New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic

Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of effect algebra/module that emerged in theoretical physics form the cornerstone. It is shown that under mild conditions on a category, its maps of the form X -> 1+1 carry such effect module structure, and can be used as predicates. Predicates are identified in many different situations, and capture for instance ordinary subsets, fuzzy predicates in a probabilistic setting, idempotents in a ring, and effects (positive elements below the unit) in a C*-algebra or Hilbert space. In quantum foundations the duality between states and effects plays an important role. It appears here in the form of an adjunction, where we use maps 1 -> X as states. For such a state s and a predicate p, the validity probability s |= p is defined, as an abstract Born rule. It captures many forms of (Boolean or probabilistic) validity known from the literature. Measurement from quantum mechanics is formalised categorically in terms of `instruments', using L\"uders rule in the quantum case. These instruments are special maps associated with predicates (more generally, with tests), which perform the act of measurement and may have a side-effect that disturbs the system under observation. This abstract description of side-effects is one of the main achievements of the current approach. It is shown that in the special case of C*-algebras, side-effect appear exclusively in the non-commutative case. Also, these instruments are used for test operators in a dynamic logic that can be used for reasoning about quantum programs/protocols. The paper describes four successive assumptions, towards a categorical axiomatisation of quantitative logic for probabilistic and quantum systems

A Calculus for Orchestration of Web Services

Service-oriented computing, an emerging paradigm for distributed computing based on the use of services, is calling for the development of tools and techniques to build safe and trustworthy systems, and to analyse their behaviour. Therefore, many researchers have proposed to use process calculi, a cornerstone of current foundational research on specification and analysis of concurrent, reactive, and distributed systems. In this paper, we follow this approach and introduce CWS, a process calculus expressly designed for specifying and combining service-oriented applications, while modelling their dynamic behaviour. We show that CWS can model all the phases of the life cycle of service-oriented applications, such as publication, discovery, negotiation, orchestration, deployment, reconfiguration and execution. We illustrate the specification style that CWS supports by means of a large case study from the automotive domain and a number of more specific examples drawn from it

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

Fuzzy decision making: A bibliometric-based review

Fuzzy decision-making consists in making decisions under complex and uncertain environments where the information can be assessed with fuzzy sets and systems. The aim of this study is to review the main contributions in this field by using a bibliometric approach. For doing so, the article uses a wide range of bibliometric indicators including the citations and the h-index. Moreover, it also uses the VOS viewer software in order to map the main trends in this area. The work considers the leading journals, articles, authors and institutions. The results indicate that the USA was the traditional leader in this field with the most significant researcher. However, during the last years, this field is receiving more attention by Asian authors that are starting to lead the field. This discipline has a strong potential and the expectations for the future is that it will continue to grow

Software Architecture Patterns for a Context-Processing Middleware Framework

International audienceUbiquitous applications are characterised by variations of their execution context. Their correct operation requires some continual adaptations based on the observation of their execution context. The design and the implementation of these observation policies is then the cornerstone of any ubiquitous applications. In this article, we propose COSMOS which is a framework for the principled specification and composition of context observation policies. With COSMOS, these policies are decomposed into fine-grained units called \emph{context nodes} implemented as software components. These units perform basic context-related operations (\emph{e.g.}, gathering data from a system or network probe, computing threshold or average values) and are assembled with a set of well-identified architectural design patterns. In this article, COSMOS is motivated and illustrated with an example from the domain of mobile e-commerce applications

FuzzTheREST - Intelligent Automated Blackbox RESTful API Fuzzer

In recent years, the pervasive influence of technology has deeply intertwined with human life, impacting diverse fields. This relationship has evolved into a dependency, with software systems playing a pivotal role, necessitating a high level of trust. Today, a substantial portion of software is accessed through Application Programming Interfaces, particularly web APIs, which predominantly adhere to the Representational State Transfer architecture. However, this architectural choice introduces a wide range of potential vulnerabilities, which are available and accessible at a network level. The significance of Software testing becomes evident when considering the widespread use of software in various daily tasks that impact personal safety and security, making the identification and assessment of faulty software of paramount importance. In this thesis, FuzzTheREST, a black-box RESTful API fuzzy testing framework, is introduced with the primary aim of addressing the challenges associated with understanding the context of each system under test and conducting comprehensive automated testing using diverse inputs. Operating from a black-box perspective, this fuzzer leverages Reinforcement Learning to efficiently uncover vulnerabilities in RESTful APIs by optimizing input values and combinations, relying on mutation methods for input exploration. The system's value is further enhanced through the provision of a thoroughly documented vulnerability discovery process for the user. This proposal stands out for its emphasis on explainability and the application of RL to learn the context of each API, thus eliminating the necessity for source code knowledge and expediting the testing process. The developed solution adheres rigorously to software engineering best practices and incorporates a novel Reinforcement Learning algorithm, comprising a customized environment for API Fuzzy Testing and a Multi-table Q-Learning Agent. The quality and applicability of the tool developed are also assessed, relying on the results achieved on two case studies, involving the Petstore API and an Emotion Detection module which was part of the CyberFactory#1 European research project. The results demonstrate the tool's effectiveness in discovering vulnerabilities, having found 7 different vulnerabilities and the agents' ability to learn different API contexts relying on API responses while maintaining reasonable code coverage levels.Ultimamente, a influência da tecnologia espalhou-se pela vida humana de uma forma abrangente, afetando uma grande diversidade dos seus aspetos. Com a evolução tecnológica esta acabou por se tornar uma dependência. Os sistemas de software começam assim a desempenhar um papel crucial, o que em contrapartida obriga a um elevado grau de confiança. Atualmente, uma parte substancial do software é implementada em formato de Web APIs, que na sua maioria seguem a arquitetura de transferência de estado representacional. No entanto, esta introduz uma série vulnerabilidade. A importância dos testes de software torna-se evidente quando consideramos o amplo uso de software em várias tarefas diárias que afetam a segurança, elevando ainda mais a importância da identificação e mitigação de falhas de software. Nesta tese é apresentado o FuzzTheREST, uma framework de teste fuzzy de APIs RESTful num modelo caixa preta, com o objetivo principal de abordar os desafios relacionados com a compreensão do contexto de cada sistema sob teste e a realização de testes automatizados usando uma variedade de possíveis valores. Este fuzzer utiliza aprendizagem por reforço de forma a compreender o contexto da API que está sob teste de forma a guiar a geração de valores de teste, recorrendo a métodos de mutação, para descobrir vulnerabilidades nas mesmas. Todo o processo desempenhado pelo sistema é devidamente documentado para que o utilizador possa tomar ações mediante os resultados obtidos. Esta explicabilidade e aplicação de inteligência artificial para aprender o contexto de cada API, eliminando a necessidade de analisar código fonte e acelerando o processo de testagem, enaltece e distingue a solução proposta de outras. A solução desenvolvida adere estritamente às melhores práticas de engenharia de software e inclui um novo algoritmo de aprendizagem por reforço, que compreende um ambiente personalizado para testagem Fuzzy de APIs e um Agente de QLearning com múltiplas Q-tables. A qualidade e aplicabilidade da ferramenta desenvolvida também são avaliadas com base nos resultados obtidos em dois casos de estudo, que envolvem a conhecida API Petstore e um módulo de Deteção de Emoções que fez parte do projeto de investigação europeu CyberFactory#1. Os resultados demonstram a eficácia da ferramenta na descoberta de vulnerabilidades, tendo identificado 7 vulnerabilidades distintas, e a capacidade dos agentes em aprender diferentes contextos de API com base nas respostas da mesma, mantendo níveis de cobertura aceitáveis

Data‐enabled cognitive modeling: Validating student engineers’ fuzzy design‐based decision‐making in a virtual design problem

The ability of future engineering professionals to solve complex real‐world problems depends on their design education and training. Because engineers engage with open‐ended problems in which there are unknown parameters and multiple competing objectives, they engage in fuzzy decision‐making, a method of making decisions that takes into account inherent imprecisions and uncertainties in the real world. In the design‐based decision‐making field, few studies have applied fuzzy decision‐making models to actual decision‐making process data. Thus, in this study, we use datasets on student decision‐making processes to validate approximate fuzzy models of student decision‐making, which we call data‐enabled cognitive modeling. The results of this study (1) show that simulated design problems provide rich datasets that enable analysis of student design decision‐making and (2) validate models of student design cognition that can inform future design curricula and help educators understand how students think about design problems

Neuro-fuzzy software for intelligent control and education

Tese de mestrado integrado. Engenharia Electrotécnica e de Computadores (Major Automação). Faculdade de Engenharia. Universidade do Porto. 200

Psychologism and neopsychologism in philosophy of logic

Thesis focuses on psychologism – a philosophical theory according to which the ontological and epistemological foundations of logic and mathematics are our mental states. Neopsychologism is a new set of psychologistic ideas that appeared already in the XXth century and are influenced by new psychology including cognitive science and artificial intelligence. Its central idea is that the main problem of the early psychologism in logic criticized by Husserl and Frege (Willard 1980) is resolved in the contemporary neopsychologistic research.https://www.ester.ee/record=b517884