In Computer Science stepwise refinement of algebraic specifications is a well-known formal methodology for rigorous program development. This paper illustrates how techniques from Algebraic Logic, in particular that of interpretation, understood as a multifunction that preserves and reflects logical consequence, capture a number of relevant transformations in the context of software design, reuse, and adaptatio...
Modal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for naming states in models. Actually, hybrid logics have recently regained interest, resulting in a number of new results and techn...
Systemic sclerosis (SSc) is a systemic disease, characterized by fibrosis and vasculopathy, with variable internal organ involvement. Skin is very often involved, namely digital ulcers (DU), seldom treatment resistant, responsible for important functional limitation. The DU can evolve from sclerodactily with superficial ulcers, isquemic lesions, deep necrosis, gangrene, loss of tissue, and consequently, to fing...
Extended version including all proofs ; Modal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for naming states in models. Actually, hybrid logics have recently regained interest, resul...
The paper discusses the role of interpretations, understood as multifunctions that preserve and reflect logical consequence, as refinement witnesses in the general setting of π-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 ref...
This paper introduces a rigorous methodology for requirements specification of systems that react to external stimulus by evolving through different operational modes. In each mode different functionalities are provided. Starting from a classical state-machine specification, the envisaged methodology interprets each state as a different mode of operation endowed with an algebraic specification of the correspond...
A large number of computational processes can suitably be described as a combination of construction, i.e. algebraic, and observation, i.e. coalgebraic, structures. This paper suggests dialgebras as a generic model in which such structures can be combined and proposes a small calculus of dialgebras including a wrapping combinator and se- quential composition. To take good care of invariants in software design, ...
The paper formulates HEQ, an institution for hybrid equational logic to provide a uniform setting to express and reasoning about different sorts of properties of complex software. It is also shown how, through the definition of a suitable comorphism to FOL, this can be integrated in Hets, providing suitable tool support for teaching and re- search. The whole exercise was motivated by the need to unify, in a sin...
This paper introduces a rigorous methodology for requirements specification of systems that react to external stimulus and consequently evolve through different operational modes, providing, in each of them, different functionalities. The proposed methodology proceeds in three stages, enriching a simple state- machine with local algebraic specifications. It resorts to an expressive variant of hybrid logic which...
Three amendments (iron oxides, Fe; organic matter, MO; calcium phosphate, PCa) were applied to a naturally contaminated soil with arsenic and their effect on the growth of tomato plants and Italian parsley was studied. The results indicate differences associated with the availability of arsenic in the soil in the presence of amendments: Fe had no influence on arsenic availability compared with the unamended soi...
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