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Switch to: References
Citations of:
A Note on Binary Inductive Logic
Journal of Philosophical Logic 36 (6):735-771 (2007)
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We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems. |
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Additionally, the text shows how to develop computationally feasible methods to mesh with this framework. |
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We give a brief account of some de Finetti style representation theorems for probability functions satisfying Spectrum Exchangeability in Polyadic Inductive Logic, together with applications to Non-splitting, Language Invariance, extensions with Equality and Instantial Relevance. |
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A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and Nix–Paris Continua. |
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A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived. |
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Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to first-order logical languages. It is argued that the objective Bayesian should choose a probability function, from all those that satisfy constraints imposed by background knowledge, that is closest to a particular frequency-induced probability function which generalises the λ = 0 function of Carnap’s continuum of inductive methods. |
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We give an account of some relationships between the principles of Constant and Atom Exchangeability and various generalizations of the Principle of Instantial Relevance within the framework of Inductive Logic. In particular we demonstrate some surprising and somewhat counterintuitive dependencies of these relationships on ostensibly unimportant parameters, such as the number of predicates in the overlying language. |
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