NOTES TOWARD A MODEL FOR THE STRUCTURE OF KNOWLEDGE SYSTEMS

This paper reviews two formulations of some structural aspects of knowledge systems. These two structural specifications of knowledge systems, by Judith Willer and by Norwood Russell Hanson, are then combined to suggest a model for relating several "ideal type" knowledge systems. Some tentative descriptions of these knowledge systems are given. The paper concludes by suggesting that scientific systems involve a particular combination of two of the systems and that sociology of knowledge and cognitive psychology have clear roles in the theoretical development of such a model.http://web.ku.edu/~starjrn

Information-theoretic Characterization of the Sub-regular Hierarchy

Our goal is to link two different formal notions of complexity: the complexity classes defined by Formal Language Theory (FLT)—in particular, the Sub-regular Hierarchy (Rogers et al., 2013; Lai, 2015; Heinz, 2018)—and Statistical Com- plexity Theory (Feldman and Crutchfield, 1998; Crutchfield and Marzen, 2015). The motivation for exploring this connection is that factors involving memory resources have been hypothesized to explain why phonological processes seem to inhabit the Sub-regular Hierarchy, and Statistical Complexity Theory gives an information-theoretic characterization of memory use. It is currently not known whether statistical complexity and FLT define equivalent complexity classes, or whether statistical complexity cross-cuts the usual FLT hierarchies. Our work begins to bridge the gap between FLT and Information Theory by presenting characterizations of certain Sub-regular languages in terms of statistical complexit

Learning Phonotactics in a Differentiable Framework of Subregular Languages

Phonotactic constraints have been argued to beregular, meaning that they can be represented usingfinite-state automata (Heinz, 2018); furthermore, they have been argued to occupy a even more restrictedregion of the regular language class known as the subregular hierarchy (Rogers & Pullum, 2011). Ourcontribution is to present a simple model of phonotactic learning from positive evidence. Our approach isbased on probabilistic finite-state automata (Vidal et al., 2005a,b). We study the model’s ability to induce localand nonlocal phonotactics from wordlist data, both with and without formal constraints on the automaton.In particular, we evaluate the ability of our learner to induce nonlocal phonotactic constraints from data ofNavajo and Quechua. Our work provides a framework in which different formal models of phonotactics canbe compared, and sheds light on the structural nature of phonological acquisition (Dai, 2021; Shibata & Heinz,2019; Heinz & Rogers, 2010, 2013)

L0-regularization induces subregular biases in LSTMs

Ongoing work attempts to identify the formal language patterns in natural language. In phonology, recent work has identified the subregular languages as a good candidate (Heinz, 2018). However, there remain few explanations for the source of this bias. This abstract proposes a means of investigating formal language learnability. We propose using a variant of minimum description length (MDL) as defined on LSTMs with varying priors on LSTM size. We will show its utility on a test case from Heinz and Idsardi (2013) and Rawski et al. (2017)