235 research outputs found
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
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
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)
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
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