The introduction presents a general discussion of syntactic theories, contrasting transformational approaches with those that adopt feature-structural representations to show how they provide differing cognitive models of the human language faculty. The three key components of the OLG framework – Linking Theory (LT), Optimality Theory (OT) and Competing Grammars (CG) – are briefly laid out. These are motivated by phenomena that necessitate multiple levels of case, linking between levels that permits mismatches in some grammars, a means of restricting the linking apparatus while still capturing the data, and a cogent account of morphosyntactic variation. One such phenomenon is introduced: case-marking facts in Insular Scandinavian. The dative–nominative Icelandic predicates are contrasted with the Faroese dative–accusative pattern, along with plural number agreement with the object in Icelandic versus non-agreement in Faroese. Next, an overview is presented of the motivation for each theoretical component of OLG, in turn outlining the advantages of LT, OT and the CG hypothesis. The introduction concludes with an outline of the specific empirical findings from surveys conducted on the Faroe Islands and Iceland, including quirky case predicates and passives, followed by an overview of the book’s structure.

Chapter 3 outlines OLG’s core components, giving the prerequisite theoretical background for understanding the data analyses that follow. The Linking Theory section answers questions regarding levels of lexical–semantic and syntactic representation, mapping between levels, and the architecture of grammar. A short review is presented of the core propositions of Optimality Theory (OT) approaches to syntax, including a list of proposed constraints governing case-assignment. Linking Theory originates in Kiparsky (1997); the central innovation is that three levels of case – abstract, morphosyntactic and morphological – are distinguished, and the same set of binary features is seen to operate at all levels, though with level-appropriate realisation. The introduction to OT focuses on its application to the syntactic module of grammar; a key point is that a huge number of unlikely candidates are harmonically bounded by undominated or high-ranked constraints. Such markedness constraints interact with faithfulness constraints enforcing realisation of all features present in the input, preventing omission of input material other than in highly marked forms. This allows us to capture long-standing generalisations about phrase structure without having to claim they will be completely unviolated across languages: language-specific rankings may result in more or less marked structures.