Distinctive signatures of recursion

Abstract

Although recursion has been hypothesized to be a necessary capacity for the evolution of language, the multiplicity of definitions being used has undermined the broader interpretation of empirical results. I propose that only a definition focused on representational abilities allows the prediction of specific behavioural traits that enable us to distinguish recursion from non-recursive iteration and from hierarchical embedding: only subjects able to represent recursion, i.e. to represent different hierarchical dependencies (related by parenthood) with the same set of rules, are able to generalize and produce new levels of embedding beyond those specified a priori (in the algorithm or in the input). The ability to use such representations may be advantageous in several domains: action sequencing, problem-solving, spatial navigation, social navigation and for the emergence of conventionalized communication systems. The ability to represent contiguous hierarchical levels with the same rules may lead subjects to expect unknown levels and constituents to behave similarly, and this prior knowledge may bias learning positively. Finally, a new paradigm to test for recursion is presented. Preliminary results suggest that the ability to represent recursion in the spatial domain recruits both visual and verbal resources. Implications regarding language evolution are discussed.

A novel approach to investigate recursion and iteration in visual hierarchical processing

“…The ability to generate recursive representations in the visual domain might be instantiated by the specific combination of several cognitive systems available for other functions. These hypotheses are discussed in detail elsewhere (Martins, 2012).…”

“…On the one hand, it has proven to be particularly difficult to establish clear distinctions between recursion and similar processes such as hierarchical embedding and iteration (Hulst, 2010). On the other hand, it has not been clear which level of analysis (process, structure, or representation) is relevant for empirical research (Lobina, 2011(Lobina, , 2014Martins, 2012).…”

“…Regarding the first theoretical difficulty, here we adopt a framework (Fitch, 2010;Martins, 2012) in which "iteration" refers to the process of repeating an operation a certain number of times. An iterative process may or may not generate hierarchical structures or create dependency relationships between different elements.…”

“…Frequently, we find an isomorphism between procedure and structure, i.e., recursive processes often generate recursive structures. However, this isomorphism does not always occur (Lobina, 2011;Luuk & Luuk, 2010;Martins, 2012). In this manuscript we explicitly focus on a third level of analysis, which is the level of representation.…”

“…A non-iterated hierarchical embedding corresponds to the establishment of a dependency without repetition. The ability to represent repetition and the ability to represent dependencies may be orthogonal (Martins, 2012) visual domain using fractal images. Because fractals exhibit hierarchical self-similarity, new hierarchical levels can be predicted by generalizing production rules and projecting them to further levels.…”