Nominal equational problems modulo associativity, commutativity and associativity-commutativity

Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Ciência da Computação, 2019.A sintaxe nominal tem sido utilizada em vários contextos por quase duas décadas. Ela é uma ferramenta poderosa para se lidar com ligação de variáveis de uma forma concreta, que pode ser aplicada a qualquer especificação na qual parâmetros são utilizados para se abstrair variáveis, tal como em predicados e funções. Na sintaxe nominal, objetos que são sintaticamente diferentes podem ter a mesma semântica módulo alfa-conversão, tal como acontece no Cálculo Lambda. O tratamento de igualdades, em especial a alphaequivalêcia, é algo essencial em linguagens formais e implementações. Este trabalho investiga a alpha-equivalência nominal com símbolos de função associativos (A), comutativos (C) e associativos-comutativos (AC). Verificação de equivalência, casamento e unificação módulo A, C e AC são investigados. Em relação a verificação de igualdade, as alphaequivalências nominais módulo A, C e AC foram especificadas em Coq e provadas ser corretas. Um algoritmo implementado em OCaml para verificação de igualdade módulo A, C e AC é automaticamente extraído da especificação e experimentos são executados utilizando-se também um algoritmo aperfeiçoado. Limites superiores para o tempo de execução na solução de problemas nominais de verificação equacional são fornecidos. Um algoritmo de unificação módulo C baseado em regras de redução é especificado em Coq e provado ser correto e completo. Por meio do uso de variáveis protegidas, este algoritmo de unificação resolve problemas de casamento nominal módulo C, o que foi também formalizado ser correto e completo. O algoritmo de unificação baseado em regras de redução fornece uma família finita de conjuntos de equações nominais de ponto fixo. Cada uma destas equações pode ter um conjunto infinito de soluções independentes. Portanto, demonstra-se que problemas de unificação nominal módulo C e AC podem gerar um conjunto infinito de soluções independentes. Este fato contrasta com unificação sintática módulo C ou AC, que são conhecidas por estar na classe finitária de problemas. Uma implementação em OCaml do algoritmo de unificação nominal é fornecida e utilizado para se construir exemplos.The nominal syntax has been used in many application contexts for almost two decades. It is a powerful tool for dealing with variable binding in a concrete manner that can be applied to any specification in which parameters are used to abstract variables, such as in predicates and functions. In the nominal syntax, syntactically different objects can have the same semantics modulo alpha-conversion, as happens in the lambda calculus. Dealing with equality, and in special with alpha-equivalence, is essential in formal languages and implementations. This work investigates the nominal alpha-equivalence with associative (A), commutative (C) and associative-comutative (AC) function symbols. Equalitychecking, matching and unification modulo A, C and AC are investigated. Regarding equality-checking, nominal alpha-equivalence modulo A, C and AC are specified in Coq and proved sound. An algorithm implemented in OCaml for equality-checking modulo A, C and AC is automatically extracted from the specification and experiments are performed using also an improved algorithm. Upper bounds for solving nominal equality-checking problems are given. A rule-based nominal unification modulo C algorithm is specified in Coq and proved sound and complete. By using protected variables, this unification algorithm solves nominal matching problems modulo C, which is formalised to be sound and complete. The rule-based nominal unification algorithm outputs a finite family of sets of fixed point nominal equations. Each of which might have an infinite set of independent solutions. Therefore, nominal unification modulo C or AC are proved to potentially generate infinite independent solutions. This contrasts with syntactic unification modulo C or AC that are known to be in the finitary class. An OCaml implementation of the nominal unification algorithm is provided and used to build examples

Expressiveness via Intensionality and Concurrency

International audienceComputation can be considered by taking into account two dimensions: extensional versus intensional, and sequential versus concurrent. Traditionally sequential extensional computation can be captured by the lambda-calculus. However, recent work shows that there are more expressive intensional calculi such as SF-calculus. Traditionally process calculi capture computation by encoding the lambda-calculus, such as in the pi-calculus. Following this increased expressiveness via intensionality, other recent work has shown that concurrent pattern calculus is more expressive than pi-calculus. This paper formalises the relative expressiveness of all four of these calculi by placing them on a square whose edges are irreversible encodings. This square is representative of a more general result: that expressiveness increases with both intensionality and concurrency

Ontology evolution in physics

With the advent of reasoning problems in dynamic environments, there is an increasing need for automated reasoning systems to automatically adapt to unexpected changes in representations. In particular, the automation of the evolution of their ontologies needs to be enhanced without substantially sacrificing expressivity in the underlying representation. Revision of beliefs is not enough, as adding to or removing from beliefs does not change the underlying formal language. General reasoning systems employed in such environments should also address situations in which the language for representing knowledge is not shared among the involved entities, e.g., the ontologies in a multi-ontology environment or the agents in a multi-agent environment. Our techniques involve diagnosis of faults in existing, possibly heterogeneous, ontologies and then resolution of these faults by manipulating the signature and/or the axioms. This thesis describes the design, development and evaluation of GALILEO (Guided Analysis of Logical Inconsistencies Lead to Evolution of Ontologies), a system designed to detect conflicts in highly expressive ontologies and resolve the detected conflicts by performing appropriate repair operations. The integrated mechanism that handles ontology evolution is able to distinguish between various types of conflicts, each corresponding to a unique kind of ontological fault. We apply and develop our techniques in the domain of Physics. This an excellent domain because many of its seminal advances can be seen as examples of ontology evolution, i.e. changing the way that physicists perceive the world, and case studies are well documented – unlike many other domains. Our research covers analysing a wide ranging development set of case studies and evaluating the performance of the system on a test set. Because the formal representations of most of the case studies are non-trivial and the underlying logic has a high degree of expressivity, we face some tricky technical challenges, including dealing with the potentially large number of choices in diagnosis and repair. In order to enhance the practicality and the manageability of the ontology evolution process, GALILEO incorporates the functionality of generating physically meaningful diagnoses and repairs and, as a result, narrowing the search space to a manageable size

Principles of Security and Trust

This open access book constitutes the proceedings of the 8th International Conference on Principles of Security and Trust, POST 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 10 papers presented in this volume were carefully reviewed and selected from 27 submissions. They deal with theoretical and foundational aspects of security and trust, including on new theoretical results, practical applications of existing foundational ideas, and innovative approaches stimulated by pressing practical problems

Principles of Security and Trust

This open access book constitutes the proceedings of the 8th International Conference on Principles of Security and Trust, POST 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 10 papers presented in this volume were carefully reviewed and selected from 27 submissions. They deal with theoretical and foundational aspects of security and trust, including on new theoretical results, practical applications of existing foundational ideas, and innovative approaches stimulated by pressing practical problems