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24Reasoning by analogy in inductive logicIn Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook, College Publications. pp. 63--76. 2011.
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19An Analogy Principle in Inductive LogicAnnals of Pure and Applied Logic 164 (12): 1293-1321. 2013.We propose an Analogy Principle in the context of Unary Inductive Logic and characterize the probability functions which satisfy it. In particular in the case of a language with just two predicates the probability functions satisfying this principle correspond to solutions of Skyrmsʼ ‘Wheel of Fortune’
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7Asymptotic conditional probabilities for binary probability functionsAnnals of Pure and Applied Logic 175 (9): 103335. 2024.
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14A mathematical incompleteness in Peano arithmeticIn Jon Barwise (ed.), Handbook of mathematical logic, North-holland. pp. 90--1133. 1977.
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7What You See Is What You GetEntropy 16 (11): 6186-6194. 2014.This paper corrects three widely held misunderstandings about Maxent when used in common sense reasoning: That it is language dependent; That it produces objective facts; That it subsumes, and so is at least as untenable as, the paradox-ridden Principle of Insufficient Reason.
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2Rethinking the End of Modernity: Empire, Hyper-Capitalism, and Cyberpunk DystopiasSocial Philosophy Today 21 173-189. 2005.This essay is comprised of two unusual pairings—Immanuel Wallerstein with Michael Hardt and Antonio Negri; and Don DeLillo with William Gibson—and a thesis: We live, today, in a period of transition between modernity and postmodernity that is best characterized as what I call hyper-capitalism. The end of modernity, as described both by Wallerstein’s world-systems theory and by the “postmodern” political philosophy of the authors of Empire, does not lead us into postmodernity proper, but into a p…Read more
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4Inexact and Inductive ReasoningIn Jens Erik Fenstad, Ivan Timofeevich Frolov & Risto Hilpinen (eds.), Logic, methodology, and philosophy of science VIII: proceedings of the Eighth International Congress of Logic, Methodology, and Philosophy of Science, Moscow, 1987, Sole Distributors For the U.s.a. and Canada, Elsevier Science. 1989.
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10Some Aspects of Polyadic Inductive LogicStudia Logica 90 (1): 3-16. 2008.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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22A survey of some recent results on Spectrum Exchangeability in Polyadic Inductive LogicSynthese 181 (S1). 2011.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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14A characterization of the language invariant families satisfying spectrum exchangeability in polyadic inductive logicAnnals of Pure and Applied Logic 161 (6): 800-811. 2010.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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6The Pigeonhole Principle and Fragments of ArithmeticMathematical Logic Quarterly 32 (1-5): 73-80. 1986.
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6A Property of 2‐Sorted Peano Models and Program VerificationMathematical Logic Quarterly 30 (19-24): 325-334. 1984.
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5On some formalized conservation results in arithmeticArchive for Mathematical Logic 30 (4): 201-218. 1990.IΣ n andBΣ n are well known fragments of first-order arithmetic with induction and collection forΣ n formulas respectively;IΣ n 0 andBΣ n 0 are their second-order counterparts. RCA0 is the well known fragment of second-order arithmetic with recursive comprehension;WKL 0 isRCA 0 plus weak König's lemma. We first strengthen Harrington's conservation result by showing thatWKL 0 +BΣ n 0 is Π 1 1 -conservative overRCA 0 +BΣ n 0 . Then we develop some model theory inWKL 0 and illustrate the use of for…Read more
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8A note on the rational closure of knowledge bases with both positive and negative knowledgeJournal of Logic, Language and Information 7 (2): 165-190. 1998.The notion of the rational closure of a positive knowledge base K of conditional assertions θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} |∼ φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrs…Read more
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12In defense of the maximum entropy inference processInternational Journal of Approximate Reasoning 17 (1): 77-103. 1997.This paper is a sequel to an earlier result of the authors that in making inferences from certain probabilistic knowledge bases the maximum entropy inference process, ME, is the only inference process respecting “common sense.” This result was criticized on the grounds that the probabilistic knowledge bases considered are unnatural and that ignorance of dependence should not be identified with statistical independence. We argue against these criticisms and also against the more general criticism…Read more
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3Logic Colloquium '84: Proceedings of the Colloquium Held in Manchester, U.K., July 1984 (edited book)North Holland. 1986.This proceedings volume contains most of the invited talks presented at the colloquium. The main topics treated are the model theory of arithmetic and algebra, the semantics of natural languages, and applications of mathematical logic to complexity theory. The volume contains both surveys by acknowledged experts and original research papers presenting advances in these disciplines.
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19Frank RamseyStanford Encyclopedia of Philosophy. 2019.Frank Plumpton Ramsey (1903–30) made seminal contributions to philosophy, mathematics and economics. Whilst he was acknowledged as a genius by his contemporaries, some of his most important ideas were not appreciated until decades later; now better appreciated, they continue to bear an influence upon contemporary philosophy. His historic significance was to usher in a new phase of analytic philosophy, which initially built upon the logical atomist doctrines of Bertrand Russell and Ludwig Wittgen…Read more
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20J. I. Friedman. Proper classes as members of extended sets. Mathematische Annalen, vol. 83 , pp. 232–240Journal of Symbolic Logic 40 (3): 462. 1975.
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5Translation Invariance and Miller’s Weather ExampleJournal of Logic, Language and Information 28 (4): 489-514. 2019.In his 1974 paper “Popper’s qualitative theory of verisimilitude” published in the British Journal for the Philosophy of Science David Miller gave his so called ‘Weather Example’ to argue that the Hamming distance between constituents is flawed as a measure of proximity to truth since the former is not, unlike the latter, translation invariant. In this present paper we generalise David Miller’s Weather Example in both the unary and polyadic cases, characterising precisely which permutations of c…Read more
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13Franco Montagna, Giulia Simi, and Andrea Sorbi. Logic and probabilistic systems. Archive for mathematical logic, vol. 35 , pp. 225–261 (review)Bulletin of Symbolic Logic 6 (2): 223-225. 2000.
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7Pure inductive logic with functionsJournal of Symbolic Logic 84 (4): 1382-1402. 2019.We consider the version of Pure Inductive Logic which obtains for the language with equality and a single unary function symbol giving a complete characterization of the probability functions on this language which satisfy Constant Exchangeability.
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8Six Problems in Pure Inductive LogicJournal of Philosophical Logic 48 (4): 731-747. 2019.We present six significant open problems in Pure Inductive Logic, together with their background and current status, with the intention of raising awareness and leading ultimately to their resolution.
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University of ManchesterRegular Faculty
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Probability |