Sena Bozdag

We revisit a recent puzzle about common knowledge, the ``sailboat" case (Lederman, 2018), and argue that Lewisian common knowledge allows us to reconcile the pre-theoretical intuition that certain facts are ``public" in such situations, while these facts cannot be common knowledge in the classical, iterative sense. The crux of the argument is to understand Lewisian common knowledge as an account of what it means for an event to be public. We first formulate this argument informally to clarify its philosophical commitment and then propose one way to capture it formally in epistemic-plausibility models. Taken together, we take the philosophical and the formal arguments as providing evidence that Lewisian common knowledge is a plausible account of what it means for an event to be public.

We study the relation between common knowledge and publicity, i.e. that certain events or facts are ”out in the open”, or ”public” in a group. Our contribution is conceptual and clarificatory. We point out, first, that while the iterative definition of common knowledge is central to the epistemic foundations of game theory, it is less so for theories of collective agency, that rather use “common knowledge” in the sense of publicity. Building on this observation, we propose to distinguish between internalist and externalist understandings of common knowledge and to associate the notion of publicity with the latter. This allows us to classify the different accounts of common knowledge that have by now been studied by logicians, game theorists, and philosophers, to defuse a recent debate in philosophy around the relation between common knowledge and publicity, and to put the emphasis on the conditions by which common knowledge and publicity emerge.

The main contribution of this dissertation is the development of a hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic, with the intention of addressing various aspects of over-idealisation and the logical omniscience problem which repeatedly occurs in the literature on belief dynamics. The models introduced in Chapter 2 make up the core of this dissertation. The starting point in the development of these models is shifting the representational focus of doxastic models from belief sets to collections of information, and defining changes of beliefs as artifacts of changes of information. In this way, the current work is aimed at achieving a flexible and less idealised account of belief representation and belief change. This is done by accommodating object-linguistic belief change operators within a state-semantics for information dynamics, which results in suggesting a non-monotonic, hyperintensional and inconsistency tolerant belief dynamics. A number of important themes concerning belief dynamics result from these models, such as hyperintensionality, inconsistency-tolerance and deductive closure. In the rest of this dissertation, these themes are investigated in more detail, with the exception of Chapter 6. In particular, Chapter 3 aims for locating this work in the hyperintensionality literature, by presenting a comparative survey of various accounts of hyperintensional belief change, besides a brief history of the debate about hyperintensional meaning. Various comparison points arise from the analysis of these accounts, in particular between possible worlds and state-semantics representations of hyperintensional belief revision, which are discussed in detail in Section 3.3. The latter themes mentioned above, namely inconsistency-tolerance and deductive closure are first investigated under the umbrella of fragmentation of belief states. The debate on fragmented beliefs is focused on the requirements of deductive closure and consistency imposed on belief sets, and how these lead to the problem of logical omniscience. The review of the literature shows various modeling solutions to the problem, Chapter 4 is then aimed at locating the current work in this literature. The issue of inconsistency-tolerance reoccurs in Chapter 5, in relation to consistency-sensitive epistemic modalities. In this part of the dissertation, two new epistemic modalities are investigated. A consistency-sensitive evidence modality picks out the consistent parts of an otherwise inconsistent collection of information, by distinguishing trusted sources of information. A consistency-sensitive safe belief modality then determines a set of persistent beliefs based on evidence. While the models introduced here are heavily inspired by the presentation in Chapter 2, they exhibit various differences due to the choice of the underlying semantics. Finally, Chapter 6 steers the discussion towards another direction. Here, the models developed in Chapter 2 are reinterpreted and applied to represent a special form of conceptual change. The aim of this application is to suggest these models as a bridging component between theories of belief revision and of scientific change. In particular, it is proposed that a belief-revision-like system can be used to mirror radical types of conceptual change that might occur as part of scientific revolutions. It is not surprising that belief revision and scientific theory revision are strikingly similar, given that both can be understood as corpus of information and inferences (or hypothesis). The parallel between the two is manifested in this chapter, also by the translation of belief revision postulates into rationality postulates for conceptual change in Section 6.4.

The paper extends a framework of information-based semantics for intuitionistic logic with a paraconsistent negation and consistency-sensitive epistemic modalities. In this framework information states represent information collected from various sources and as such they can be inconsistent because they receive contradictory information either from a single inconsistent source or from various mutually incompatible sources. The modalities reflect only those sources that are consistent and trusted. For the paraconsistent logic generated by this framework, we present a Hilbert style system, we prove completeness, the disjunction property, the finite model property and various other results.

Thagard presented a framework for conceptual change in science based on conceptual systems. Thagard challenged belief revision theorists, claiming that traditional belief-revision systems are able to model only the two most conservative types of changes in his framework, but not the more radical ones. The main aim of this work is to take up Thagard’s challenge, presenting a belief-revision-like system able to mirror radical types of conceptual change. We will do that with a conceptual revision system, i.e. a belief-revision-like system that takes conceptual structures as units of revisions. We will show how our conceptual revision and contraction operations satisfy analogous of the AGM postulates at the conceptual level and are able to mimic Thagard’s radical types of conceptual change.

I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided.