Previous research has proposed that any model of language learning should use the Subset Principle to guide hypothesis selection when the language domain contains at least two languages such that one is a subset of the other (Gold, 1967; Berwick, 1985; Manzini & Wexler, 1987; Wexler & Manzini, 1987). Informally, the Subset Principle states that the learner should select a language that: (a) is compatible with the input data, and, (b) does not properly contain any other language that is compatible with the input data. This thesis puts forth a comprehensive investigation of psychocomputational models of language learning that abide by the Subset Principle from both an empirical and theoretical perspective. We intend "psychocomputational models" to include computational models that are in line with research in psycholinguistics, developmental psychology and theoretical linguistics (Sakas, 2004). This thesis is divided into three principal areas: (1) an analysis of partial ordering learners which are given a priori knowledge of subset-superset relationships, (2) a comparison of those partial ordering learners and variants of traditional Gold-paradigm total ordering (enumeration) learners, and (3) a preliminary investigation into how the shape of the language domain, in terms of both the partial ordering of subset-superset relationships and cross-language ambiguity, affects learning performance of learners that abide by the Subset Principle. Results show that the partial ordering learners perform best when Subset Principle constraints and parsing are given equal weight with regards to hypothesis selection. The comparison study shows that the partial ordering learners outperform the total ordering learners. Finally, preliminary results stemming from the investigation of language domain shape indicate that language domains exhibiting greater breadth than depth are more computationally demanding to learn. Although there exists a number of computational studies that attempt to address the problems that are introduced when learning in domains that contain superset languages, this research makes its contribution by modeling the Subset Principle under assumptions that are psychologically realistic in terms of the computational workload required of the learning algorithms under investigation.