8 research outputs found

    A semantics and a logic for Fuzzy Arden Syntax

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    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 CiĂȘncia e a Tecnologia, within projects POCI-01-0145-FEDER-030947and POCI-01-0145-FEDER-02994

    Demonic Kleene Algebra

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    Nous rappelons d’abord le concept d’algĂšbre de Kleene avec domaine (AKD). Puis, nous expliquons comment utiliser les opĂ©rateurs des AKD pour dĂ©finir un ordre partiel appelĂ© raffinement dĂ©moniaque ainsi que d’autres opĂ©rateurs dĂ©moniaques (plusieurs de ces dĂ©finitions proviennent de la littĂ©rature). Nous cherchons Ă  comprendre comment se comportent les AKD munies des opĂ©rateurs dĂ©moniaques quand on exclut les opĂ©rateurs angĂ©liques usuels. C’est ainsi que les propriĂ©tĂ©s de ces opĂ©rateurs dĂ©moniaques nous servent de base pour axiomatiser une algĂšbre que nous appelons AlgĂšbre dĂ©moniaque avec domaine et opĂ©rateur t-conditionnel (ADD-[opĂ©rateur t-conditionnel]). Les lois des ADD-[opĂ©rateur t-conditionnel] qui ne concernent pas l’opĂ©rateur de domaine correspondent Ă  celles prĂ©sentĂ©es dans l’article Laws of programming par Hoare et al. publiĂ© dans la revue Communications of the ACM en 1987. Ensuite, nous Ă©tudions les liens entre les ADD-[opĂ©rateur t-conditionnel] et les AKD munies des opĂ©rateurs dĂ©moniaques. La question est de savoir si ces structures sont isomorphes. Nous dĂ©montrons que ce n’est pas le cas en gĂ©nĂ©ral et nous caractĂ©risons celles qui le sont. En effet, nous montrons qu’une AKD peut ĂȘtre transformĂ©e en une ADD-[opĂ©rateur t-conditionnel] qui peut ĂȘtre transformĂ©e Ă  son tour en l’AKD de dĂ©part. Puis, nous prĂ©sentons les conditions nĂ©cessaires et suffisantes pour qu’une ADD-[opĂ©rateur t-conditionnel] puisse ĂȘtre transformĂ©e en une AKD qui peut ĂȘtre transformĂ©e Ă  nouveau en l’ADD-[opĂ©rateur t-conditionnel] de dĂ©part. Les conditions nĂ©cessaires et suffisantes mentionnĂ©es prĂ©cĂ©demment font intervenir un nouveau concept, celui de dĂ©composition. Dans un contexte dĂ©moniaque, il est difficile de distinguer des transitions qui, Ă  partir d’un mĂȘme Ă©tat, mĂšnent Ă  des Ă©tats diffĂ©rents. Le concept de dĂ©composition permet d’y arriver simplement. Nous prĂ©sentons sa dĂ©finition ainsi que plusieurs de ses propriĂ©tĂ©s.We first recall the concept of Kleene algebra with domain (KAD). Then we explain how to use the operators of KAD to define a demonic refinement ordering and demonic operators (many of these definitions come from the literature). We want to know how do KADs with the demonic operators but without the usual angelic ones behave. Then, taking the properties of the KAD-based demonic operators as a guideline, we axiomatise an algebra that we call Demonic algebra with domain and t-conditional (DAD-[opĂ©rateur t-conditionnel]). The laws of DAD-[opĂ©rateur t-conditionnel] not concerning the domain operator agree with those given in the 1987 Communications of the ACM paper Laws of programming by Hoare et al. Then, we investigate the relationship between DAD-[opĂ©rateur t-conditionnel] and KAD-based demonic algebras. The question is whether every DAD-[opĂ©rateur t-conditionnel] is isomorphic to a KAD-based demonic algebra. We show that it is not the case in general. However, we characterise those that are. Indeed, we demonstrate that a KAD can be transformed into a DAD-[opĂ©rateur t-conditionnel] which can be transformed back into the initial KAD. We also establish necessary and sufficient conditions for which a DAD-[opĂ©rateur t-conditionnel] can be transformed into a KAD which can be transformed back into the initial DAD-[opĂ©rateur t-conditionnel]. Finally, we define the concept of decomposition. This notion is involved in the necessary and sufficient conditions previously mentioned. In a demonic context, it is difficult to distinguish between transitions that, from a given state, go to different states. The concept of decomposition enables to do it easily. We present its definition together with some of its properties

    Monotone predicate transformers as Up-closed multirelations

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    In the study of semantic models for computations two independent views predominate: relational models and predicate transformer semantics. Recently the traditional relational view of computations as binary relations between states has been generalised to multirelations between states and properties allowing the simultaneous treatment of angelic and demonic nondeterminism. In this paper the two-level nature of multirelations is exploited to provide a factorisation of up-closed multirelations which clarifies exactly how multirelations model nondeterminism. Moreover, monotone predicate transformers are, in the precise sense of duality, up-closed multirelations. As such they are shown to provide a notion of effectivity of a specification for achieving a given postcondition. © Springer-Verlag Berlin Heidelberg 2006.Conference Pape

    Algebraic Verification of Probabilistic and Concurrent Systems

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    This thesis provides an algebraic modelling and verification of probabilistic concurrent systems in the style of Kleene algebra. Without concurrency, it is shown that the equational theory of continuous probabilistic Kleene algebra is complete with respect to an automata model under standard simulation equivalence. This yields a minimisation-based decision procedure for the algebra. Without probability, an event structure model of Hoare et al.'s concurrent Kleene algebra is constructed. These two algebras are then ``merged" to provide probabilistic concurrent Kleene algebra which is used to discover and prove development rules for probabilistic concurrent systems (e.g. rely/guarantee calculus). Soundness of the new algebra is ensured by models based on probabilistic automata (interleaving) and probabilistic bundle event structures (true concurrency) quotiented with the respective simulation equivalences. Lastly, event structures with implicit probabilities are constructed to provide a state based model for the soundness of the probabilistic rely/guarantee rules

    Collected Papers (on various scientific topics), Volume XII

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    This twelfth volume of Collected Papers includes 86 papers comprising 976 pages on Neutrosophics Theory and Applications, published between 2013-2021 in the international journal and book series “Neutrosophic Sets and Systems” by the author alone or in collaboration with the following 112 co-authors (alphabetically ordered) from 21 countries: Abdel Nasser H. Zaied, Muhammad Akram, Bobin Albert, S. A. Alblowi, S. Anitha, Guennoun Asmae, Assia Bakali, Ayman M. Manie, Abdul Sami Awan, Azeddine Elhassouny, Erick GonzĂĄlez-Caballero, D. Dafik, Mithun Datta, Arindam Dey, Mamouni Dhar, Christopher Dyer, Nur Ain Ebas, Mohamed Eisa, Ahmed K. Essa, Faruk Karaaslan, JoĂŁo Alcione Sganderla Figueiredo, Jorge Fernando Goyes GarcĂ­a, N. Ramila Gandhi, Sudipta Gayen, Gustavo Alvarez GĂłmez, Sharon Dinarza Álvarez GĂłmez, Haitham A. El-Ghareeb, Hamiden Abd El-Wahed Khalifa, Masooma Raza Hashmi, Ibrahim M. Hezam, German Acurio Hidalgo, Le Hoang Son, R. Jahir Hussain, S. Satham Hussain, Ali Hussein Mahmood Al-Obaidi, Hays Hatem Imran, Nabeela Ishfaq, Saeid Jafari, R. Jansi, V. Jeyanthi, M. Jeyaraman, Sripati Jha, Jun Ye, W.B. Vasantha Kandasamy, Abdullah Kargın, J. Kavikumar, Kawther Fawzi Hamza Alhasan, Huda E. Khalid, Neha Andalleb Khalid, Mohsin Khalid, Madad Khan, D. Koley, Valeri Kroumov, Manoranjan Kumar Singh, Pavan Kumar, Prem Kumar Singh, Ranjan Kumar, Malayalan Lathamaheswari, A.N. Mangayarkkarasi, Carlos Rosero MartĂ­nez, Marvelio Alfaro Matos, Mai Mohamed, Nivetha Martin, Mohamed Abdel-Basset, Mohamed Talea, K. Mohana, Muhammad Irfan Ahamad, Rana Muhammad Zulqarnain, Muhammad Riaz, Muhammad Saeed, Muhammad Saqlain, Muhammad Shabir, Muhammad Zeeshan, Anjan Mukherjee, Mumtaz Ali, Deivanayagampillai Nagarajan, Iqra Nawaz, Munazza Naz, Roan Thi Ngan, Necati Olgun, Rodolfo GonzĂĄlez Ortega, P. Pandiammal, I. Pradeepa, R. Princy, Marcos David Oviedo RodrĂ­guez, JesĂșs Estupiñån Ricardo, A. Rohini, Sabu Sebastian, Abhijit Saha, Mehmet Șahin, Said Broumi, Saima Anis, A.A. Salama, Ganeshsree Selvachandran, Seyed Ahmad Edalatpanah, Sajana Shaik, Soufiane Idbrahim, S. Sowndrarajan, Mohamed Talea, Ruipu Tan, Chalapathi Tekuri, Selçuk Topal, S. P. Tiwari, Vakkas Uluçay, Maikel Leyva VĂĄzquez, Chinnadurai Veerappan, M. Venkatachalam, Luige Vlădăreanu, ƞtefan VlăduĆŁescu, Young Bae Jun, Wadei F. Al-Omeri, Xiao Long Xin.‬‬‬‬‬
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