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  1. Peter Roeper (2010). Reasoning with Truth. 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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  2. Peter Roeper (2006). The Aristotelian Continuum. A Formal Characterization. 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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  3. Peter Roeper (2004). A Sequent Formulation of Conditional Logic Based on Belief Change Operations. 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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  4. Peter Roeper (2004). First- and Second-Order Logic of Mass Terms. 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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  5. Peter Roeper (2003). Giving an Account of Provability Within a Theory. 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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  6. Peter Roeper & Hugues Leblanc (1999). Absolute Probability Functions for Intuitionistic Propositional Logic. 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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  7. Peter Roeper (1997). Region-Based Topology. 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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  8. Peter Roeper (1997). The Link Between Probability Functions and Logical Consequence. Dialogue 36 (01):15-.
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  9. Peter Roeper & Hugues Leblanc (1997). De A Et B, de Leur Indépendance Logique, Et de Ce Qu'ils N'ont Aucun Contenu Factuel Commun. Dialogue 36 (01):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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  10. Peter Roeper & Hugues Leblanc (1995). Consequence and Confirmation. 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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  11. Peter Roeper & Hugues Leblanc (1995). Of A and B Being Logically Independent of Each Other and of Their Having No Common Factual Content. Theoria 61 (1):61-79.
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  12. Hugues Leblanc & Peter Roeper (1993). Getting the Constraints on Popper's Probability Functions Right. 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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  13. Hugues Leblanc & Peter Roeper (1992). Les fonctions de probabilité: la question de leur définissabilité récursive. Dialogue 31 (04):643-.
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  14. Hugues Leblanc & Peter Roeper (1992). Probability Functions: The Matter of Their Recursive Definability. 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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  15. Hugues Leblanc, Peter Roeper, Michael Thau & George Weaver (1991). Henkin's Completeness Proof: Forty Years Later. Notre Dame Journal of Formal Logic 32 (2):212-232.
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  16. Hugues Leblanc & Peter Roeper (1990). Conditionals and Conditional Probabilities: Three Triviality Theorems. In. In Kyburg Henry E., Loui Ronald P. & Carlson Greg N. (eds.), Knowledge Representation and Defeasible Reasoning. Kluwer. 287--306.
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  17. Hugues Leblanc & Peter Roeper (1990). What Are Absolute Probabilities a Function Of? In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer. 307--325.
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  18. Peter Roeper & Hugues Leblanc (1990). Indiscernibility and Identity in Probability Theory. Notre Dame Journal of Formal Logic 32 (1):1-46.
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  19. Hugues Leblanc & Peter Roeper (1989). On Relativizing Kolmogorov's Absolute Probability Functions. Notre Dame Journal of Formal Logic 30 (4):485-512.
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  20. Peter Roeper (1987). Principles of Abstraction for Events and Processes. Journal of Philosophical Logic 16 (3):273 - 307.
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  21. Peter Roeper (1983). Semantics for Mass Terms with Quantifiers. 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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