574 research outputs found
Hierarchies of modal and temporal logics with reference pointers
. We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: "point of reference --- reference pointer" which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. The universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and strong completeness theorem is proved for them and extended to some classes of their extensions. Key words: Modal and Temporal Logics, Reference Pointers, Expressi..
A hybrid logic for XML reference constraints
XML emerged as the (meta) mark-up language for representing, exchanging, and storing semistructured data. The structure of an XML document may be specified either through DTD (Document Type Definition) language or through the specific language XML Schema. While the expressiveness of XML Schema allows one to specify both the structure and constraints for XML documents, DTD does not allow the specification of integrity constraints for XML documents. On the other side, DTD has a very compact notation opposed to the complex notation and syntax of XML Schema. Thus, it becomes important to consider the issue of how to express further constraints on DTD-based XML documents, still retaining the simplicity and succinctness of DTDs. According to this scenario, in this paper we focus on a (as much as possible) simple logic, named XHyb, expressive enough to allow the specification of the most common integrity and reference constraints in XML documents. In particular, we focus on constraints on ID and IDREF(S) attributes, which are the common way of logically connecting parts of XML documents, besides the usual parent-child relationship of XML elements. Differently from other previously proposed hybrid logics, in XHyb IDREF(S) attributes are explicitly expressible by means of suitable syntactical constructors. Moreover, we propose a refinement of the usual graph representation of XML documents in order to represent XML documents in a formal and intuitive way without flatten accessibility through IDREF(S) to the usual parent-child relationship. Model checking algorithms are then proposed, to verify that a given XML document satisfies the considered constraints
Crossing the Undecidability Border with Extensions of Propositional Neighborhood Logic over Natural Numbers
Propositional Neighborhood Logic (PNL) is an interval temporal logic featuring two modalities corresponding to the relations of right and left neighborhood between two intervals on a linear order (in terms of Allen's relations, meets and met by). Recently, it has been shown that PNL interpreted over several classes of linear orders, including natural numbers, is decidable (NEXPTIME-complete) and that some of its natural extensions preserve decidability. Most notably, this is the case with PNL over natural numbers extended with a limited form of metric constraints and with the future fragment of PNL extended with modal operators corresponding to Allen's relations begins, begun by, and before. This paper aims at demonstrating that PNL and its metric version MPNL, interpreted over natural numbers, are indeed very close to the border with undecidability, and even relatively weak extensions of them become undecidable. In particular, we show that (i) the addition of binders on integer variables ranging over interval lengths makes the resulting hybrid extension of MPNL undecidable, and (ii) a very weak first-order extension of the future fragment of PNL, obtained by replacing proposition letters by a restricted subclass of first-order formulae where only one variable is allowed, is undecidable (in contrast with the decidability of similar first-order extensions of point-based temporal logics)
Synchronous Online Philosophy Courses: An Experiment in Progress
There are two main ways to teach a course online: synchronously or asynchronously. In an asynchronous course, students can log on at their convenience and do the course work. In a synchronous course, there is a requirement that all students be online at specific times, to allow for a shared course environment. In this article, the author discusses the strengths and weaknesses of synchronous online learning for the teaching of undergraduate philosophy courses. The author discusses specific strategies and technologies he uses in the teaching of online philosophy courses. In particular, the author discusses how he uses videoconferencing to create a classroom-like environment in an online class
Hybrid Languages and Temporal Logic
Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages. Although developed in interesting ways by Robert Bull, and by the Sofia school (notably, George Gargov, Valentin Goranko, Solomon Passy and Tinko Tinchev) the method remains little known. In our view this has deprived temporal logic of a valuable tool.
The aim of the paper is to explain why hybridization is useful in temporal logic. We make two major points, the first technical, the second conceptual. First, we show that hybridization gives rise to well-behaved logics that exhibit an interesting synergy between modal and classical ideas. This synergy, obvious for hybrid languages with full first-order expressive strength, is demonstrated for a weaker local language capable of defining the Until operator, we provide a minimal axiomatization, and show that in a wide range of temporally interesting cases extended completeness results can be obtained automatically. Second, we argue that the idea of sorted atomic symbols which underpins the hybrid enterprise can be developed further. To illustrate this, we discuss the advantages and disadvantages of a simple hybrid language which can quantify over paths
Exploring the landscapes of "computing": digital, neuromorphic, unconventional -- and beyond
The acceleration race of digital computing technologies seems to be steering
toward impasses -- technological, economical and environmental -- a condition
that has spurred research efforts in alternative, "neuromorphic" (brain-like)
computing technologies. Furthermore, since decades the idea of exploiting
nonlinear physical phenomena "directly" for non-digital computing has been
explored under names like "unconventional computing", "natural computing",
"physical computing", or "in-materio computing". This has been taking place in
niches which are small compared to other sectors of computer science. In this
paper I stake out the grounds of how a general concept of "computing" can be
developed which comprises digital, neuromorphic, unconventional and possible
future "computing" paradigms. The main contribution of this paper is a
wide-scope survey of existing formal conceptualizations of "computing". The
survey inspects approaches rooted in three different kinds of background
mathematics: discrete-symbolic formalisms, probabilistic modeling, and
dynamical-systems oriented views. It turns out that different choices of
background mathematics lead to decisively different understandings of what
"computing" is. Across all of this diversity, a unifying coordinate system for
theorizing about "computing" can be distilled. Within these coordinates I
locate anchor points for a foundational formal theory of a future
computing-engineering discipline that includes, but will reach beyond, digital
and neuromorphic computing.Comment: An extended and carefully revised version of this manuscript has now
(March 2021) been published as "Toward a generalized theory comprising
digital, neuromorphic, and unconventional computing" in the new open-access
journal Neuromorphic Computing and Engineerin
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