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  • Articles  (1,033)
  • Oxford University Press  (1,033)
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  • Articles  (1,033)
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  • Oxford University Press  (1,033)
  • American Meteorological Society
  • Blackwell Publishing Ltd
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  • 1
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    Reasoning about types of action and agent capabilities (2013)
    Oxford University Press
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    Publication Date: 2013-09-27
    Description: We present a logical system for reasoning about types of actions (processes) and about agent capabilities to execute types of actions. The syntax of the system is based on that of Propositional Dynamic Logic ( PDL ), though the semantics we define is different (interpreting process terms as types, i.e. sets of binary relations). The standard PDL syntax is extended with capabilities statements, as in the KARO framework, atomic process types specified as precondition-effect pairs, written as , as well as backwards possibility operators. The resulting system is shown (by filtration) to have a decidable satisfiability problem and a sound and complete Gentzen-style proof system is presented.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
    Published by Oxford University Press
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  • 2
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    Epsilon-invariant substitutions and indefinite descriptions (2013)
    Oxford University Press
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    Publication Date: 2013-09-27
    Description: It is known that an epsilon-invariant sentence has a first-order reformulation, although it is not in an explicit form, since, the proof uses the non-constructive interpolation theorem. We make an attempt to describe the explicit meaning of sentences containing epsilon-terms, adopting the strong assumption of their first-order reformulability. We will prove that, if a monadic predicate is syntactically independent from an epsilon-term and if the sentence obtained by substituting the variable of the predicate with the epsilon-term is epsilon-invariant, then the sentence has an explicit first-order reformulation. Finally, we point out that the formula gives a contextual-quantificational meaning for the indefinite descriptions, provided that one accepts Kneebone’s read of epsilon-terms.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
    Published by Oxford University Press
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  • 3
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    An algebraic look at filtrations in modal logic (2013)
    Oxford University Press
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    Publication Date: 2013-09-27
    Description: Filtration constructions are among the oldest and best known methods for obtaining finite model properties for modal logics, and appear in the literature in both model-theoretic and algebraic versions. In this article we investigate definitions of algebraic filtrations by means of different types of binary relations on modal algebras, and the relationships between these. We generalize the notion of a model-theoretic filtration somewhat while simultaneously lifting it to the level of frames. We proceed to link algebraic filtrations with their model- or frame-theoretic counterparts by showing how our filtration notions interface neatly with the well-known duality theory of modal algebras and Kripke frames. We illustrate, by means of some examples, how this theory enables one to easily translate between algebraic and model-theoretic versions of some well-known filtrations. We obtain some order theoretic insights regarding the (usually model-theoretically specified) smallest and largest filtrations by considering their algebraic versions, thus demonstrating the utility of having ready access to both versions.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
    Published by Oxford University Press
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  • 4
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    Conservativity: a necessary property for the maximization of witness sets (2013)
    Oxford University Press
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    Publication Date: 2013-09-27
    Description: It is generally assumed that Conservativity is a necessary ingredient for interpreting collective and cumulative predicates or, more in general, for interpreting—what I termed as—Independent Set (IS) readings (a.k.a. Scopeless readings). Under this assumption, several approaches aiming at formally providing logical representations of collective/cumulative readings implement Conservativity. This is done also in the frameworks defined in Winter (2001, Flexibility Principles in Boolean Semantics: Coordination, Plurality, and Scope in Natural Language , MIT Press) and in Robaldo (2011, J. Logic Lang. Infor. , 20, 233–271). This article investigates further the role played by Conservativity in the interpretation of IS readings, and argues that its need is not specifically due to the use of collective/cumulative predicates. Rather, it serves to maximize witness sets for quantifiers thereby guaranteeing correct truth conditions in several cases.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
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  • 5
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    On second-order characterizability (2013)
    Oxford University Press
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    Publication Date: 2013-09-27
    Description: We investigate the extent of second-order characterizable structures by extending Shelah's Main Gap dichotomy to second-order logic. For this end we consider a countable complete first-order theory T . We show that all sufficiently large models of T have a characterization up to isomorphism in the extension of second-order logic obtained by adding a little bit of infinitary logic if and only if T is shallow superstable with NDOP and NOTOP. Our result relies on cardinal arithmetic assumptions. Under weaker assumptions we get consistency results or alternatively results about second-order logic with Henkin semantics. Mathematics Subject Classification: 03C85, 03C75.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
    Published by Oxford University Press
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  • 6
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    A proof procedure for adaptive logics (2013)
    Oxford University Press
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    Publication Date: 2013-09-27
    Description: In this article, I present a procedure that generates proofs for finally derivable adaptive logic consequences. A proof procedure for the inconsistency adaptive logic CLuN r is already presented in [ 7 ]. In this article a procedure for CLuN m is presented and the results for both logics are generalized to all adaptive logics, on the presupposition that there exists a proof procedure for the lower limit logic. The generated proofs are so called goal-directed proofs, i.e. proofs that (i) start with the formula (the goal) of which one wants to know whether it is a consequence of a certain premise set and (ii) only consist of lines that may potentially be useful for proving or disproving the goal. The goal-directed proofs form good explications of actual problem-solving reasoning processes.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
    Published by Oxford University Press
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  • 7
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    Malinowski modalization, modalization through fibring and the Leibniz hierarchy (2013)
    Oxford University Press
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    Publication Date: 2013-09-27
    Description: We show how various modal systems considered by Malinowski as extensions of classical propositional calculus may be obtained as fibrings of classical propositional calculus and corresponding implicative modal logics, using the fibring framework for combining logics of Fern'andez and Coniglio. Taking advantage of this construction and known results of Malinowski, we draw some useful conclusions concerning some limitations of the fibring process. Finally, Malinowski's constructions are extended to obtain some modal extensions of arbitrary equivalential logics in the context of abstract algebraic logic. These are studied with respect to their algebraic character.
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
    Published by Oxford University Press
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  • 8
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    Two direct proofs that LLPO implies the detachable fan theorem (2013)
    Oxford University Press
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    Publication Date: 2013-09-27
    Description: It is shown, directly and in two ways, that Brouwer’s fan theorem for detachable bars can be proved within Bishop-style constructive mathematics supplemented by (countably many applications of) the omniscience principle LLPO .
    Print ISSN: 1367-0751
    Electronic ISSN: 1368-9894
    Topics: Mathematics
    Published by Oxford University Press
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  • 9
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    The fortified Weiszfeld algorithm for solving the Weber problem (2014)
    Oxford University Press
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    Publication Date: 2014-12-05
    Description: An improved Weiszfeld algorithm, termed the fortified Weiszfeld algorithm, for the solution of the single facility Weber problem with Euclidean distances is proposed. The new approach is based on a parabolic approximation of the objective function and testing demand points for optimality. Computational experiments show the superiority of the fortified approach to the original Weiszfeld algorithm.
    Print ISSN: 1471-678X
    Electronic ISSN: 1471-6798
    Topics: Mathematics
    Published by Oxford University Press
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  • 10
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    Estimating Malmquist indices and semi-parametric censored regressions with a coherent data-generating process (2014)
    Oxford University Press
    Details
    Publication Date: 2014-12-05
    Description: This paper presents a semi-parametric method for bootstrapping non-stochastic estimates of Malmquist indices and the second-stage regressions with a coherent data-generating process (DGP) for panel data. It emphasizes the importance of using censoring techniques instead of truncation in the DGP. To keep the panel structure, the fixed effects censored least square (CLS) method is preferred in the algorithm. Two smoothing processes in the DGP using fixed effects CLSs and cross-sectional censored least absolute deviations are proposed and compared. This semi-parametric bootstrap process can be used to delete artificial correlation amongst the estimated efficiencies in panel data. Although the exposition gives only output-oriented indices, the method can easily be extended to the input-oriented model. Finally, an empirical case study is carried out on Irish dairy farms.
    Print ISSN: 1471-678X
    Electronic ISSN: 1471-6798
    Topics: Mathematics
    Published by Oxford University Press
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