40,037 research outputs found

    Choosing Your Nonmonotonic Logic: A Shopper’s Guide

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    The paper presents an exhaustive menu of nonmonotonic logics. The options are individuated in terms of the principles they reject. I locate, e.g., cumulative logics and relevance logics on this menu. I highlight some frequently neglected options, and I argue that these neglected options are particularly attractive for inferentialists

    GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions

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    We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.Comment: 12 pages, LaTeX, v2: some clarifications added, updated package availabl

    Extended supersymmetry of semichiral sigma model in 4D

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    Briefly: Using a novel (1,1)(1,1) superspace formulation of semichiral sigma models with 4D4D target space, we investigate if an extended supersymmetry in terms of semichirals is compatible with having a 4D4D target space with torsion. In more detail: Semichiral sigma models have (2,2)(2,2) supersymmetry and Generalized K\"ahler target space geometry by construction. They can also support (4,4)(4,4) supersymmetry and Generalized Hyperk\"ahler geometry, but when the target space is four dimensional indications are that the geometry is restricted to Hyperk\"ahler. To investigate this further, we reduce the model to (1,1)(1,1) superspace and construct the extra (on-shell) supersymmetries there. We then find the conditions for a lift to (2,2)(2,2) super space and semichiral fields to exist. Those conditions are shown to hold for Hyperk\"ahler geometries. The SU(2)⊗U(1)SU(2)\otimes U(1) WZW model, which has (4,4)(4,4) supersymmetry and a semichiral description, is also investigated. The additional supersymmetries are found in (1,1)(1,1) superspace but shown {\em not} to be liftable to a (2,2)(2,2) semichiral formulation.Comment: 23 pages. Resubmitted after compilation problem

    Expressing Validity: Towards a Self-Sufficient Inferentialism

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    For semantic inferentialists, the basic semantic concept is validity. An inferentialist theory of meaning should offer an account of the meaning of "valid." If one tries to add a validity predicate to one's object language, however, one runs into problems like the v-Curry paradox. In previous work, I presented a validity predicate for a non-transitive logic that can adequately capture its own meta-inferences. Unfortunately, in that system, one cannot show of any inference that it is invalid. Here I extend the system so that it can capture invalidities

    A stability criterion for systems with neutrally stable modes and deadzone nonlinearities

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    Stability analysis is considered for feedback interconnections of deadzone nonlinearities with linear systems that has a neutrally stable mode. Such systems do not have a unique equilibrium point and the standard techniques from passivity and Lyapunov theory cannot be applied. A stability criterion that generalizes the Popov criterion for this class of systems is derived in this report and several examples will prove its applicability
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