Rational Defeasible Belief Change

We present a formal framework for modelling belief change within a non-monotonic reasoning system. Belief change and non-monotonic reasoning are two areas that are formally closely related, with recent attention being paid towards the analysis of belief change within a non-monotonic environ- ment. In this paper we consider the classical AGM belief change operators, contraction and revision, applied to a de- feasible setting in the style of Kraus, Lehmann, and Magidor. The investigation leads us to the formal characterisation of a number of classes of defeasible belief change operators. For the most interesting classes we need to consider the problem of iterated belief change, generalising the classical work of Darwiche and Pearl in the process. Our work involves be- lief change operators aimed at ensuring logical consistency, as well as the characterisation of analogous operators aimed at obtaining coherence—an important notion within the field of logic-based ontologies

The Philosophical Foundations of PLEN: A Protocol-theoretic Logic of Epistemic Norms

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in terms of the protocol (or program) constructions of dynamic logic. I defend (i) and (ii) at length and in multi-faceted ways, and I argue that they entail a set of criteria of adequacy for models of epistemic dynamics and abstract accounts of epistemic norms. I then define PLEN, the protocol-theoretic logic of epistemic norms. PLEN is a dynamic logic that analyzes epistemic rationality norms with protocol constructions interpreted over multi-graph based models of epistemic dynamics. The kernel of the overall argument of the dissertation is showing that PLEN uniquely satisfies the criteria defended; none of the familiar, rival frameworks for modeling epistemic dynamics or normative concepts are capable of satisfying these criteria to the same degree as PLEN. The overarching argument of the dissertation is thus a theory-preference argument for PLEN

Computational Complexity of Strong Admissibility for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments arecalled semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexityof the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument

Topics of Thought

This book concerns mental states such as thinking that Obama is tall, imagining that there will be a climate change catastrophe, knowing that one is not a brain in a vat, or believing that Martina Navratilova is the greatest tennis player ever. Such states are usually understood as having intentionality, that is, as being about things or situations to which the mind is directed. The contents of such states are often taken to be propositions. The book presents a new framework for the logic of thought, so understood—an answer to the question: Given that one thinks (believes, knows, etc.) something, what else must one think (ditto) as a matter of logic? This should depend on the propositions which make for the contents of the relevant thoughts. And the book defends the idea that propositions should be individuated hyperintensionally, i.e. not just by the sets of worlds at which they are true (as in standard ‘intensional’ possible worlds semantics), but also by what they are about: their topic or subject matter. Thus, the logic of thought should be ‘topic-sensitive’. After the philosophical foundations have been presented in Chapters 1−2, Chapter 3 develops a theory of Topic-Sensitive Intentional Modals (TSIMs): modal operators representing attitude ascriptions, which embed a topicality or subject matter constraint. Subsequent chapters explore applications ranging from mainstream epistemology (dogmatism, scepticism, fallibilism: Chapter 4), to the nature of suppositional thinking and imagination (Chapter 5), conditional belief and belief revision (Chapter 6), framing effects (Chapter 7), probabilities and indicative conditionals (Chapter 8)