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Jeffrey Paris
University of Manchester
  1.  16
    On the Scheme of Induction for Bounded Arithmetic Formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (3):261-302.
  2.  24
    The Uncertain Reasoner's Companion: A Mathematical Perspective.J. B. Paris - 1994 - Cambridge University Press.
    Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the (...)
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  3.  48
    McAloon K.. Introduction. Modèles de l'Arithmétique, Séminaire Paris VII, Edited by McAloon K., Asterisque, No. 73, Société Mathématique de France, Paris 1980, Pp. 1–2.Kirby L. A. S.. La Méthode des Indicatrices Et le Théorème D'Incomplétude. Modèles de l'Arithmétique, Séminaire Paris VII, Edited by McAloon K., Asterisque, No. 73, Société Mathématique de France, Paris 1980, Pp. 5–18.Lascar Daniel. Une Indicatrice de Type “Ramsey” Pour l'Arithmétique de Peano Et la Formule de Paris-Harrington. Modèles de l'Arithmétique, Séminaire Paris VII, Edited by McAloon K., Asterisque, No. 73, Société Mathématique de France, Paris 1980, 19–30.McAloon Kenneth. Les Rapports Entre la Méthode des Indicatrices Et la Méthode de Gödel Pour Obtenir des Résultats D'Indépendance. Modèles de l'Arithmétique, Séminaire Paris VII, Edited by McAloon K., Asterisque, No. 73, Société Mathématique de France, Paris 1980, Pp. 31–39.McAloon Kenneth. Progressions Transfinies de Théories Axiomatiques, Formes Combinatoires. [REVIEW]J. B. Paris - 1983 - Journal of Symbolic Logic 48 (2):483-484.
  4.  33
    Atom Exchangeability and Instantial Relevance.J. B. Paris & P. Waterhouse - 2009 - Journal of Philosophical Logic 38 (3):313-332.
    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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  5.  3
    The Uncertain Reasoner’s Companion.J. B. Paris - 1994 - Erkenntnis 46 (3):397-400.
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  6.  31
    A Continuum of Inductive Methods Arising From a Generalized Principle of Instantial Relevance.C. J. Nix & J. B. Paris - 2006 - Journal of Philosophical Logic 35 (1):83-115.
    In this paper we consider a natural generalization of the Principle of Instantial Relevance and give a complete characterization of the probabilistic belief functions satisfying this principle as a family of discrete probability functions parameterized by a single real δ ∊ [0, 1).
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  7.  59
    Some Observations on Induction in Predicate Probabilistic Reasoning.M. J. Hill, J. B. Paris & G. M. Wilmers - 2002 - Journal of Philosophical Logic 31 (1):43-75.
    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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  8.  34
    O is Not Enough.J. B. Paris & R. Simmonds - 2009 - Review of Symbolic Logic 2 (2):298-309.
    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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  9. $ZF \Vdash \Sum^0_4$ Determinateness.J. B. Paris - 1972 - Journal of Symbolic Logic 37 (4):661 - 667.
  10.  20
    Provability of the Pigeonhole Principle and the Existence of Infinitely Many Primes.J. B. Paris, A. J. Wilkie & A. R. Woods - 1988 - Journal of Symbolic Logic 53 (4):1235-1244.
  11.  56
    A Note on Binary Inductive Logic.C. J. Nix & J. B. Paris - 2007 - Journal of Philosophical Logic 36 (6):735-771.
    We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.
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  12.  20
    An Analogy Principle in Inductive Logic.A. Hill & J. B. Paris - 2013 - Annals of Pure and Applied Logic 164 (12):1293-1321.
    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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  13.  22
    Franco Montagna, Giulia Simi, and Andrea Sorbi. Logic and Probabilistic Systems. Archive for Mathematical Logic, Vol. 35 , Pp. 225–261. [REVIEW]J. B. Paris - 2000 - Bulletin of Symbolic Logic 6 (2):223-225.
  14.  19
    J. I. Friedman. Proper Classes as Members of Extended Sets. Mathematische Annalen, Vol. 83 , Pp. 232–240.J. B. Paris - 1975 - Journal of Symbolic Logic 40 (3):462.
  15. Ancient Indian Logic and Analogy.J. B. Paris & A. Vencovska - 2017 - In S. Ghosh & S. Prasad (eds.), Logic and its Applications, Lecture Notes in Computer Science 10119. Springer. pp. 198-210.
    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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  16. Second Order Inductive Logic and Wilmers' Principle.M. S. Kliess & J. B. Paris - 2014 - Journal of Applied Logic 12 (4):462-476.
    We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.
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  17.  20
    A Note on Priest's Finite Inconsistent Arithmetics.J. B. Paris & N. Pathmanathan - 2006 - Journal of Philosophical Logic 35 (5):529-537.
    We give a complete characterization of Priest's Finite Inconsistent Arithmetics observing that his original putative characterization included arithmetics which cannot in fact be realized.
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  18.  54
    A Survey of Some Recent Results on Spectrum Exchangeability in Polyadic Inductive Logic.J. Landes, J. B. Paris & A. Vencovská - 2011 - Synthese 181 (S1):19 - 47.
    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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  19.  4
    Initial Segments of Models of Peano's Axioms.L. A. S. Kirby, J. B. Paris, A. Lachlan, M. Srebrny & A. Zarach - 1983 - Journal of Symbolic Logic 48 (2):482-483.
  20.  19
    On LP -Models of Arithmetic.J. B. Paris & A. Sirokofskich - 2008 - Journal of Symbolic Logic 73 (1):212-226.
    We answer some problems set by Priest in [11] and [12], in particular refuting Priest's Conjecture that all LP-models of Th(N) essentially arise via congruence relations on classical models of Th(N). We also show that the analogue of Priest's Conjecture for I δ₀ + Exp implies the existence of truth definitions for intervals [0,a] ⊂ₑ M ⊨ I δ₀ + Exp in any cut [0,a] ⊂e K ⊆ M closed under successor and multiplication.
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  21.  20
    Six Problems in Pure Inductive Logic.J. B. Paris & A. Vencovská - 2019 - Journal of Philosophical Logic 48 (4):731-747.
    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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  22.  8
    Translation Invariance and Miller’s Weather Example.J. B. Paris & A. Vencovská - forthcoming - Journal of Logic, Language and Information:1-26.
    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 constituents/atoms can be effected by (...)
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  23.  5
    An Examination of the SEP Candidate Analogical Inference Rule Within Pure Inductive Logic.E. Howarth, J. B. Paris & A. Vencovská - 2016 - Journal of Applied Logic 14:22-45.
  24.  6
    A Hierarchy of Cuts in Models of Arithmetic.J. B. Paris, L. Pacholski, J. Wierzejewski, A. J. Wilkie, George Mills & Jussi Ketonen - 1986 - Journal of Symbolic Logic 51 (4):1062-1066.
  25.  76
    An Observation on Carnapʼs Continuum and Stochastic Independencies.J. B. Paris - 2013 - Journal of Applied Logic 11 (4):421-429.
    We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson's Sufficientness Principle holds, thus giving Carnap's Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap's Continuum for the language with just a single predicate.
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  26.  6
    O is Not Enough: O is Not Enough.J. B. Paris - 2009 - Review of Symbolic Logic 2 (2):298-309.
    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 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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  27.  7
    Pure Inductive Logic with Functions.E. Howarth & J. B. Paris - forthcoming - Journal of Symbolic Logic:1-22.
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  28.  34
    Some Independence Results for Peano Arithmetic.J. B. Paris - 1978 - Journal of Symbolic Logic 43 (4):725-731.
  29.  13
    A Note on the Undefinability of Cuts.J. B. Paris & C. Dimitracopoulos - 1983 - Journal of Symbolic Logic 48 (3):564-569.
  30. Pure Inductive Logic.J. B. Paris & A. Vencovska - 2011 - Cambridge, UK: Cambridge University Press.
    Pure Inductive Logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years, plus the main contributions of the authors and their collaborators over the last decade, to present a comprehensive account of the discipline within a single unified context.
     
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  31.  2
    The Emergence of Reasons Conjecture.J. B. Paris & A. Vencovská - 2003 - Journal of Applied Logic 1 (3-4):167-195.
  32.  5
    Common Sense and Stochastic Independence.J. B. Paris & A. Vencovská - 2001 - In David Corfield & Jon Williamson (eds.), Foundations of Bayesianism. Kluwer Academic Publishers. pp. 203--240.
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  33. Reasoning by Analogy in Inductive Logic.Alexandra Hill & J. B. Paris - 2011 - In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications. pp. 63--76.
  34. A Note on the Rational Closure of Knowledge Bases with Both Positive and Negative Knowledge.R. Booth & J. B. Paris - 1998 - Journal of Logic, Language and Information 7 (2):165-190.
    The notion of the rational closure of a positive knowledge base K of conditional assertions | (standing for if then normally ) was first introduced by Lehmann (1989) and developed by Lehmann and Magidor (1992). Following those authors we would also argue that the rational closure is, in a strong sense, the minimal information, or simplest, rational consequence relation satisfying K. In practice, however, one might expect a knowledge base to consist not just of positive conditional assertions, | , but (...)
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  35.  41
    European Summer Meeting of the Association for Symbolic Logic, Manchester, England, 1984.P. Aczel, J. B. Paris, A. J. Wilkie, G. M. Wilmers & C. E. M. Yates - 1986 - Journal of Symbolic Logic 51 (2):480-502.
  36.  48
    A New Criterion for Comparing Fuzzy Logics for Uncertain Reasoning.A. D. C. Bennett, J. B. Paris & A. Vencovská - 2000 - Journal of Logic, Language and Information 9 (1):31-63.
    A new criterion is introduced for judging the suitability of various fuzzy logics for practical uncertain reasoning in a probabilistic world and the relationship of this criterion to several established criteria, and its consequences for truth functional belief, are investigated.
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  37.  19
    Combining Analogical Support in Pure Inductive Logic.J. B. Paris & A. Vencovská - 2016 - Erkenntnis (2):01-19.
    We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would (...)
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  38.  28
    Review: Franco Montagna, Giulia Simi, Andrea Sorbi, Logic and Probabilistic Systems. [REVIEW]J. B. Paris - 2000 - Bulletin of Symbolic Logic 6 (2):223-225.
  39.  38
    Symmetry in Polyadic Inductive Logic.J. B. Paris & A. Vencovská - 2012 - Journal of Logic, Language and Information 21 (2):189-216.
    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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  40.  2
    Measure and Minimal Degrees.J. B. Paris - 1977 - Annals of Mathematical Logic 11 (2):203-216.
  41.  17
    A Property of 2-Sorted Peano Models and Program Verification.L. Csirmaz & J. B. Paris - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (19-24):325-334.
  42.  16
    Review: J. I. Friedman, Proper Classes as Members of Extended Sets. [REVIEW]J. B. Paris - 1975 - Journal of Symbolic Logic 40 (3):462-462.
  43.  30
    Note on an Induction Axiom.J. B. Paris - 1978 - Journal of Symbolic Logic 43 (1):113-117.
  44.  15
    The Theory of Spectrum Exchangeability.E. Howarth & J. B. Paris - 2015 - Review of Symbolic Logic 8 (1):108-130.
  45.  11
    A Natural Prior Probability Distribution Derived From the Propositional Calculus.J. B. Paris, A. Vencovská & G. M. Wilmers - 1994 - Annals of Pure and Applied Logic 70 (3):243-285.
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  46.  5
    Second Order Inductive Logic and Wilmers' Principle.M. S. Kließ & J. B. Paris - 2014 - Journal of Applied Logic 12 (4):462-476.
  47. Review: K. McAloon, Modeles de l'Arithmetique, Siminaire Paris VII. [REVIEW]J. B. Paris - 1983 - Journal of Symbolic Logic 48 (2):483-484.
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  48.  3
    A Property of 2‐Sorted Peano Models and Program Verification.L. Csirmaz & J. B. Paris - 1984 - Mathematical Logic Quarterly 30 (19‐24):325-334.
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  49. Principles of Remembering and Forgetting.E. Howarth & J. B. Paris - 2014 - Logique Et Analyse 57 (228):489-511.
    We propose two principles of inductive reasoning related to how observed information is handled by conditioning, and justify why they may be said to represent aspects of rational reasoning. A partial classification is given of the probability functions which satisfy these principles.
     
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  50. The Finite Values Property.E. Howarth & J. B. Paris - 2016 - In C. Beierle, C. Brewka & M. Thimm (eds.), Computational Models of Rationality, Essays Dedicated to Gabriele Kern-Isberner on the Occasion of her 60th Birthday. London, UK: College Publications. pp. 316-331.
    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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