Computational methods and grammars in language evolution: a survey

Abstract

The interest in language evolution by various disciplines, such as linguistics, computer science, biology, etc., makes language evolution models an active research topic and many models have been defined in the last decade. In this work, an overview of computational methods and grammars in language evolution models is given. It aims to introduce readers to the main concepts and the current approaches in language evolution research. Some of the language evolution models, developed during the decade 2003–2012, have been described and classified considering both the grammatical representation (context-free, attribute, Christiansen, fluid construction, or universal grammar) and the computational methods (agent-based, evolutionary computation-based or game theoretic). Finally, an analysis of the surveyed models has been carried out to evaluate their possible extension towards multimodal language evolution.

Appendix

The basic concepts and definitions provided in this appendix are extracted from some books on formal language theory including Harrison (1978) and Hopcroft (1979) and from the work of Nowak et al. (2002).

The fundamental elements of a formal language theory are alphabets, sentences, languages, and grammars (Harrison 1978).

An alphabet is a finite set of symbols (Nowak et al. 2002). The formal definition is as follows.

Definition 1

An alphabet is a set containing finitely many symbols. Conventionally, this alphabet is referred to as $\Sigma$.

For instance, in natural languages¹ the set of all phonemes or graphemes or the set of all words are possible alphabets. Another example of alphabet is the binary alphabet consisting of the symbols (0, 1).

A sentence is a string of symbols in the alphabet (Nowak et al. 2002). Formally, it is defined in the following way:

Definition 2

A sentence is a sequence of finite length that can be constructed from an alphabet $\Sigma$. The set of all sentences over $\Sigma$ is denoted by $\Sigma ^*$.

As observed by Chomsky (1957), there are infinitely many sentences in natural languages, due to the compositionality principle that allows constructing arbitrarily long sentences from shorter pieces. Some examples of sentences for the English language are “the cat mews”, “John works at CNR”.

A language is defined as a set of sentences over the alphabet (Nowak et al. 2002). The formal definition is as follows:

Definition 3

A language L is a subset of $\Sigma ^*$.

Not all sentences are admissible in a language but only sentences that follow the specific rules of that language. For instance, the sentence “the cat mews” is valid (or meaningful) for the English language, while the sentence “mews cat the” is not.

A grammar is a set of rules that allows the valid sentences of the language to be established (Nowak et al. 2002). A grammar is formally defined by Chomsky (1957) as follows:

Definition 4

A grammar is a tuple ($\hbox {N}, \Sigma , \hbox {P, S}$) where:

• N is a finite set of non-terminal symbols;

• $\Sigma$ is a finite set of terminal symbols (disjoint from N);

• P is a finite set of productions of the form $\upalpha \rightarrow \upbeta$ with at least one non-terminal in N;

• S is a member of N called the start symbol.

Each production is a rule that may contain elements of the alphabet (named terminal symbols) and other elements, which act as variables (named non-terminal symbols). The rules replace the string on the left with another string on the right, starting from a non-terminal symbol that is designed as the start symbol. A valid sentence of the language is produced by taking the start symbol and repeatedly replacing substrings with the strings they generate, as defined by the rules of the grammar. An example of grammar producing the sentence “the cat mews” is shown in Fig. 5.

Fig. 5

An example of grammar

The hierarchy proposed by Chomsky (1965) classifies grammars as regular, context-free, context-sensitive, and unrestricted, based on the power of expression of their representation. The expressive power (also known as expressiveness) is that which can be represented using that language, i.e. the set of sets of strings its instances describe. Languages generated by regular grammar are the least expressive, while languages generated by unrestricted grammars are the most expressive.

The most used class of Chomsky grammars in natural language are CFGs, which are defined by rules of the form $\hbox {A} \rightarrow \upgamma$, where A is a non-terminal symbol and $\upgamma$ is a string of terminals and non-terminals. The formal definition of a CFG is as follows:

Definition 5

A grammar $\hbox {G} = (\hbox {N}, \Sigma , \hbox {P, S})$ is said to be context-free if all productions in P have the form $\hbox {A} \rightarrow \upgamma$, where $\hbox {A} \in \hbox {N}$ and $\upgamma \in \hbox {N} \cup \Sigma$.

Despite the classification of grammars provided by Chomsky, many further formal grammars have been developed by linguists and by computer scientists by extending or modifying those in Chomsky’s hierarchy for improving the expressive power and simplifying parsing. Most of these extensions start from the CFG, which is a very simple and intuitively appealing formalism for representing natural language, and extend it for introducing context-dependent language features. For instance, AGs and CGs retain a CFG kernel, and improve it with a distinct facility that handles context-dependence (Shutt 1998).