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

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

Two-ballot versus plurality rule: an empirical investigation on the number of candidates

Duverger claimed more than 50 years ago that the number of candidates in elections should be a function of electoral rules. Both his “law” and “hypothesis” suggest the number of candidates vying for seats in elections to be tightly linked to characteristics of the electoral process such as its degree of proportionality and the presence of runoffs. Here we test the validity of Duverger’s claim using data from municipal elections in Brazil. Our study differs from others in the field in two important dimensions. First, by using municipal data we avoid the usual problems that plague statistical analysis using cross-country data. Secondly, we have a truly exogenous source of variation due to a change in electoral legislation introduced by the constitutional reform of 1988: simple plurality remained the rule only in municipalities with less than 200,000 voters, and a second-ballot became mandatory for the others above that threshold. This allows for a neat identification strategy using panel data. Our main finding is that elections with runoffs lure greater numbers of candidates in municipalities with sufficiently high levels of heterogeneity.Duverger's law, runoff, heterogeneity

Paraconsistent transition systems

Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such formalism: states evolve through two accessibility relations capturing weighted evidence of a transition or its absence, respectively. Their weights come from a specific residuated lattice. A category of these systems, and the corresponding algebra, is defined as providing a formal setting to model different application scenarios. One of them, dealing with the effect of quantum decoherence in quantum programs, is used for illustration purposes.publishe

Generalising KAT to verify weighted computations

Kleene algebra with tests (KAT) was introduced as an algebraic structure to model and reason about classic imperative programs, i.e. sequences of discrete transitions guarded by Boolean tests. This paper introduces two generalisations of this structure able to express programs as weighted transitions and tests with outcomes in non necessarily bivalent truth spaces: graded Kleene algebra with tests (GKAT) and a variant where tests are also idempotent (I-GKAT). In this context, and in analogy to Kozen's encoding of Propositional Hoare Logic (PHL) in KAT we discuss the encoding of a graded PHL in I-GKAT and of its while-free fragment in GKAT. Moreover, to establish semantics for these structures four new algebras are de ned: FSET (T ), FREL(K; T ) and FLANG(K; T ) over complete residuated lattices K and T , and M(n;A) over a GKAT or I-GKAT A. As a nal exercise, the paper discusses some program equivalence proofs in a graded context.POCI-01-0145-FEDER-03094, NORTE-01-0145-FEDER-000037. ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project POCI-01-0145-FEDER-030947. This paper is also a result of the project SmartEGOV, NORTE-01-0145-FEDER-000037. The second author is supported in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article 23, of the Decree-Law 57/2016, of August 29, changed by Portuguese Law 57/2017, of July 19, at CIDMA (Centro de Investigação e Desenvolvimento em Matemática e Aplicações) UID/MAT/04106/2019

Boilerplates for reconfigurable systems: a language and its semantics

Boilerplates are simplified, normative English texts,intended to capture software requirements in a controlled way. This paper proposes a pallet of boilerplates as a requirements modelling language for reconfigurable systems, i.e., systems structured in different modes of execution among which they can dynamically commute. The language semantics is given as an hybrid logic, in an institutional setting. The mild use made of the theory of institutions, which, to a large extent, may be hidden from the working software engineer, not only provides a rigorous and generic semantics, but also paves the way to tool-supported validation.FC