MoL-2021-16: Hyperintensional Logics for Evidence, Knowledge and Belief

MoL-2021-16: Siemers, Maximilian (2021) Hyperintensional Logics for Evidence, Knowledge and Belief. [Report]

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Traditional epistemic logics generally define knowledge as truth in all epistemic alternatives. This approach has two shortcomings: first, the link between knowledge and justification is not represented. Second, epistemic agents are highly idealised and suffer from the defect of logical omniscience. In this thesis, we propose a framework that aims at bringing together knowledge, belief and evidence possession of less idealised epistemic agents.
Our contribution consists of a combination and enrichment of existing approaches that address each of these issues individually. On the one hand, there are possible-worlds based semantic representations of evidence and corresponding notions of knowledge and belief based on this conception of evidence. On the other hand, it has been argued that epistemic attitudes are topic-sensitive, which makes them hyperintensional.
Our framework combines the semantic representation of evidence with strategies to formalise hyperintensional knowledge and belief. We suggest that evidence itself should be understood as a hyperintensional concept. We demonstrate how some of the closure principles for knowledge and belief related to logical omniscience are consequences of the purely possible worlds-based approach of interpreting the underlying evidence. In particular, we suggest that the missing component that cannot be captured by these approaches is the relation that holds between a piece of evidence and a proposition whenever the former is relevant for the latter.
Based on existing frameworks modelling subject matters, we develop a topic-sensitive notion of evidence and show that knowledge and belief can be defined based on this novel kind of evidence. As a consequence of grounding knowledge and belief entirely in hyperintensional evidence, our target notions of knowledge and belief are themselves hyperintensional. In particular, our approach circumvents many of the defects pertaining to logical omniscience.
Our main technical contribution consists of a sound and complete axiomatisation of a logic for hyperintensional evidence and knowledge, which is expressive enough to define all evidence, knowledge and belief modalities developed throughout this thesis. We also provide a separate sound and complete axiomatisation of a belief fragment.

Item Type: Report
Report Nr: MoL-2021-16
Series Name: Master of Logic Thesis (MoL) Series
Year: 2021
Subjects: Computation
Depositing User: Dr Marco Vervoort
Date Deposited: 17 Sep 2021 01:04
Last Modified: 17 Sep 2021 01:04

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