We propose a probabilistic account of semantic inference and classification formulated in terms of probabilistic type theory with records, building on Cooper et. al. (2014) and Cooper et. al. (2015). We suggest probabilistic type theoretic formulations of Naive Bayes Classifiers and Bayesian Networks. A central element of these constructions is a type-theoretic version of a random variable. We illustrate this account with a simple language game combining probabilistic classification of perceptual input with probabilistic (semantic) inference.

In this paper we will argue that the nature of dogwhistle communication is essentially dialogical, and that to account for dogwhistle meaning we must consider dialogical events in which dialogue partners can draw different conclusions based on communicative events. This leads us to a theory based on inference. However, as identified by Khoo (2017) and emphasised by Henderson & McCready (2018), a problematic aspect of this approach is that expressions that have a similar meaning are analysed as generating the same dogwhistle inferences, which appears not always to be the case. By modelling meaning in terms of intensional types in TTR, we avoid this problem.

In this paper, we propose a probabilistic model of social signalling which adopts a persona-based account of social meaning. We use this model to develop a socio-semantic theory of conventionalised reasoning patterns, known as topoi. On this account the social meaning of a topos, as conveyed in a argument, is based on the set of idealogically-related topoi it indicates in context. We draw a connection between the role of personae in social meaning and the category adjustment effect, a well-known psychological phenomenon in which the representation of a stimulus is biased in the direction of the category in which it falls. Finally, we situate the interpretation of social signals as an update to the information state of an agent in a formal TTR model of dialogue.

Much work in contemporary computational semantics follows the distributional hypothesis (DH), which is understood as an approach to semantics according to which the meaning of a word is a function of its distribution over contexts which is represented as vectors (word embeddings) within a multi-dimensional semantic space. In practice, use is identified with occurrence in text corpora, though there are some efforts to use corpora containing multi-modal information. In this paper we argue that the distributional hypothesis is intrinsically misguided as a self-supporting basis for semantics, as Firth was entirely aware. We mention philosophical arguments concerning the lack of normativity within DH data. Furthermore, we point out the shortcomings of DH as a model of learning, by discussing a variety of linguistic classes that cannot be learnt on a distributional basis, including indexicals, proper names, and wh-phrases. Instead of pursuing DH, we sketch an account of the problematic learning cases by integrating a rich, Firthian notion of dialogue context with interactive learning in signalling games backed by in probabilistic Type Theory with Records. We conclude that the success of the DH in computational semantics rests on a post hoc effect: DS presupposes a referential semantics on the basis of which utterances can be produced, comprehended and analysed in the first place.

Type theory has played an important role in specifying the formal connection between syntactic structure and semantic interpretation within the history of formal semantics. In recent years rich type theories developed for the semantics of programming languages have become influential in the semantics of natural language. The use of probabilistic reasoning to model human learning and cognition has become an increasingly important part of cognitive science. In this paper we offer a probabilistic formulation of a rich type theory, Type Theory with Records (TTR), and we illustrate how this framework can be used to approach the problem of semantic learning. Our probabilistic version of TTR is intended to provide an interface between the cognitive process of classifying situations according to the types that they instantiate, and the compositional semantics of natural language.