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10On the emergence of reasons in inductive logicLogic Journal of the IGPL 9 (2): 207-216. 2001.We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating finite predicate knowledge bases as potentially infinite propositional knowledge bases. It is shown that for a range of predicate knowledge bases and several key propositional inference processes this procedure is well defined, and furthermore yields an explanation for the validity of the induction in terms of 'reasons'
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31Proof systems for probabilistic uncertain reasoningJournal of Symbolic Logic 63 (3): 1007-1039. 1998.The paper describes and proves completeness theorems for a series of proof systems formalizing common sense reasoning about uncertain knowledge in the case where this consists of sets of linear constraints on a probability function
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5Proof Systems for Probabilistic Uncertain ReasoningJournal of Symbolic Logic 63 (3): 1007-1039. 1998.The paper describes and proves completeness theorems for a series of proof systems formalizing common sense reasoning about uncertain knowledge in the case where this consists of sets of linear constraints on a probability function.
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57On parameter free induction schemasJournal of Symbolic Logic 53 (4): 1082-1097. 1988.We present a comprehensive study of the axiom schemas IΣ - n , BΣ - n (induction and collection schemas for parameter free Σ n formulas) and some closely related schemas
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14Truth definitions without exponentiation and the Σ1 collection schemeJournal of Symbolic Logic 77 (2): 649. 2012.
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110The liar paradox and fuzzy logicJournal of Symbolic Logic 65 (1): 339-346. 2000.Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying "x is true" and satisfying the "dequotation schema" $\varphi \equiv \text{Tr}(\bar{\varphi})$ for all sentences φ? This problem is investigated in the frame of Lukasiewicz infinitely valued logic
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29Review: J. I. Friedman, Proper Classes as Members of Extended Sets (review)Journal of Symbolic Logic 40 (3): 462-462. 1975.
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487Ancient 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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40A Note on Priest's Finite Inconsistent ArithmeticsJournal of Philosophical Logic 35 (5): 529-537. 2006.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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42The liar paradox and fuzzy logicJournal of Symbolic Logic 65 (1): 339-346. 2000.Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying “xis true” and satisfying the “dequotation schema”for all sentences φ? This problem is investigated in the frame of Łukasiewicz infinitely valued logic.
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36The Type Theoretic Interpretation of Constructive Set TheoryJournal of Symbolic Logic 49 (1): 313-314. 1984.
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36Provability of the pigeonhole principle and the existence of infinitely many primesJournal of Symbolic Logic 53 (4): 1235-1244. 1988.
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103Common sense and maximum entropySynthese 117 (1): 75-93. 1998.This paper concerns the question of how to draw inferences common sensically from uncertain knowledge. Since the early work of Shore and Johnson (1980), Paris and Vencovská (1990), and Csiszár (1989), it has been known that the Maximum Entropy Inference Process is the only inference process which obeys certain common sense principles of uncertain reasoning. In this paper we consider the present status of this result and argue that within the rather narrow context in which we work this complete a…Read more
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The Finite Values PropertyIn Beierle C., Brewka C. & Thimm M. (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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73A Note on Binary Inductive LogicJournal of Philosophical Logic 36 (6): 735-771. 2007.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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67Rationality As ConformitySynthese 144 (2): 249-285. 2005.We argue in favour of identifying one aspect of rational choice with the tendency to conform to the choice you expect another like-minded, but non-communicating, agent to make and study this idea in the very basic case where the choice is from a non-empty subset K of 2 A and no further structure or knowledge of A is assumed.
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34The 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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72A new criterion for comparing fuzzy logics for uncertain reasoningJournal of Logic, Language and Information 9 (1): 31-63. 2000.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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2Review: K. McAloon, Modeles de l'arithmetique, Siminaire Paris VII (review)Journal of Symbolic Logic 48 (2): 483-484. 1983.
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414An observation on Carnapʼs Continuum and stochastic independenciesJournal of Applied Logic 11 (4): 421-429. 2013.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 lan…Read more
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32Subsets of models of arithmeticArchive for Mathematical Logic 32 (1): 65-73. 1992.We define certain properties of subsets of models of arithmetic related to their codability in end extensions and elementary end extensions. We characterize these properties using some more familiar notions concerning cuts in models of arithmetic
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90Some 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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45The uncertain reasoner's companion: a mathematical perspectiveCambridge University Press. 1994.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 concentra…Read more
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University of ManchesterRegular Faculty
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Probability |