45 found
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  1.  79
    Region-Based Topology.Peter Roeper - 1997 - Journal of Philosophical Logic 26 (3):251-309.
    A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of points and of open and closed sets of points and to be characteristic of locally compact T2 spaces. The effect of adding further constraints is investigated, especially those that characterise continua. Finally, the properties of mappings in region-based topology are studied. Not all such mappings correspond to point (...)
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  2. Probability Theory and Probability Logic.Peter Roeper & Hugues Leblanc - 1999
  3.  18
    Semantics for Mass Terms with Quantifiers.Peter Roeper - 1983 - Noûs 17 (2):251-265.
    It is argued that the usual proposals for dealing with mass-Quantification--All x is f--Are inadequate with the predicate is complex or when multiple quantification is considered. Mass-Quantification is seen as a generalisation of ordinary (thing) quantification in that the specialising assumption that the domain of quantification is atomic is not made. It is suggested that the semantic values of predicates are complete ideals of the boolean algebra consisting of the quantity which is the domain of quantification and all its sub-Quantities, (...)
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  4.  77
    Reasoning with Truth.Peter Roeper - 2010 - Journal of Philosophical Logic 39 (3):275-306.
    The aim of the paper is to formulate rules of inference for the predicate 'is true' applied to sentences. A distinction is recognised between (ordinary) truth and definite truth and consequently between two notions of validity, depending on whether truth or definite truth is the property preserved in valid arguments. Appropriate sets of rules of inference governing the two predicates are devised. In each case the consequence relation is in harmony with the respective predicate. Particularly appealing is a set of (...)
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  5.  37
    The Aristotelian Continuum. A Formal Characterization.Peter Roeper - 2006 - Notre Dame Journal of Formal Logic 47 (2):211-232.
    While the classical account of the linear continuum takes it to be a totality of points, which are its ultimate parts, Aristotle conceives of it as continuous and infinitely divisible, without ultimate parts. A formal account of this conception can be given employing a theory of quantification for nonatomic domains and a theory of region-based topology.
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  6. First- and Second-Order Logic of Mass Terms.Peter Roeper - 2004 - Journal of Philosophical Logic 33 (3):261-297.
    Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation.
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  7.  13
    Indiscernibility and Identity in Probability Theory.Peter Roeper & Hugues Leblanc - 1990 - Notre Dame Journal of Formal Logic 32 (1):1-46.
  8.  8
    Giving an Account of Provability Within a Theory.Peter Roeper - 2003 - Philosophia Mathematica 11 (3):332-340.
    This paper offers a justification of the ‘Hilbert-Bernays Derivability Conditions’ by considering what is required of a theory which gives an account of provability in itself.
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  9.  19
    Principles of Abstraction for Events and Processes.Peter Roeper - 1987 - Journal of Philosophical Logic 16 (3):273 - 307.
  10.  16
    On Relativizing Kolmogorov's Absolute Probability Functions.Hugues Leblanc & Peter Roeper - 1989 - Notre Dame Journal of Formal Logic 30 (4):485-512.
  11.  29
    Of A and B Being Logically Independent of Each Other and of Their Having No Common Factual Content.Peter Roeper & Hugues Leblanc - 1995 - Theoria 61 (1):61-79.
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  12. Probability Theory and Probability Semantics.Peter Roeper & Hughes Leblanc (eds.) - 1999 - University of Toronto Press.
     
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  13.  16
    Getting the Constraints on Popper's Probability Functions Right.Hugues Leblanc & Peter Roeper - 1993 - Philosophy of Science 60 (1):151-157.
    Shown here is that a constraint used by Popper in The Logic of Scientific Discovery (1959) for calculating the absolute probability of a universal quantification, and one introduced by Stalnaker in "Probability and Conditionals" (1970, 70) for calculating the relative probability of a negation, are too weak for the job. The constraint wanted in the first case is in Bendall (1979) and that wanted in the second case is in Popper (1959).
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  14.  19
    Consequence and Confirmation.Peter Roeper & Hugues Leblanc - 1995 - Notre Dame Journal of Formal Logic 36 (3):341-363.
    Gentzen's account of logical consequence is extended so as to become a matter of degree. We characterize and study two kinds of function G, where G(X,Y) takes values between 0 and 1, which represent the degree to which the set X of statements (understood conjunctively) logically implies the set Y of statements (understood disjunctively). It is then shown that these functions are essentially the same as the absolute and the relative probability functions described by Carnap.
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  15.  12
    A Vindication of Logicism.Peter Roeper - 2016 - Philosophia Mathematica 24 (3):360-378.
    Frege regarded Hume's Principle as insufficient for a logicist account of arithmetic, as it does not identify the numbers; it does not tell us which objects the numbers are. His solution, generally regarded as a failure, was to propose certain sets as the referents of numerical terms. I suggest instead that numbers are properties of pluralities, where these properties are treated as objects. Given this identification, the truth-conditions of the statements of arithmetic can be obtained from logical principles with the (...)
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  16.  31
    Absolute Probability Functions for Intuitionistic Propositional Logic.Peter Roeper & Hugues Leblanc - 1999 - Journal of Philosophical Logic 28 (3):223-234.
    Provided here is a characterisation of absolute probability functions for intuitionistic (propositional) logic L, i.e. a set of constraints on the unary functions P from the statements of L to the reals, which insures that (i) if a statement A of L is provable in L, then P(A) = 1 for every P, L's axiomatisation being thus sound in the probabilistic sense, and (ii) if P(A) = 1 for every P, then A is provable in L, L's axiomatisation being thus (...)
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  17.  29
    A Sequent Formulation of Conditional Logic Based on Belief Change Operations.Peter Roeper - 2004 - Studia Logica 77 (3):425 - 438.
    Peter Gärdenfors has developed a semantics for conditional logic, based on the operations of expansion and revision applied to states of information. The account amounts to a formalisation of the Ramsey test for conditionals. A conditional A > B is declared accepted in a state of information K if B is accepted in the state of information which is the result of revising K with respect to A. While Gärdenfors's account takes the truth-functional part of the logic as given, the (...)
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  18. Conditionals and Conditional Probabilities: Three Triviality Theorems.Hugues Leblanc & Peter Roeper - 1990 - In Kyburg Henry E., Loui Ronald P. & Carlson Greg N. (eds.), Knowledge Representation and Defeasible Reasoning. Kluwer Academic Publishers. pp. 287--306.
  19.  14
    Henkin's Completeness Proof: Forty Years Later.Hugues Leblanc, Peter Roeper, Michael Thau & George Weaver - 1991 - Notre Dame Journal of Formal Logic 32 (2):212-232.
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  20.  15
    Probability Functions: The Matter of Their Recursive Definability.Hugues Leblanc & Peter Roeper - 1992 - Philosophy of Science 59 (3):372-388.
    This paper studies the extent to which probability functions are recursively definable. It proves, in particular, that the (absolute) probability of a statement A is recursively definable from a certain point on, to wit: from the (absolute) probabilities of certain atomic components and conjunctions of atomic components of A on, but to no further extent. And it proves that, generally, the probability of a statement A relative to a statement B is recursively definable from a certain point on, to wit: (...)
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  21.  5
    Les fonctions de probabilité: la question de leur définissabilité récursive.Hugues Leblanc & Peter Roeper - 1992 - Dialogue 31 (4):643-.
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  22.  5
    De A Et B, de Leur Indépendance Logique, Et de Ce Qu'ils N'ont Aucun Contenu Factuel Commun.Peter Roeper & Hugues Leblanc - 1997 - Dialogue 36 (1):137-.
    The logical independence of two statements is tantamount to their probabilistic independence, the latter understood in a sense that derives from stochastic independence. And analogous logical and probabilistic senses of having the same factual content similarly coincide. These results are extended to notions of non-symmetrical independence and independence among more than two statements.
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  23.  7
    The Link Between Probability Functions and Logical Consequence.Peter Roeper - 1997 - Dialogue 36 (1):15-.
  24.  3
    What Are Absolute Probabilities a Function Of?Hugues Leblanc & Peter Roeper - 1990 - In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer Academic Publishers. pp. 307--325.
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  25.  2
    Chapter 1. Probability Functions for Prepositional Logic.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 5-25.
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  26.  1
    Chapter 7. Absolute Probability Functions Construed as Representing Degrees of Logical Truth.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 114-141.
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  27.  1
    Chapter 6. Families of Probability Functions Characterised by Equivalence Relations.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 99-108.
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  28.  1
    Chapter 3. Relative Probability Functions and Their T-Restrictions.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 45-58.
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  29.  1
    Chapter 4. Representing Relative Probability Functions by Means of Classes of Measure Functions.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 59-77.
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  30.  1
    Chapter 8. Relative Probability Functions Construed as Representing Degrees of Logical Consequence.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 142-166.
  31.  1
    Chapter 2. The Probabilities of Infinitary Statements and of Quantifications.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 26-44.
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  32. Acknowledgments.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press.
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  33. Appendix I.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 191-222.
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  34. Appendix II.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 223-224.
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  35. Bibliography.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 231-234.
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  36. Contents.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press.
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  37. Chapter 9. Absolute Probability Functions for Intuitionistic Logic.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 167-181.
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  38. Chapter 10. Relative Probability Functions for Intuitionistic Logic.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 182-190.
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  39. Chapter 5. The Recursive Definability of Probability Functions.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 78-98.
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  40. Frontmatter.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press.
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  41. Introduction.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 3-4.
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  42. Introduction.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 111-113.
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  43. Index.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 235-238.
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  44. Index of Constraints.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 239-240.
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  45. Notes.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 225-230.
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