Rules are an efficient feature of natural languages which allow speakers to use a finite set of instructions to generate a virtually infinite set of utterances. Yet, for many regular rules, there are irregular exceptions. There has been lively debate in cognitive science about how individual learners acquire rules and exceptions; for example, how they learn the past tense of preach is preached, but for teach it is taught. In this paper, we take a different perspective, examining the dynamics of regularity and irregularity across a population of interacting agents to investigate how inflectional rules are applied to verbs. We show that in the absence of biases towards either regularity or irregularity, the outcome is determined by the initial condition, irrespective of the frequency of usage of the given lemma. On the other hand, in presence of biases, rule systems exhibit frequency dependent patterns in regularity reminiscent of patterns in natural language corpora. We examine the case where individuals are biased towards linguistic regularity in two ways: either as child learners, or through a memory constraint wherein irregular forms can only be remembered by an individual agent for a finite time period. We provide theoretical arguments for the prediction of a critical frequency below which irregularity cannot persist in terms of the duration of the finite time period which constrains agent memory.
