Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.664572
Title: New rationality principles in pure inductive logic
Author: Howarth, Elizabeth
ISNI:       0000 0004 5364 263X
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2015
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Abstract:
We propose and investigate several new principles of rational reasoning within the framework of Pure Inductive Logic, PIL, where probability functions defined on the sentences of a first-order language are used to model an agent's beliefs. The Elephant Principle is concerned with how learning, modelled by conditioning, may be uniquely `remembered'. The Perspective Principle requires that, from a given prior, conditioning on statistically similar experiences should result in similar assignments, and is found to be a necessary condition for Reichenbach's Axiom to hold. The Abductive Inference Principle and some variations are proposed as possible formulations of a restriction of C.S. Peirce's notion of hypothesis in the context of PIL, though characterization results obtained for these principles suggest that they may be too strong. The Finite Values Property holds when a probability function takes only finitely many values when restricted to sentences containing only constant symbols from some fixed finite set. This is shown to entail a certain systematic method of assigning probabilities in terms of possible worlds, and it is considered in this light as a possible principle of inductive reasoning. Classification results are given, stating which members of certain established families of probability functions satisfy each of these new principles. Additionally, we define the theory of a principle P of PIL to be the set of those sentences which are assigned probability 1 by every probability function which satisfies P. We investigate the theory of the established principle of Spectrum Exchangeability by finding separately the theories of heterogeneous and homogeneous functions. The theory of Spectrum Exchangeability is found to be equal to the theory of finite structures. The theory of Johnson's Sufficientness Postulate is also found. Consequently, we find that Spectrum Exchangeability, Johnson's Sufficientness Postulate and the Finite Values Property are all inconsistent with the principle of Super-Regularity: that any consistent sentence should be assigned non-zero probability.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.664572  DOI: Not available
Keywords: Inductive Logic ; Logical Probability ; Rationality ; Uncertain Reasoning ; Spectrum Exchangeability
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