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

FLC or not FLC: the other side of vernalization

Vernalization is the promotion of the competence for flowering by long periods of low temperatures such as those typically experienced during winters. In Arabidopsis, the vernalization response is, to a large extent, mediated by the repression of the floral repressor FLC, and the stable epigenetic silencing of FLC after cold treatments is essential for vernalization. In addition to FLC, other vernalization targets exist in Arabidopsis. In grasses, vernalization seems to be entirely independent of FLC. Here, the current understanding of FLC-independent branches of the vernalization pathway in Arabidopsis and vernalization without FLC in grasses is discussed. This review focuses on the role of AGL19, AGL24, and the MAF genes in Arabidopsis. Interestingly, vernalization acts through related molecular machineries on distinct targets. In particular, protein complexes similar to Drosophila Polycomb Repressive Complex 2 play a prominent role in establishing an epigenetic cellular memory for cold-regulated expression states of AGL19 and FLC. Finally, the similar network topology of the apparently independently evolved vernalization pathways of grasses and Arabidopsis is discusse

Capturing Qubit decoherence through paraconsistent transition systems

This position paper builds on the authors’ previous work on paraconsistent transition systems to propose a modelling framework for quantum circuits with explicit representation of decoherence.The authors are grateful to V. Goranko for helpful insights. Work conducted within IBEX (PTDC/CCI-COM/4280/2021), a project funded by Fct, the Portuguese funding agency for Science and Technology

Behavioural and abstractor specifications revisited

In the area of algebraic specification there are two main approaches for defining observational abstraction: behavioural specifications use a notion of observational satisfaction for the axioms of a specification, whereas abstractor specifications define an abstraction from the standard semantics of a specification w.r.t. an observational equivalence relation between algebras. Earlier work by Bidoit, Hennicker, Wirsing has shown that in the case of first-order logic specifications both concepts coincide semantically under mild assumptions. Analogous results have been shown by Sannella and Hofmann for higher-order logic specifications and recently, by Hennicker and Madeira, for specifications of reactive systems using a dynamic logic with binders. In this paper, we bring these results into a common setting: we isolate a small set of characteristic principles to express the behaviour/abstractor equivalence and show that all three mentioned specification frameworks satisfy these principles and therefore their behaviour and abstractor specifications coincide semantically (under mild assumptions). As a new case we consider observational modal logic where observational satisfaction of Hennessy–Milner logic formulae is defined “up to” silent transitions and observational abstraction is defined by weak bisimulation. We show that in this case the behaviour/abstractor equivalence can only be obtained, if we restrict models to weakly deterministic labelled transition systems.publishe

Applying abstract algebraic logic to classical automata theory : an exercise

In [4], Blok and Pigozzi have shown that a deterministic finite au- tomaton can be naturally viewed as a logical matrix. Following this idea, we use a generalisation of the matrix concept to deal with other kind of automata in the same algebraic perspective. We survey some classical concepts of automata theory using tools from algebraic logic. The novelty of this approach is the understand- ing of the classical automata theory within the standard abstract algebraic logic theory

A family of graded epistemic logics

Multi-Agent Epistemic Logic has been investigated in Computer Science [5] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [4] and also with a fuzzy semantics have been proposed [6,13]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [11,12]. The parameter in both methods is the same: an action lattice [9]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice)

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

Structured specification of paraconsistent transition systems

This paper sets the basis for a compositional and structured approach to the specification of paraconsistent transitions systems, framed as an institution. The latter and theirs logics were previously introduced in [CMB22] to deal with scenarios of inconsistency in which several requirements are on stake, either reinforcing or contradicting each other.EC -European Commission(PTDC/CCI-COM/4280/2021

A family of graded epistemic logics

Multi-Agent Epistemic Logic has been investigated in Computer Science [5] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [4] and also with a fuzzy semantics have been proposed [6,13]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [11,12]. The parameter in both methods is the same: an action lattice [9]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice)