A logic for n-dimensional hierarchical refinement

Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high level states into inner sub-states, and of their transitions into inner sub-transitions is common refinement procedure adopted in a number of specification formalisms. This paper introduces a hybrid modal logic for k-layered transition systems, its first-order standard translation, a notion of bisimulation, and a modal invariance result. Layered and hierarchical notions of refinement are also discussed in this setting.Comment: In Proceedings Refine'15, arXiv:1606.0134

Institutional complementarities and gender diversity on boards: a configurational approach

Manuscript Type: Empirical Research Question/Issue: To address the lack of a complementarities-based approach in studies of board diversity, this paper seeks to understandwhether and howcertain country-level factors are causally and jointly related towomen on boards and the nature of their complementarities (are they synergic or substitutes?). Moreover, we intend to learn more about the adoption/diffusion of board gender quotas, by taking into account their role in the existing national configurations (whether they are necessary and/or sufficient conditions). Research Findings/Insights: Using fs/QCA, our findings reveal a particular configuration of country-level conditions that supports the existence of a joint causal relation between given institutional arrangements. Furthermore, we find that board gender quota legislation is not a sufficient condition on its own to achieve a higher number of women on boards. Such evidence suggests that its diffusion across countries could be the result of institutional isomorphismor social legitimacy more than to rational reasons. Theoretical/Academic Implications: For scholars, our paper refines and expands insights from the extant comparative corporate governance literature. By finding support for the “bundled” or jointly causal nature of given institutional factors,we open a window for further research that investigates board-level phenomena in a complementarities-based perspective. Practitioner/Policy Implications: For policymakers, this study provides some insights that could better drive their choice about which mix of policies is necessary to improve female representation on boards, and especially in which institutional areas they should be implemented. It is particularly relevant, because once gender quotas are endorsed at board level, they could have ambiguous effects on firm performance and corporate governance

Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning

Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, the satisfaction of which is parametrized by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided.Comment: 36 page

Norms and Law: Putting the Horse Before the Cart

Law and society scholars have long been fascinated with the interplay of formal legal and informal extralegal procedures. Unfortunately, the fascination has been accompanied by imprecision, and scholars have conceptually conflated two very different mechanisms that extralegally resolve disputes. One set of mechanisms might be described as the shadow of the law, made famous by seminal works by Professors Stewart Macaulay and Marc Galanter, in which social coercion and custom have force because formal legal rights are credible and reasonably defined. The other set of mechanisms, recently explored by economic historians and legal institutionalists, might be described as order without law, borrowing from Professor Robert Ellickson\u27s famous work.1 In this second mechanism, extralegal mechanisms—whether organized shunning, violence, or social disdain—replace legal coercion to bring social order and are an alternative to, not an extension of, formal legal sanctions. One victim of conflating these mechanisms has been our understanding of industry-wide systems of private law and private adjudication, or private legal systems. Recent examinations of private legal systems have chiefly understood those systems as efforts to economize on litigation and dispute-resolution costs, but private legal systems are better understood as mechanisms that economize on enforcement costs. This is not a small mischaracterization. Instead, it reveals a deep misunderstanding of when and why private enforcement systems arise in a modern economy. This Essay provides a taxonomy for the various mechanisms of private ordering. These assorted mechanisms, despite their important differences, have been conflated in large part because there has been a poor understanding of the particular institutional efficiencies and costs of the alternative systems. Specifically, enforcement costs have often been inadequately distinguished from procedural or disputeresolution costs, and this imprecision has produced theories that inaccurately predict when private ordering will thrive and when the costs of private ordering overwhelm corresponding efficiencies. The implications for institutional theory are significant, as confusion in the literature has led to overappreciation of private ordering, underappreciation of social institutions, and Panglossian attitudes toward both lawlessness and legal development

Refinement by interpretation in {\pi}-institutions

The paper discusses the role of interpretations, understood as multifunctions that preserve and reflect logical consequence, as refinement witnesses in the general setting of pi-institutions. This leads to a smooth generalization of the refinement-by-interpretation approach, recently introduced by the authors in more specific contexts. As a second, yet related contribution a basis is provided to build up a refinement calculus of structured specifications in and across arbitrary pi-institutions.Comment: In Proceedings Refine 2011, arXiv:1106.348

An Institutional Framework for Heterogeneous Formal Development in UML

We present a framework for formal software development with UML. In contrast to previous approaches that equip UML with a formal semantics, we follow an institution based heterogeneous approach. This can express suitable formal semantics of the different UML diagram types directly, without the need to map everything to one specific formalism (let it be first-order logic or graph grammars). We show how different aspects of the formal development process can be coherently formalised, ranging from requirements over design and Hoare-style conditions on code to the implementation itself. The framework can be used to verify consistency of different UML diagrams both horizontally (e.g., consistency among various requirements) as well as vertically (e.g., correctness of design or implementation w.r.t. the requirements)