MoL-2017-12: Steps out of Logical Omniscience

MoL-2017-12: Solaki, Anthia (2017) Steps out of Logical Omniscience. [Report]

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This thesis discusses the problem of logical omniscience, a defect of standard epistemic and doxastic logics which – unrealistically – predict that agents know/believe all consequences of their knowledge/beliefs. We first give a detailed account of the problem, argue for its importance and describe the kind of solution we are interested in. More specifically, we attach great value to the ability of real-life agents to engage in bounded reasoning. Then, once we provide the appropriate background notions from Dynamic Epistemic Logic, we continue with a comprehensive review of selected approaches to the problem. In doing so, certain criteria are flagged, in order to assess these attempts on a solid ground. Keeping these remarks in mind, we proceed with our own proposals against the problem, in hope of overcoming the challenges emphasized in the critical survey. These proposals prioritize the need to take reasoning steps in order to attain knowledge or belief. First, we improve step-wise solutions to the problem by providing two frameworks, RW, that captures reasoning steps as transitions between worlds, and IW, that employs impossible worlds. We present the main elements of RW, explain how it refines existing attempts and escapes omniscience, and provide a sound and complete logic with respect to a class of its models. We similarly analyze the contribution of IW, and extend it to a quantitative system, sensitive to the idea of resource consumption. Other extended settings, such as IWPA and IWp, facilitate a more elaborate study of reasoning and belief change. Finally, we devise a method to obtain complete axiomatizations for IW-like systems, that relies on a reduction of models with impossible worlds.

Item Type: Report
Report Nr: MoL-2017-12
Series Name: Master of Logic Thesis (MoL) Series
Year: 2017
Subjects: Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 31 Jul 2017 09:55
Last Modified: 31 Jul 2017 09:55

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