In Chapters 10 and 12, we focused on two common usages of recurrent neural networks and transformer networks: acceptors and transducers. In this chapter, we discuss a third architecture for both recurrent neural networks and transformer networks: encoder-decoder methods. We introduce three encoder-decoder architectures, which enable important NLP applications such as machine translation. In particular, we discuss the sequence-to-sequence method of Sutskever et al. (2014), which couples an encoder long short-term memory with a decoder long short-term memory. We follow this method with the approach of Bahdanau et al. (2015), which extends the previous decoder with an attention component, which produces a different encoding of the source text for each decoded word. Last, we introduce the complete encoder-decoder transformer network, which relies on three attention mechanisms: one within the encoder (which we discussed in Chapter 12), a similar one that operates over decoded words, and, importantly, an attention component that connects the input words with the decoded ones.

This chapter explores the ideational function of emoji as they concur with language to construe experience as items and activities in social media posts. The chapter details a system network for modelling ideational concurrence. This network defines two main kinds of relations: depiction and embellishment. Depiction is where emoji congruently illustrate their co-text or integrate themselves into the ideational structure of the post. Embellishment, on the other hand, is where emoji make less congruent meanings by either metaphorising through figurative meanings or emblematising through symbols that activate preconfigured meanings for particular communities. The chapter draws on the discourse semantic system of ideation introduced in Chapter 3 to understand the concurrence of emoji and linguistic sequences, figures, and elements.

The prevailing view of Buridan’s theory of cognition and his epistemology is that he is a kind of externalist as well as a reliabilist. This essay argues that this reading is mistaken and that Buridan instead must be seen as a semantic and epistemic internalist. The essay develops the arguments for both these views. The first part of the essay supplements an argument already made by Claude Panaccio, but the second part is a new argument for why Buridan must be seen as an epistemological internalist. The essay also compares Buridan to later empiricists such as David Hume.

In this chapter we discuss some related random graph models that have been studied in the literature. We explain their relevance, as well as some of the properties in them. We discuss directed random graphs, random graphs with local and global community structures, as well as spatial random graphs.

After many years during which indigenous laws were mostly absent from narratives of Latin American law, presently, legal historians wish to integrate them. However, to do so requires answering the question of what we know about indigenous laws and how we can approach them. Writing the history of indigenous laws from precolonial times is especially challenging not only because of the diversity of human groups that occupied the continent, but also because of the disparity of available sources, ranging from material vestiges and pictographic documents to texts produced in indigenous writing systems. Furthermore, the colonial period has left us with a wide range of alphabetic texts, diverse in authorship, languages, formats, degree of accuracy, and sources selected, that describe precolonial law. Indigenous peoples, mestizos, and Spaniards also wrote historical narratives and accounts of deeds and services; furthermore, they participated as litigants in lawsuits in which they expressed their vision of law and justice. What does this evidence tell us about precolonial normative orders and the way in which they intersected with colonial law after the Iberian imperial conquests? To answer this question, this chapter proposes an interdisciplinary approach, surveying what has been done, and what could still be done.

As mentioned in Chapter 8, the distributional similarity algorithms discussed there conflate all senses of a word into a single numerical representation (or embedding). For example, the word bank receives a single representation, regardless of its financial (e.g., as in the bank gives out loans) or geological (e.g., bank of the river) sense. This chapter introduces a solution for this limitation in the form of a new neural architecture called transformer networks, which learns contextualized embeddings of words, which, as the name indicates, change depending on the context in which the words appear. That is, the word bank receives a different numerical representation for each of its instances in the two texts above because the contexts in which they occur are different. We also discuss several architectural choices that enabled the tremendous success of transformer networks: self attention, multiple heads, stacking of multiple layers, and subword tokenization, as well as how transformers can be pretrained on large amounts of data through through masked language modeling and next-sentence prediction.

Rudolf Carnap’s began to write on probability and inductive logic in 1945, marking a surprising shift in his research interests midway through his post-PhD career (1921–1970). His 1950 Logical Foundations of Probability is unquestionably his best-known work in this area, and yet his views afterwards underwent a substantial change over the next two decades, the extent of which was (and remains) often unappreciated. Inevitably some of his views underwent critical examination, both during his lifetime and after, but he was fortunate in being able to benefit in meeting these from the contributions and support of a number of mathematically and philosophically gifted collaborators. This essay traces the origins of his interest, the nature of these shifts, and some of the contributions of the members of his invisible college. Although the special technical contributions of Carnap continue to engage the attention of a small but influential group of individuals, his more general impact was much broader, often shaping as it did the current widespread epistemic and Bayesian view of the field.