39,945 research outputs found

    Dialectica Categories for the Lambek Calculus

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    We revisit the old work of de Paiva on the models of the Lambek Calculus in dialectica models making sure that the syntactic details that were sketchy on the first version got completed and verified. We extend the Lambek Calculus with a \kappa modality, inspired by Yetter's work, which makes the calculus commutative. Then we add the of-course modality !, as Girard did, to re-introduce weakening and contraction for all formulas and get back the full power of intuitionistic and classical logic. We also present the categorical semantics, proved sound and complete. Finally we show the traditional properties of type systems, like subject reduction, the Church-Rosser theorem and normalization for the calculi of extended modalities, which we did not have before

    Unified Theory of Relativistic Identification of Information in a Systems Age: Proposed Convergence of Unique Identification with Syntax and Semantics through Internet Protocol version 6

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    Unique identification of objects are helpful to the decision making process in many domains. Decisions, however, are often based on information that takes into account multiple factors. Physical objects and their unique identification may be one of many factors. In real-world scenarios, increasingly decisions are based on collective information gathered from multiple sources (or systems) and then combined to a higher level domain that may trigger a decision or action. Currently, we do not have a globally unique mechanism to identify information derived from data originating from objects and processes. Unique identification of information, hence, is an open question. In addition, information, to be of value, must be related to the context of the process. In general, contextual information is of greater relevance in the decision making process or in decision support systems. In this working paper, I shall refer to such information as decisionable information. The suggestion here is to utilize the vast potential of internet protocol version six (IPv6) to uniquely identify not only objects and processes but also relationships (semantics) and interfaces (sensors). Convergence of identification of diverse entities using the globally agreed structure of IPv6 offers the potential to identify 3.4x10[subscript 38] instances based on the fact that the 128-bit IPv6 structure can support 3.4x10[subscript 38] unique addresses. It is not necessary that all instances must be connected to the internet or routed or transmitted simply because an IP addressing scheme is suggested. This is a means for identification that will be globally unique and offers the potential to be connected or routed via the internet. In this working paper, scenarios offer [1] new revenue potential from data routing (P2P traffic track and trace) for telecommunication industries, [2] potential for use in healthcare and biomedical community, [3] scope of use in the semantic web structure by transitioning URIs used in RDF, [4] applications involving thousands of mobile ad hoc sensors (MANET) that demand dynamic adaptive auto-reconfiguration. This paper presents a confluence of ideas

    Changing a semantics: opportunism or courage?

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    The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

    Subtyping for Hierarchical, Reconfigurable Petri Nets

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    Hierarchical Petri nets allow a more abstract view and reconfigurable Petri nets model dynamic structural adaptation. In this contribution we present the combination of reconfigurable Petri nets and hierarchical Petri nets yielding hierarchical structure for reconfigurable Petri nets. Hierarchies are established by substituting transitions by subnets. These subnets are themselves reconfigurable, so they are supplied with their own set of rules. Moreover, global rules that can be applied in all of the net, are provided

    The Landscape of Salesforce for Nonprofits: A Report on the Current Marketplace for Apps

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    Do you use Salesforce as a Constituent Relationship Management database at your organization, or are you considering it? Since it launched in 1999, more than 20,000 nonprofits have employed the cloud-based system, which is made available to them for free through the philanthropic Salesforce Foundation. What's the catch? Making such a powerful system work for the particular needs of a nonprofit isn't always straightforward. This report can tell you everything you need to know.What's in it? To learn more about the benefits and drawbacks of Salesforce, we interviewed nine prominent consultants specializing in implementing Salesforce for nonprofits along with several members of the Salesforce.com Foundation about what the platform does well, and what you'll want to add to it to suit your needs. We evaluated some of the constituent management packages built on top of Salesforce, including the Salesforce Foundation's Nonprofit Starter Pack, which is aimed at turning the sales automation platform into a tool for nonprofits. We also took a look at the universe of add-ons to the base Salesforce platform -- called "apps" because of Salesforce's online marketplace, the App Exchange -- to find out which might be useful to support a nonprofit's processes.The goal for this report was to break down misconceptions about the tool and to collect disparate information in one place to help you make informed decisions. Whether you're already using Salesforce, are thinking about adopting it, or have yet to even consider it, there's information here for you.What's more, we've included a directory of consultants or firms with experience working with nonprofits to implement Salesforce and the additional App Exchange modules that we cover in this report to make it easier for you to find the help you'll need

    From images via symbols to contexts: using augmented reality for interactive model acquisition

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    Systems that perform in real environments need to bind the internal state to externally perceived objects, events, or complete scenes. How to learn this correspondence has been a long standing problem in computer vision as well as artificial intelligence. Augmented Reality provides an interesting perspective on this problem because a human user can directly relate displayed system results to real environments. In the following we present a system that is able to bootstrap internal models from user-system interactions. Starting from pictorial representations it learns symbolic object labels that provide the basis for storing observed episodes. In a second step, more complex relational information is extracted from stored episodes that enables the system to react on specific scene contexts

    State space c-reductions for concurrent systems in rewriting logic

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    We present c-reductions, a state space reduction technique. The rough idea is to exploit some equivalence relation on states (possibly capturing system regularities) that preserves behavioral properties, and explore the induced quotient system. This is done by means of a canonizer function, which maps each state into a (non necessarily unique) canonical representative of its equivalence class. The approach exploits the expressiveness of rewriting logic and its realization in Maude to enjoy several advantages over similar approaches: exibility and simplicity in the definition of the reductions (supporting not only traditional symmetry reductions, but also name reuse and name abstraction); reasoning support for checking and proving correctness of the reductions; and automatization of the reduction infrastructure via Maude's meta-programming features. The approach has been validated over a set of representative case studies, exhibiting comparable results with respect to other tools

    Root system chip-firing I: Interval-firing

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    Jim Propp recently introduced a variant of chip-firing on a line where the chips are given distinct integer labels. Hopkins, McConville, and Propp showed that this process is confluent from some (but not all) initial configurations of chips. We recast their set-up in terms of root systems: labeled chip-firing can be seen as a root-firing process which allows the moves λλ+α\lambda \to \lambda + \alpha for αΦ+\alpha\in \Phi^{+} whenever λ,α=0\langle\lambda,\alpha^\vee\rangle = 0, where Φ+\Phi^{+} is the set of positive roots of a root system of Type A and λ\lambda is a weight of this root system. We are thus motivated to study the exact same root-firing process for an arbitrary root system. Actually, this central root-firing process is the subject of a sequel to this paper. In the present paper, we instead study the interval root-firing processes determined by λλ+α\lambda \to \lambda + \alpha for αΦ+\alpha\in \Phi^{+} whenever λ,α[k1,k1]\langle\lambda,\alpha^\vee\rangle \in [-k-1,k-1] or λ,α[k,k1]\langle\lambda,\alpha^\vee\rangle \in [-k,k-1], for any k0k \geq 0. We prove that these interval-firing processes are always confluent, from any initial weight. We also show that there is a natural way to consistently label the stable points of these interval-firing processes across all values of kk so that the number of weights with given stabilization is a polynomial in kk. We conjecture that these Ehrhart-like polynomials have nonnegative integer coefficients.Comment: 54 pages, 12 figures, 2 tables; v2: major revisions to improve exposition; v3: to appear in Mathematische Zeitschrift (Math. Z.
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