In addition, the higher the initial overlap between form and culturally salient features, the higher the degree of iconicity.

#### Appendix A.2. The Number of Concepts

**Figure A2.**The mean lexical variability over the 2000 model stages for numbers of concepts (n_concepts): 1, 5, 10, 20, 50, 100. The dark line represents the mean and the shaded area represents the standard deviation of the 100 repetitions. When there are more concepts, the initial value of lexical variability increases. While the runs with few concepts quickly stabilize at a fairly high degree of lexical variability, the runs with more concepts have a lexical variability value which continues to decrease. The degree of iconicity is comparable across runs with different numbers of concepts, though runs with more concepts retain a higher degree of iconicity longer before stabilizing.

#### Appendix A.3. The Number of Bits

**Figure A3.**The mean lexical variability over the 2000 model stages for runs with a different number of bits (n_bits): 5, 10, 20, 50, 100 and for different numbers of groups that agents can be assigned to (n_groups): 1, 5, 10. The dark line represents the mean and the shaded area represents the standard deviation of the 100 repetitions. The lexical variability value is higher when there are more bits. The number of bits also affects the lexical variability value at stage 0. The more bits, the higher the iconicity level.

## Notes

1 | We refer to cases with only one form per concept as uniform, while some researchers use the term conventionalized. Here, we use the term conventionalized for cases when form-concept pairings are generally accepted, so this would apply to cases where there are potentially more than one existing form associated with a concept as long as the form is used and understood. For example, Figure 1 shows three variants for pig in Kata Kolok which are conventionalized but not uniform. |

2 | We opted not to assign the opposite bit if the initial event fails (and to instead randomly assign 0 or 1) because assigning the opposite bit (0 for 1 and 1 for 0) would still result in a structured relationship. For example, if the culturally salient features are 1111 and the initial_degree_of_iconicity = 0, in the current version of the model, this means that the form is comprised of four random bits (ex. 1001), while if the opposite had been assigned, the form would be 0000, where there is still a structured relationship between the culturally salient features and form. |

3 | We chose to use a binary distance measure to calculate the lexical variability between agents, as opposed to a continuous distance measure, because lexical variants in the literature about sign languages are often treated categorically. This is true especially in studies of shared sign languages which consider the iconic motivation of signs (e.g., Ergin et al. 2021; Mudd et al. 2020). Unless two forms are identical, in the model, we treat them as different: Two different forms have a lexical variability score of 1, while identical forms have a lexical variability score of 0. However, with larger values of n_bits, it may make more sense to use a continuous distance measure for lexical variability. With larger values of n_bits, the individual bits may come closer to representing phonetic variation, and hence a continuous distance measure may be more appropriate. |

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**Figure 1.**Three variants for pig in Kata Kolok produced in response to a picture description task (Lutzenberger et al. 2021; Mudd et al. 2020). The iconic motivation underlying PIG-1 is how a pig is killed, for PIG-2 is how a pig eats and for PIG-3 is the ears of a pig. It is clear that the cultural context of the Kata Kolok community has shaped lexical preferences, illustrated with iconic signs (i.e., mappings between culturally salient features and forms). For instance, the iconic motivations of PIG-1 and PIG-2 stem from farming practices in the community.

**Figure 2.**The semiotic triangle used in the current study, consisting of a concept, culturally salient features and a form. The triangle on the left shows the traditional view of the relationship, in which an arbitrary link between the form and concept are made. Depicted in the triangle on the right, we present an alternative route to connecting the form to the concept, through culturally salient features, which we call the iconic–inferential pathway. Figure based on Vogt and Divina (2007), adapted from Ogden and Richards (1925), updated with terminology used in the current study.

**Figure 3.**Visualization of the steps and parameters in the agent-based model. During the initialization phase, the number of groups (n_groups) determines how many subsets of the population have the same set of identical culturally salient features associated with concepts. Then, a number of agents are created (n_agents). Each agent is randomly assigned to a group, and their language representation is set given the following parameters: the number of concepts (n_concepts), the number of bits (n_bits) and the initial degree of overlap between the culturally salient features and form (initial_degree_of_overlap). At each time step, all agents initiate a language game (i.e., they take a turn as the sender). At the end of each time step, data on the mean degree of iconicity and the mean lexical variability are calculated. The model continues for a number of steps (n_steps).

**Figure 6.**Example agents for calculating the mean degree of iconicity and the mean lexical variability.

**Figure 7.**The proportion of language game results (form success, culturally salient features success or bit update) with 10 agents all belonging to the same group (n_groups = 1) for the first 10 model stages (

**left**) and over the 2000 stages (

**right**). At each stage, 10 language games were played. The x-axis starts at stage one because in stage zero there is only model set up and no language game. Across all stages of this run, the majority of the language games end with form success, with a small proportion ending with culturally salient features success (here abbreviated as CS features success). Over 2000 stages, shown on the right, the results were averaged over 50 consecutive model stages (i.e., each bar of the histogram represents the mean of 50 stages).

**Figure 8.**The proportion of language game results (form success, culturally salient features success or bit update) for a model run with 10 agents randomly assigned to 1 of 10 groups (n_groups = 10) for the first 10 model stages (

**left**) and over the 2000 stages (

**right**). At each stage, 10 language games were played. The x-axis starts at stage one because in stage zero there is only model set up and no language game. The majority of the language games at the start of the simulation end with bit update, while later, more end with form success and still a considerable amount end with bit update. Few language games end with culturally salient features success (here abbreviated as CS features success). Over 2000 stages, shown on the right, the results were averaged over 50 consecutive model stages (i.e., each bar of the histogram represents the mean of 50 stages).

**Figure 9.**The mean lexical variability and iconicity over the 2000 model stages for one run with 1 group (

**left**) and 10 groups (

**right**). With all agents belonging to the same group (n_groups = 1), the degree of iconicity remains high, and the mean lexical variability across the population remains relatively constant, with more than half of the forms across the population being different. With 10 groups that agents could be assigned to (n_groups = 10), the degree of iconicity drops and then stabilizes slightly above 0.5, with 0.5 representing an unstructured relationship between the bits of the form and culturally salient features. The mean lexical variability across the population drops sharply and then continues to drop slowly, indicating that forms become more and more uniform in the population over time.

**Figure 10.**The mean lexical variability over the 2000 model stages for 100 repetitions of a run with 10 agents being assigned to different groups depending on the run. The dark line represents the mean and the shaded area represents the standard deviation of the 100 repetitions. It is evident that there is a relationship between the number of groups and the speed of the decrease of lexical variability, as well as the final amount of lexical variability in the population: The more groups in the population, the higher the initial lexical variability (at stage 0) but the lower the final lexical variability (at stage 2000). In addition, when there are fewer groups, the degree of iconicity is higher.

**Figure 11.**The mean lexical variability over 4000 model stages for different population sizes (n_agents), showing three different group values (n_groups) determining the sets of culturally salient features of the agents. The dark line represents the mean and the shaded area represents the standard deviation of the 100 repetitions. Regardless of the number of groups, it is clear that the larger population sizes exhibit a lower mean lexical variability than small population sizes. In addition, when there are more agents, the level of iconicity is lower.

**Figure 12.**The feedback loop from bit updating to the use of culturally salient features success visualized.

Process | Pseudo-Code | Parameters |
---|---|---|

Initialization | for each group G in n_groupsfor each concept C in n_conceptsset the culturally salient features for concept C in group G to a list of length n_bits of randomly chosen 0s and 1s create a population with size n_agents for each agent A in the populationrandomly assign agent A to a group set all culturally salient features based on assigned group for each concept Cfor each culturally salient features F associated with concept Cfor each bit B of culturally salient features Fwith probability initial_degree_of_overlap set bit B of corresponding form to bit B of culturally salient features Felseset bit B of corresponding form to 0 or 1 with equal probability | n_groups n_agents n_concepts n_bits initial_degree_of_overlap |

Step | repeat for n_steps | n_steps |

Language game | for each agent A in the populationrandomly choose another agent and play the language game | |

Collect data | calculate the mean iconicity and lexical variability across the population |

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**MDPI and ACS Style**

Mudd, K.; de Vos, C.; de Boer, B.
Shared Context Facilitates Lexical Variation in Sign Language Emergence. *Languages* **2022**, *7*, 31.
https://doi.org/10.3390/languages7010031

**AMA Style**

Mudd K, de Vos C, de Boer B.
Shared Context Facilitates Lexical Variation in Sign Language Emergence. *Languages*. 2022; 7(1):31.
https://doi.org/10.3390/languages7010031

**Chicago/Turabian Style**

Mudd, Katie, Connie de Vos, and Bart de Boer.
2022. "Shared Context Facilitates Lexical Variation in Sign Language Emergence" *Languages* 7, no. 1: 31.
https://doi.org/10.3390/languages7010031