
235The Counterpart Principle of Analogical Support by Structural SimilarityErkenntnis 79 (S6): 116. 2014.We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures.

200Ancient Indian Logic and AnalogyIn S. Ghosh & S. Prasad (eds.), Logic and its Applications, Lecture Notes in Computer Science 10119, Springer. pp. 198210. 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 NyayaSutra 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.

177Second Order Inductive Logic and Wilmers' PrincipleJournal of Applied Logic 12 (4): 462476. 2014.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.

139An observation on Carnapʼs Continuum and stochastic independenciesJournal of Applied Logic 11 (4): 421429. 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

87The liar paradox and fuzzy logicJournal of Symbolic Logic 65 (1): 339346. 2000.Can one extend crisp Peano arithmetic PA by a possibly manyvalued 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

78Some observations on induction in predicate probabilistic reasoningJournal of Philosophical Logic 31 (1): 4375. 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

72Regularity in models of arithmeticJournal of Symbolic Logic 49 (1): 272280. 1984.This paper investigates the quantifier "there exist unboundedly many" in the context of firstorder arithmetic. An alternative axiomatization is found for Peano arithmetic based on an axiom schema of regularity: The union of boundedly many bounded sets is bounded. We also obtain combinatorial equivalents of certain secondorder theories associated with cuts in nonstandard models of arithmetic

64Common sense and maximum entropySynthese 117 (1): 7593. 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

59A Note on Binary Inductive LogicJournal of Philosophical Logic 36 (6): 735771. 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.

58Rational Pavelka predicate logic is a conservative extension of łukasiewicz predicate logicJournal of Symbolic Logic 65 (2): 669682. 2000.Rational Pavelka logic extends Lukasiewicz infinitely valued logic by adding truth constants r̄ for rationals in [0, 1]. We show that this is a conservative extension. We note that this shows that provability degree can be defined in Lukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963

57A new criterion for comparing fuzzy logics for uncertain reasoningJournal of Logic, Language and Information 9 (1): 3163. 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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51Symmetry’s End?Erkenntnis 74 (1): 5367. 2011.We examine the idea that similar problems should have similar solutions (to paraphrase van Fraassen’s slogan ‘Problems which are essentially the same must receive essentially the same solution’, see van Fraassen in Laws and symmetry, Oxford Univesity Press, Oxford, 1989, p. 236) in the context of symmetries of sentence algebras within Inductive Logic and conclude that by itself this is too generous a notion upon which to found the rational assignment of probabilities. We also argue that within o…Read more

51Rationality As ConformitySynthese 144 (2): 249285. 2005.We argue in favour of identifying one aspect of rational choice with the tendency to conform to the choice you expect another likeminded, but noncommunicating, agent to make and study this idea in the very basic case where the choice is from a nonempty subset K of 2 A and no further structure or knowledge of A is assumed.

50Symmetry in Polyadic Inductive LogicJournal of Logic, Language and Information 21 (2): 189216. 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

43European summer meeting of the Association for Symbolic Logic, Manchester, England, 1984Journal of Symbolic Logic 51 (2): 480502. 1986.

41O is not enoughReview of Symbolic Logic 2 (2): 298309. 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

40Atom Exchangeability and Instantial RelevanceJournal of Philosophical Logic 38 (3): 313332. 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.

37Frank 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

34A 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 NixParis Continuum. We argue that t…Read more

34A Continuum of Inductive Methods Arising from a Generalized Principle of Instantial RelevanceJournal of Philosophical Logic 35 (1): 83115. 2006.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)

33Franco 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): 223225. 2000.

33Truth definitions without exponentiation and the Σ₁ collection schemeJournal of Symbolic Logic 77 (2): 649655. 2012.We prove that: • if there is a model of I∆₀ + ¬ exp with cofinal Σ₁definable elements and a Σ₁ truth definition for Σ₁ sentences, then I∆₀ + ¬ exp +¬BΣ₁ is consistent, • there is a model of I∆₀ Ω₁ + ¬ exp with cofinal Σ₁definable elements, both a Σ₂ and a ∏₂ truth definition for Σ₁ sentences, and for each n > 2, a Σ n truth definition for Σ n sentences. The latter result is obtained by constructing a model with a recursive truthpreserving translation of Σ₁ sentences into boolean combinations …Read more

32On parameter free induction schemasJournal of Symbolic Logic 53 (4): 10821097. 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

30Six Problems in Pure Inductive LogicJournal of Philosophical Logic 48 (4): 731747. 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.

29Review: Franco Montagna, Giulia Simi, Andrea Sorbi, Logic and Probabilistic Systems (review)Bulletin of Symbolic Logic 6 (2): 223225. 2000.

26The 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 selfcontained, 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

University of ManchesterRegular Faculty
Areas of Interest
Logic and Philosophy of Logic 
Philosophy of Probability 