[pt] Confiança é um aspecto fundamental em sistemas distribuídos abertos de larga-escala. Ela está no núcleo de todas as interações entre as entidades que precisam operar em ambientes com muita incerteza e que se modificam constantemente. Dada essa complexidade, esses componentes, e o sistema resultante, são cada vez mais contextualizados, desenhados e construídos usando técnicas baseadas em agentes. Portanto, confiança é fundamental em um sistema multi-agentes (MAS) aberto. Logo, este trabalho investiga como se ter um modelo de confiança explicitamente em um agente inteligente, que possui crenças (Beliefs), desejos (Desires) e intenções (Intentions), chamado de agente BDI. Ou seja, o agente passa a ter um quarto componente chamado confiança (Trust). Dessa forma, é necessário uma lógica para englobar o conceito de confiança em um MAS BDI aberto. Isso é feito usando uma lógica multi-modal indexada, onde os mundos possíveis que modelam um sistema multi-agentes representam quais agentes estão presentes em um dado instante de tempo. E, para cada uma três componentes originais de um agente BDI, há também uma representação de mundos possíveis, pois as mesmas são tratadas como modalidades. Já a confiança é modelada como sendo um predicado, e não uma modalidade. / [en] Trust is a fundamental concern in large-escale open distributed sytems. It lies at the core of all interactios between the entities that have to operate in such uncertain and constantly changing environmonts. Given the complexity of the interactions, these components, and the ensuing system, are increasingly being conceptualised, desined, and built using agent-based techiques. Therefore, the presence of trust is imperative in a multi-agent system (MAS). Consequently, this work studies how to have a explicit trust model in intelligent agent, which has beliefs, desires and intentions (BDI agent). Thas is, the agent now has a fourth component called Trust. This way, a logic to include the concept of trust in an open BDI MAS is interesting, so that the different aspects of a trust model can be expressed formally and accuratelly. This is achieved by using an indexed multi-modal logic, where the possible worlds which model a multi-agent system represent which agents are in the system in a given moment. Moreover, for each one of the three original components of a BDI agent, where the components represent beliefs, desires and intentions, there is a representation of possible worlds, because these are treated as modalities. However, trust is modelled as predicate, not as a modality.

This paper investigates (modal) extensions of Heyting–Brouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We first develop matrix as well as Kripke style semantics for those logics. Then, by extending the Gödel-embedding of intuitionistic logic into S4 , it is shown that all (modal) extensions of Heyting–Brouwer logic can be embedded into tense logics (with additional modal operators). An extension of the Blok–Esakia-Theorem is proved for this embedding.

Operators which map subsets of a given set to the set of their minimal elements with respect to some relation R form the basis of a semantic approach in non-monotonic logic, belief revision, conditional logic and updating. In this paper we investigate operators of this type from an algebraic viewpoint. A representation theorem is proved and various properties of the resulting algebras are investigated. It is shown that they behave quite differently from known algebras related to logics, e.g. modal algebras and Heyting algebras.

This paper is a comparative study of the propositional intuitionistic (non-modal) and classical modal languages interpreted in the standard way on transitive frames. It shows that, when talking about these frames rather than conventional quasi-orders, the intuitionistic language displays some unusual features: its expressive power becomes weaker than that of the modal language, the induced consequence relation does not have a deduction theorem and is not protoalgebraic. Nevertheless, the paper develops a manageable model theory for this consequence and its extensions which also reveals some unexpected phenomena. The balance between the intuitionistic and modal languages is restored by adding to the former one more implication.

The paper considers the standard concept description language ALC augmented with various kinds of modal operators which can be applied to concepts and axioms. The main aim is to develop methods of proving decidability of the satisfiability problem for this language and apply them to description logics with most important temporal and epistemic operators, thereby obtaining satisfiability checking algorithms for these logics. We deal with the possible world semantics under the constant domain assumption and show that the expanding and varying domain assumptions are reducible to it. Models with both finite and arbitrary constant domains are investigated. We begin by considering description logics with only one modal operator and then prove a general transfer theorem which makes it possible to lift the obtained results to many systems of polymodal description logic.

This chapter is a continuation of the preceding one, and we begin it at the place where the authors of Basic Modal Logic left us about fifteen years ago. Concluding his historical overview, Krister Segerberg wrote: “Where we stand today is difficult to say. Is the picture beginning to break up, or is it just the contemporary observer’s perennial problem of putting his own time into perspective?” So, where did modal logic of the 1970s stand? Where does it stand now? Modal logicians working in philosophy, computer science, artificial intelligence, linguistics or some other fields would probably give different answers to these questions. Our interpretation of the history of modal logic and view on its future is based upon understanding it as part of mathematical logic.

Unification has been investigated both in modal logics and in description logics, albeit with different motivations. In description logics, unification can be used to detect redundancies in ontologies. In this context, it is not sufficient to decide unifiability, one must also compute appropriate unifiers and present them to the user. For the description logic EL, which is used to define several large biomedical ontologies, deciding unifiability is an NP-complete problem. It is known that every solvable EL-unification problem has a minimal unifier, and that every minimal unifier is a local unifier. Existing unification algorithms for EL compute all minimal unifiers, but additionally (all or some) non-minimal local unifiers. Computing only the minimal unifiers would be better since there are considerably less minimal unifiers than local ones, and their size is usually also quite small. In this paper we investigate the question whether the known algorithms for EL-unification can be modified such that they compute exactly the minimal unifiers without changing the complexity and the basic nature of the algorithms. Basically, the answer we give to this question is negative.

[pt] Lógica Proposicional Dinâmica (PDL) é um sistema lógico multi-modal utilizada para especificar e verificar propriedades em programas sequenciais. Redes de Petri são um formalismo largamente utilizado na especificação de sistemas concorrentes e possuem uma interpretação gráfica bastante intuitiva. Neste trabalho apresentam-se extensões da Lógica Proposicional Dinâmica onde os programas são substituídos por Redes de Petri. Define-se uma codificação composicional para as Redes de Petri através de redes básicas, apresentando uma semântica composicional. Uma axiomatização é definida para a qual o sistema é provado ser correto, e completo em relação à semântica proposta. Três Lógicas Dinâmicas são apresentadas: uma para efetuar inferências sobre Redes de Petri Marcadas ordinárias e duas para inferências sobre Redes de Petri Estocásticas marcadas, possibilitando a modelagem de cenários mais complexos. Alguns sistemas dedutivos para essas lógicas são apresentados. A principal vantagem desta abordagem concerne em possibilitar efetuar inferências sobre Redes de Petri [Estocásticas] marcadas sem a necessidade de traduzí-las a outros formalismos. / [en] Propositional Dynamic Logic (PDL) is a multi-modal logic used for specifying and reasoning on sequential programs. Petri Net is a widely used formalism to specify and to analyze concurrent programs with a very intuitive graphical representation. In this work, we propose some extensions of Propositional Dynamic Logic for reasoning about Petri Nets. We define a compositional encoding of Petri Nets from basic nets as terms. Second, we use these terms as PDL programs and provide a compositional semantics to PDL Formulas. Then we present an axiomatization and prove completeness regarding our semantics. Three versions of Dynamic Logics to reasoning with Petri Nets are presented: one of them for ordinary Marked Petri Nets and two for Marked Stochastic Petri Nets yielding to the possibility of model more complex scenarios. Some deductive systems are presented. The main advantage of our approach is that we can reason about [Stochastic] Petri Nets using our Dynamic Logic and we do not need to translate it into other formalisms. Moreover our approach is compositional allowing for construction of complex nets using basic ones.