This chapter develops the first collection of results around change of enrichment along a (possibly nonsymmetric) multifunctor. As in Chapter 6, it is shown that this theory extends the classical theory for enrichment over (possibly symmetric) monoidal categories. Compositionality and 2-functoriality for the change-of-enrichment constructions are treated in Sections 7.4 and 7.5, respectively.

This chapter describes the theory of self-enrichment for closed multicategories, and of standard enrichment for multifunctors between closed multicategories. The self-enrichment of the multicategory of permutative categories, from Chapter 8, is a special case. Compositionality of standard enrichment is discussed in Section 9.3, and applied to the factorization of Elmendorf–Mandell K-theory in Section 9.4.

In this chapter the focus moves beyond Pāṇini’s grammar to address a topic of major concern within the broader Indian tradition: semantics. While some observations regarding semantics can be drawn from Pāṇini, for the most part semantics was treated as a separate field of inquiry within the Indian tradition until the early modern period. This chapter provides introductions to the traditions of semantic analysis in ancient India and the modern West, and a comparison of their approaches to one issue of central concern in semantic theory: compositionality.

Motor neuroscience centers on characterizing human movement, and the way it is represented and generated by the brain. A key concept in this field is that despite the rich repertoire of human movements and their variability across individuals, both the behavioral and neuronal aspects of movement are highly stereotypical, and can be understood in terms of basic principles or low dimensional systems. Highlighting this concept, this chapter outlines three core topics in this research field: (1) Trajectory planning, where prominent theories based on optimal control and geometric invariance aim at describing end-effector kinematics using basic unifying principles; (2) Compositionality, and specifically the ideas of motor primitives and muscle synergies that account for motion generation and muscle activations, using hierarchical low-dimensional structures; and (3) Neural control models, which regard the neural machinery that gives rise to sequences of motor commands, exploiting dynamical systems and artificial neural network approaches.

This chapter reviews the theoretical and conceptual issues central to acceptability judgment tasks, and related paradigms, at the syntax–semantics interface, and provides a broad overview of core results obtained from research in this domain. Challenges faced by studies in experimental semantics are distinct from those in experimental syntax, which at times requires different linking hypotheses, research questions, or experimental paradigms. However, the current state of affairs suggests that acceptability and other offline judgments will continue to contribute highly informative and profitable tools for exploration of phenomena at the syntax–semantics interface.

This chapter covers morphological productivity. We first look at the main factors that contribute to or detract from productivity, including transparency, compositionality, and usefulness. We review types of restrictions on word formation rules including categorial, phonological, syntactic, semantic, and etymological restrictions.Students consider the difficulty of measuring productivity and learn to calculate productivity using Baayen’s P formula. We then take a historical perspective and look at changes to productivity over time. The chapter ends with a consideration of the distinction between morphological productivity and morphological creativity.

Semantic communication is about transmitting mental representations of reality. Three research questions address the nature of this process in primates. Can primates produce signals that are meaningful in a lexical sense? Are they capable of compositional semantics? Can they create and infer meaning by integrating context and intention? There is good evidence that, as recipients, primates have capacities at all three levels, whereas for signallers the evidence is less compelling. This difference may have cognitive roots, due to the fact that primate signallers are typically engaged in the here-and-now and, unlike humans, less able to refer to memory content. Future research will have to clarify what mental structures primates can take into account during communication, including entities that are not physically present.

This chapter begins with an overview of several terms important to a discussion of meaning in language, and introduces the reader to the theory of linguistic relativism and the relationship between language and thought. This section transitions into a review of the extension, reference, and the features that begin to form a comprehensive theory of semantics. With this foundation, students turn to a deeper investigation of formal semantics, including definitions for logical expressions and relationships, and then to a presentation of word sense, and the interactions between various parts of speech in the lexicon. The principle of compositionality is introduced, and it is used to explore several examples of non-compositional language. The end of the chapter ties these concepts to an investigation of pragmatics, including politeness, Gricean Maxims, and implicature.

This chapter introduces the theoretical context for the compositional semantic framework to be developed in the book. A key innovation is to posit explicit representations of context – formally, variables for assignment functions – in the syntax and semantics of natural language. A primary focus is on a spectrum of linguistic shifting phenomena, in which the context relevant for interpretation depends on features of the linguistic environment. The proposed theory affords a standardization of quantification across domains, and an improved framework for theorizing about linguistic meaning and the role of context in interpretation. Comparisons with alternative operator-based theories are briefly considered. An outline of the subsequent chapters is presented.

This chapter develops an improved assignment-variable-based compositional semantics for head-raising analyses of restrictive relative clauses, and applies the account to certain types of pronominal anaphora. The speculative choice-function based analysis of names from Chapter 4 is extended to certain indefinites, relative words, and donkey pronouns. An analysis of donkey pronouns as copies of their linguistic antecedent is supported by crosslinguistic data. Nominal quantifiers are treated as introducing quantification over assignments. The proposed semantics for quantifiers helps capture linguistic shifting data in universal, existential, and asymmetric readings of donkey sentences. Additional composition rules or principles for interpreting reconstructed phrases aren’t required (e.g., Predicate Abstraction, Predicate Modification, Trace Conversion). The semantics is fully compositional. Critical challenges are discussed.

This chapter draws on independent work on the syntax–semantics interface to motivate a more complex clausal architecture for an assignment-variable-based theory. Binding across syntactic categories and semantic domains is captured uniformly from a generalized binder-index feature, which attaches directly to expressions undergoing movement for type reasons. World-binding (intensionality) arises from the complementizer, which moves from the world-argument position of the clause’s main predicate; assignment-binding arises from modal elements, which move from an internal assignment-argument position of the complementizer. The semantics is fully compositional. The remainder of the book develops the account and applies it to a range of constructions and types of linguistic shifting phenomena.