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  1. A. Hill & J. B. Paris (2013). An Analogy Principle in Inductive Logic. Annals of Pure and Applied Logic 164 (12):1293-1321.
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  2. J. B. Paris & A. Vencovská (2012). Symmetry in Polyadic Inductive Logic. 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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  3. Alexandra Hill & J. B. Paris (2011). Reasoning by Analogy in Inductive Logic. In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications. 63--76.
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  4. J. Landes, J. B. Paris & A. Vencovská (2011). A Survey of Some Recent Results on Spectrum Exchangeability in Polyadic Inductive Logic. Synthese 181 (1):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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  5. J. B. Paris & R. Simmonds (2009). O is Not Enough. 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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  6. J. B. Paris & P. Waterhouse (2009). Atom Exchangeability and Instantial Relevance. 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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  7. J. B. Paris & A. Sirokofskich (2008). On LP -Models of Arithmetic. 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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  8. C. J. Nix & J. B. Paris (2007). A Note on Binary Inductive Logic. 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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  9. C. J. Nix & J. B. Paris (2006). A Continuum of Inductive Methods Arising From a Generalized Principle of Instantial Relevance. 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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  10. J. B. Paris & N. Pathmanathan (2006). A Note on Priest's Finite Inconsistent Arithmetics. 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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  11. M. J. Hill, J. B. Paris & G. M. Wilmers (2002). Some Observations on Induction in Predicate Probabilistic Reasoning. 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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  12. J. B. Paris & A. Vencovská (2001). Common Sense and Stochastic Independence. In David Corfield & Jon Williamson (eds.), Foundations of Bayesianism. Kluwer Academic Publishers. 203--240.
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  13. A. D. C. Bennett, J. B. Paris & A. Vencovská (2000). A New Criterion for Comparing Fuzzy Logics for Uncertain Reasoning. 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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  14. J. B. Paris (2000). Montagna Franco, Simi Giulia, and Sorbi Andrea. Logic and Probabilistic Systems. Archive for Mathematical Logic, Vol. 35 (1996), Pp. 225–261. [REVIEW] Bulletin of Symbolic Logic 6 (2):223-225.
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  15. J. B. Paris (2000). Review: Franco Montagna, Giulia Simi, Andrea Sorbi, Logic and Probabilistic Systems. [REVIEW] Bulletin of Symbolic Logic 6 (2):223-225.
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  16. R. Booth & J. B. Paris (1998). A Note on the Rational Closure of Knowledge Bases with Both Positive and Negative Knowledge. 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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  17. J. B. Paris (1994). The Uncertain Reasoner's Companion: A Mathematical Perspective. 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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  18. J. B. Paris, A. Vencovská & G. M. Wilmers (1994). A Natural Prior Probability Distribution Derived From the Propositional Calculus. Annals of Pure and Applied Logic 70 (3):243-285.
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  19. J. B. Paris, A. J. Wilkie & A. R. Woods (1988). Provability of the Pigeonhole Principle and the Existence of Infinitely Many Primes. Journal of Symbolic Logic 53 (4):1235-1244.
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  20. A. J. Wilkie & J. B. Paris (1987). On the Scheme of Induction for Bounded Arithmetic Formulas. Annals of Pure and Applied Logic 35:261-302.
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  21. P. Aczel, J. B. Paris, A. J. Wilkie, G. M. Wilmers & C. E. M. Yates (1986). European Summer Meeting of the Association for Symbolic Logic: Manchester, England, 1984. Journal of Symbolic Logic 51 (2):480-502.
  22. L. Csirmaz & J. B. Paris (1984). A Property of 2‐Sorted Peano Models and Program Verification. Mathematical Logic Quarterly 30 (19‐24):325-334.
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  23. J. B. Paris (1983). Review: K. McAloon, Modeles de l'Arithmetique, Siminaire Paris VII. [REVIEW] Journal of Symbolic Logic 48 (2):483-484.
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  24. J. B. Paris & C. Dimitracopoulos (1983). A Note on the Undefinability of Cuts. Journal of Symbolic Logic 48 (3):564-569.
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  25. J. B. Paris (1978). Note on an Induction Axiom. Journal of Symbolic Logic 43 (1):113-117.
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  26. J. B. Paris (1978). Some Independence Results for Peano Arithmetic. Journal of Symbolic Logic 43 (4):725-731.
  27. J. B. Paris (1977). Measure and Minimal Degrees. Annals of Mathematical Logic 11 (2):203-216.
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  28. J. B. Paris (1975). Review: J. I. Friedman, Proper Classes as Members of Extended Sets. [REVIEW] Journal of Symbolic Logic 40 (3):462-462.
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  29. K. J. Devlin & J. B. Paris (1973). More on the Free Subset Problem. Annals of Mathematical Logic 5 (4):327-336.
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  30. J. B. Paris (1972). $ZF \Vdash \Sum^0_4$ Determinateness. Journal of Symbolic Logic 37 (4):661 - 667.
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  31. K. Kunen & J. B. Paris (1971). Boolean Extensions and Measurable Cardinals. Annals of Mathematical Logic 2 (4):359-377.
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