A Formal Approach based on Fuzzy Logic for the Specification of Component-Based Interactive Systems

Formal methods are widely recognized as a powerful engineering method for the specification, simulation, development, and verification of distributed interactive systems. However, most formal methods rely on a two-valued logic, and are therefore limited to the axioms of that logic: a specification is valid or invalid, component behavior is realizable or not, safety properties hold or are violated, systems are available or unavailable. Especially when the problem domain entails uncertainty, impreciseness, and vagueness, the appliance of such methods becomes a challenging task. In order to overcome the limitations resulting from the strict modus operandi of formal methods, the main objective of this work is to relax the boolean notion of formal specifications by using fuzzy logic. The present approach is based on Focus theory, a model-based and strictly formal method for componentbased interactive systems. The contribution of this work is twofold: i) we introduce a specification technique based on fuzzy logic which can be used on top of Focus to develop formal specifications in a qualitative fashion; ii) we partially extend Focus theory to a fuzzy one which allows the specification of fuzzy components and fuzzy interactions. While the former provides a methodology for approximating I/O behaviors under imprecision, the latter enables to capture a more quantitative view of specification properties such as realizability.Comment: In Proceedings FESCA 2015, arXiv:1503.0437

Fuzzy hh-ideals of hemirings

A characterization of an $h$-hemiregular hemiring in terms of a fuzzy $h$-ideal is provided. Some properties of prime fuzzy $h$-ideals of $h$-hemiregular hemirings are investigated. It is proved that a fuzzy subset $\zeta$ of a hemiring $S$ is a prime fuzzy left (right) $h$-ideal of $S$ if and only if $\zeta$ is two-valued, $\zeta(0) = 1$, and the set of all $x$ in $S$ such that $\zeta(x) = 1$ is a prime (left) right $h$-ideal of $S$. Finally, the similar properties for maximal fuzzy left (right) $h$-ideals of hemirings are considered

Soft behaviour modelling of user communities

A soft modelling approach for describing behaviour in on-line user communities is introduced in this work. Behaviour models of individual users in dynamic virtual environments have been described in the literature in terms of timed transition automata; they have various drawbacks. Soft multi/agent behaviour automata are defined and proposed to describe multiple user behaviours and to recognise larger classes of user group histories, such as group histories which contain unexpected behaviours. The notion of deviation from the user community model allows defining a soft parsing process which assesses and evaluates the dynamic behaviour of a group of users interacting in virtual environments, such as e-learning and e-business platforms. The soft automaton model can describe virtually infinite sequences of actions due to multiple users and subject to temporal constraints. Soft measures assess a form of distance of observed behaviours by evaluating the amount of temporal deviation, additional or omitted actions contained in an observed history as well as actions performed by unexpected users. The proposed model allows the soft recognition of user group histories also when the observed actions only partially meet the given behaviour model constraints. This approach is more realistic for real-time user community support systems, concerning standard boolean model recognition, when more than one user model is potentially available, and the extent of deviation from community behaviour models can be used as a guide to generate the system support by anticipation, projection and other known techniques. Experiments based on logs from an e-learning platform and plan compilation of the soft multi-agent behaviour automaton show the expressiveness of the proposed model

Near-Optimal Scheduling for LTL with Future Discounting

We study the search problem for optimal schedulers for the linear temporal logic (LTL) with future discounting. The logic, introduced by Almagor, Boker and Kupferman, is a quantitative variant of LTL in which an event in the far future has only discounted contribution to a truth value (that is a real number in the unit interval [0, 1]). The precise problem we study---it naturally arises e.g. in search for a scheduler that recovers from an internal error state as soon as possible---is the following: given a Kripke frame, a formula and a number in [0, 1] called a margin, find a path of the Kripke frame that is optimal with respect to the formula up to the prescribed margin (a truly optimal path may not exist). We present an algorithm for the problem; it works even in the extended setting with propositional quality operators, a setting where (threshold) model-checking is known to be undecidable

Timed contract compliance under event timing uncertainty

Despite that many real-life contracts include time constraints, for instance explicitly specifying deadlines by when to perform actions, or for how long certain behaviour is prohibited, the literature formalising such notions is surprisingly sparse. Furthermore, one of the major challenges is that compliance is typically computed with respect to timed event traces with event timestamps assumed to be perfect. In this paper we present an approach for evaluating compliance under the effect of imperfect timing information, giving a semantics to analyse contract violation likelihood.peer-reviewe

Supervisory Control of Fuzzy Discrete Event Systems

In order to cope with situations in which a plant's dynamics are not precisely known, we consider the problem of supervisory control for a class of discrete event systems modelled by fuzzy automata. The behavior of such discrete event systems is described by fuzzy languages; the supervisors are event feedback and can disable only controllable events with any degree. The concept of discrete event system controllability is thus extended by incorporating fuzziness. In this new sense, we present a necessary and sufficient condition for a fuzzy language to be controllable. We also study the supremal controllable fuzzy sublanguage and the infimal controllable fuzzy superlanguage when a given pre-specified desired fuzzy language is uncontrollable. Our framework generalizes that of Ramadge-Wonham and reduces to Ramadge-Wonham framework when membership grades in all fuzzy languages must be either 0 or 1. The theoretical development is accompanied by illustrative numerical examples.Comment: 12 pages, 2 figure