Using mathematical models of language experimentally

Timothy J. O'Donnell, Marc D. Hauser, W. Tecumseh Fitch
2005 Trends in Cognitive Sciences  
Understanding developmental and evolutionary aspects of the language faculty requires comparing adult languages users' abilities with those of non-verbal subjects, such as babies and non-human animals. Classically, comparative work in this area has relied on the rich theoretical frameworks developed by linguists in the generative grammar tradition. However, the great variety of generative theories and the fact that they are models of language specifically makes it difficult to know what to test
more » ... in animals and children lacking the expressive abilities of normal, mature adults. We suggest that this problem can be mitigated by tapping equally rich, but more formal mathematical approaches to language. Modern linguistics is dominated by an approach known as the generative paradigm. Generative theory is built around several core ideas about the nature of language and its study. One important cornerstone of the approach since its inception has been the way in which it envisions building theories of human language. Under the generative framework, researchers construct clear, precise models, called grammars, to describe the mature speaker's knowledge and use of language. These models are often constructed using tools from logic, mathematics and the theory of computation. The advantage of constructing such precise, and often mathematically formalized models is that the consequences of modeling decisions can be deduced directly from assumptions [1]. One of the most important questions for generative linguists and other language scientists is what biological features endow our species with its linguistic ability. Often this is expressed as the problem of determining the innate resources the child has for acquiring language [2] . It can also be reframed as an evolutionary question: Do we share some, all, or none of the key components of the language faculty with other species, and in cases where we are uniquely endowed as a species, did these capacities evolve for language in particular or for multiple domains of cognition [3, 4] ? Clearly such questions about language development and evolution require comparing normal adult human language abilities with the corresponding (if any) abilities in non-verbal subjects such as babies and animals. However, there are several challenges for the comparative experimentalist interested in turning generative theories into testable empirical predictions. First, there are a great number of generative theories of language to choose from (e.g. just in the realm of syntactic theory [5-9]). To varying degrees these theories have their own notations, their own terminology, and their own analogies with other mathematical and scientific theories. Moreover, because these theories characterize brain computations and systems of knowledge at a very high level of abstraction it is often the case that theories with radically different appearances can 'do the same work' in not-soobvious ways (e.g. see [10] ) The choice of which components of which theories to explore in non-verbal subjects is far from trivial. Second, generative theories are built to account for the knowledge and use of normal human adult language. As such it is not always clear what they have to say about the abilities of pre-or non-linguistic subjects, such as human infants and non-human animals. It is therefore important to isolate aspects of generative theories that can be plausibly expected to show up in the non-verbal abilities of test subjects. The subfield of mathematical linguistics offers a number of tools that allow abstract theories of language and mental computation to be compared and contrasted with one another (e.g. see [11] ). We suggest that formulating comparative hypotheses with enough precision to make use of these tools can reduce some of the difficulties mentioned above. We use one set of tools from mathematical linguistics, formal language theory, to illustrate the potential power of mathematical approaches, sketching its basic concepts and discussing how they were used in one empirical example from the animal literature. We fully acknowledge that this is an area with varied opinion concerning the merits of different mathematical approaches, and the theories that back them. Brevity, however, forces us to be selective, focusing on a small corner of this potentially broad research space. Formal language universals One of the major goals of linguistics is to discover universal or near universal aspects of linguistic structure. Many such phenomena have been uncovered. These include things such as the way in which the presence of words in a sentence depends on the presence of other words [12], the distinction
doi:10.1016/j.tics.2005.04.011 pmid:15925807 fatcat:z7six35zrja2rp3mn4s6woihgi