Well-orders in the transfinite Japaridze algebra

This paper studies the transfinite propositional provability logics \glp_\Lambda and their corresponding algebras. These logics have for each ordinal $\xi< \Lambda$ a modality \la \alpha \ra. We will focus on the closed fragment of \glp_\Lambda (i.e., where no propositional variables occur) and \emph{worms} therein. Worms are iterated consistency expressions of the form \la \xi_n\ra \ldots \la \xi_1 \ra \top. Beklemishev has defined well-orderings $<_\xi$ on worms whose modalities are all at least $\xi$ and presented a calculus to compute the respective order-types. In the current paper we present a generalization of the original $<_\xi$ orderings and provide a calculus for the corresponding generalized order-types $o_\xi$. Our calculus is based on so-called {\em hyperations} which are transfinite iterations of normal functions. Finally, we give two different characterizations of those sequences of ordinals which are of the form \la {\formerOmega}_\xi (A) \ra_{\xi \in \ord} for some worm $A$. One of these characterizations is in terms of a second kind of transfinite iteration called {\em cohyperation.}Comment: Corrected a minor but confusing omission in the relation between Veblen progressions and hyperation

Theory of constructive semigroups with apartness -- foundations, development and practice

This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also draw attention to its possible applications in other (constructive) mathematics disciplines, in computer science, social sciences, economics, etc. Another important goal of this paper is to provide a clear, understandable picture of constructive semigroups with apartness in Bishop's style both to (classical) algebraists and the ones who apply algebraic knowledge

Bureaucratic routines and error management in algorithmic systems

This article discusses how an analogy between algorithms and bureaucratic decision-making could help conceptualize error management in algorithmic systems. It argues that a view of algorithms as irreflexive bureaucratic processes is insufficient as an account of errors in complex public sector contexts, where algorithms operate jointly with other organizational work practices. To conceptualize such contexts, the article proposes that algorithms could be viewed as analogous to work routines in bureaucratic organizations. Doing so helps clarify that algorithmic irreflexivity becomes problematic when the coordination of routine work around automation fails. Thus, also the challenges of error management come to concern the wider context of organized work. This argument is illustrated using known examples from the critical literature on algorithms. Finally, drawing on recent studies in routine dynamics, the article formulates empirical research directions on error management in algorithmic systems.This article discusses how an analogy between algorithms and bureaucratic decision-making could help conceptualize error management in algorithmic systems. It argues that a view of algorithms as irreflexive bureaucratic processes is insufficient as an account of errors in complex public sector contexts, where algorithms operate jointly with other organizational work practices. To conceptualize such contexts, the article proposes that algorithms could be viewed as analogous to more traditional work routines in bureaucratic organizations. Doing so helps clarify that algorithmic irreflexivity becomes problematic when the coordination of routine work around automation fails. Thus, also the challenges of error management come to concern the wider context of organized work. This argument is illustrated using known examples from the critical literature on algorithms. Finally, drawing on recent studies in routine dynamics, the article formulates empirical research directions on error management in algorithmic systems.Peer reviewe

Security Policy Consistency

With the advent of wide security platforms able to express simultaneously all the policies comprising an organization's global security policy, the problem of inconsistencies within security policies become harder and more relevant. We have defined a tool based on the CHR language which is able to detect several types of inconsistencies within and between security policies and other specifications, namely workflow specifications. Although the problem of security conflicts has been addressed by several authors, to our knowledge none has addressed the general problem of security inconsistencies, on its several definitions and target specifications.Comment: To appear in the first CL2000 workshop on Rule-Based Constraint Reasoning and Programmin

Automated reasoning for proving non-orderability of groups

We demonstrate how a generic automated theorem prover can be applied to establish the non-orderability of groups. Our approach incorporates various tools such as positive cones, torsions, generalised torsions and cofinal elements.Comment: 35 pages, 0 figure

Conditional control of equivalence and the relations different and opposite : a behavior analytic model of complex verbal behavior

Behavior analytic approaches to the explanation of verbal behavior have been criticized because of difficulty explaining verbal productivity---the ability to make novel verbalizations which are in some way appropriate to the context. Match to sample procedures have resulted in the formation of equivalence classes which allow productive responding to untrained stimulus combinations. The central hypothesis of this study is that arbitrarily applicable relations other than equivalence can come to control human responding in ways which are productive. A second-order conditional discrimination procedure was used to establish control over sample-comparison selections where samples and comparisons were arbitrary visual stimuli. Pretraining with non-arbitrary stimuli gave second-order conditional stimuli the function of signaling which relation—same, different, or opposite---was to control sample-comparison discriminations. These pretrained second-order conditional stimuli were used to establish networks of relations between arbitrary visual stimuli. It was predicted that the network of relations could come to control untrained responding to probes which presented second-order conditional stimuli, samples, and comparisons in novel arrangements. The predicted pattern of responding was derived from formal logic