Burke, Luke Edward; (2022) Monads, applicatives and the semantics of perspective: a solution to the problems of logical omniscience and granularity. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis elaborates a framework, P-HYPE, in which to capture fine-grained, `hyperintensional' distinctions in meaning and in which to model the compositional sub-sentential semantics of a variety of natural language constructions. In part I of the thesis, two problems which natural language semantic theory has faced from its inception are discussed: the problem of granularity and the problem of logical omniscience. The former problem regards issues that arise if we treat all sentences which express mathematical truths as having the same meaning, and issues that arise if we treat seemingly synonymous predicates such as "doctor" and "physician" as semantically equivalent. The latter problem concerns certain closure conditions on knowledge and belief, which entail, contrary to fact, that agents are omniscient in their logical powers. In part II of the thesis, it is argued that the fine-grained semantic values which we require in order to solve the problems of granularity and logical omniscience can be understood as linguistic side-effects (Shan 2007), where the notion of a `side effect' is taken from the literature on functional programming (Wadler 1995). In this way, we build upon a recent tradition in natural language semantic theory, which argues that various semantic phenomena can be understood as linguistic side-effects (Shan 2007, Charlow 2014). We then develop P-HYPE, which is a combination of the logic HYPE (Leitgeb 2019) with the perspective relative semantic theory of (Asudeh & Giorgolo 2016). In P-HYPE, perspective relativity is used to capture the subjective understanding of words and expressions of individual language users. Via perspective relativity, we can model a variety of phenomena, such as the behaviour of co-intensional predicates, focus, metalinguistic focus and anaphora. In addition, we show that P-HYPE can be used to solve the problem of logical omniscience, without introducing so-called `impossible worlds' into the semantic theory, and in a way which is fully compositional at the subsentential level, unlike certain accounts of logical omniscience (Berto 2019, Solaki 2019, Rantala 1982).

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