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193Some observations on induction in predicate probabilistic reasoningJournal of Philosophical Logic 31 (1): 43-75. 2002.We consider the desirability, or otherwise, of various forms of induction in the light of certain principles and inductive methods within predicate uncertain reasoning. Our general conclusion is that there remain conflicts within the area whose resolution will require a deeper understanding of the fundamental relationship between individuals and properties
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1207Ancient Indian Logic and AnalogyIn S. Ghosh & S. Prasad (eds.), Logic and its Applications, Lecture Notes in Computer Science 10119, Springer. pp. 198-210. 2017.B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.
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176Symmetry in Polyadic Inductive LogicJournal of Logic, Language and Information 21 (2): 189-216. 2012.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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130A Note on Irrelevance in Inductive LogicJournal of Philosophical Logic 40 (3). 2011.We consider two formalizations of the notion of irrelevance as a rationality principle within the framework of (Carnapian) Inductive Logic: Johnson's Sufficientness Principle, JSP, which is classically important because it leads to Carnap's influential Continuum of Inductive Methods and the recently proposed Weak Irrelevance Principle, WIP. We give a complete characterization of the language invariant probability functions satisfying WIP which generalizes the Nix-Paris Continuum. We argue that t…Read more
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160The Type Theoretic Interpretation of Constructive Set TheoryJournal of Symbolic Logic 49 (1): 313-314. 1984.
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The Finite Values PropertyIn C. Beierle, C. Brewka & M. Thimm (eds.), Computational Models of Rationality, Essays Dedicated to Gabriele Kern-Isberner on the Occasion of her 60th Birthday, College Publications. pp. 316-331. 2016.We argue that the simplicity condition on a probability function on sentences of a predicate language L that it takes only finitely many values on the sentences of any finite sublanguage of L can be viewed as rational. We then go on to investigate consequences of this condition, linking it to the model theoretic notion of quantifier elimination.
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68The Twin Continua of Inductive MethodsIn Åsa Hirvonen, Juha Kontinen, Roman Kossak & Andrés Villaveces (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics, De Gruyter. pp. 355-366. 2015.
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257O is not enoughReview of Symbolic Logic 2 (2): 298-309. 2009.We examine the closure conditions of the probabilistic consequence relation of Hawthorne and Makinson, specifically the outstanding question of completeness in terms of Horn rules, of their proposed (finite) set of rules O. We show that on the contrary no such finite set of Horn rules exists, though we are able to specify an infinite set which is complete
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154Atom Exchangeability and Instantial RelevanceJournal of Philosophical Logic 38 (3): 313-332. 2009.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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University of ManchesterRegular Faculty
Areas of Interest
| Logic and Philosophy of Logic |
| Philosophy of Probability |