A semantics and a logic for Fuzzy Arden Syntax

Fuzzy programming languages, such as the Fuzzy Arden Syntax (FAS), are used to describe behaviours which evolve in a fuzzy way and thus cannot be characterized neither by a Boolean outcome nor by a probability distribution. This paper introduces a semantics for FAS, focusing on the weighted parallel interpretation of its conditional statement. The proposed construction is based on the notion of a fuzzy multirelation which associates with each state in a program a fuzzy set of weighted possible evolutions. The latter is parametric on a residuated lattice which models the underlying semantic ‘truth space’. Finally, a family of dynamic logics, equally parametric on the residuated lattice, is introduced to reason about FAS programsThis work was founded by the ERDF — European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation — COMPETE 2020 Pro gramme and by National Funds through the Portuguese funding agency, FCT — Fundação para a Ciência e a Tecnologia, within projects POCI-01-0145-FEDER-030947and POCI-01-0145-FEDER-02994

Subjects, Models, Languages, Transformations

Discussions about model-driven approaches tend to be hampered by terminological confusion. This is at least partially caused by a lack of formal precision in defining the basic concepts, including that of "model" and "thing being modelled" - which we call subject in this paper. We propose a minimal criterion that a model should fulfill: essentially, it should come equipped with a clear and unambiguous membership test; in other words, a notion of which subjects it models. We then go on to discuss a certain class of models of models that we call languages, which apart from defining their own membership test also determine membership of their members. Finally, we introduce transformations on each of these layers: a subject transformation is essentially a pair of subjects, a model transformation is both a pair of models and a model of pairs (namely, subject transformations), and a language transformation is both a pair of languages and a language of model transformations. We argue that our framework has the benefits of formal precision (there can be no doubt about whether something satifies our criteria for being a model, a language or a transformation) and minimality (it is hard to imagine a case of modelling or transformation not having the characterstics that we propose)

Map Calculus in GIS: a proposal and demonstration

This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin's (1990) Map Algebra, the term 'Map Calculus' is used for this new representation. In Map Calculus, GIS layers are stored as functions, and new layers can be created by combinations of other functions. This paper explains the principles of Map Calculus and demonstrates the creation of function-based layers and their supporting management mechanism. The proposal is based on Church's (1941) Lambda Calculus and elements of functional computer languages (such as Lisp or Scheme)