Non-normal modal logics, quantification, and deontic dilemmas. A study in multi-relational semantics

This dissertation is devoted to the study of non-normal (modal) systems for deontic logics, both on the propositional level, and on the first order one. In particular we developed our study the Multi-relational setting that generalises standard Kripke Semantics. We present new completeness results concerning the semantic setting of several systems which are able to handle normative dilemmas and conflicts. Although primarily driven by issues related to the legal and moral field, these results are also relevant for the more theoretical field of Modal Logic itself, as we propose a syntactical, and semantic study of intermediate systems between the classical propositional calculus CPC and the minimal normal modal logic K.

Proof theory of quantified modal logics

We introduce labelled sequent calculi for indexed modal logics. We prove that the structural rules of weakening and contraction are height-preserving admissible, that all rules are invertible, and that cut is admissible. Then we prove that each calculus introduced is sound and complete with respect to the appropriate class of transition frames.

A Hennessy-Milner Property for Many-Valued Modal Logics

A Hennessy-Milner property, relating modal equivalence and bisimulations, is defined for many-valued modal logics that combine a local semantics based on a complete MTL-chain (a linearly ordered commutative integral residuated lattice) with crisp Kripke frames. A necessary and sufficient algebraic condition is then provided for the class of image-finite models of these logics to admit the Hennessy-Milner property. Complete characterizations are obtained in the case of many-valued modal logics based on BL-chains (divisible MTL-chains) that are finite or have universe [0,1], including crisp Lukasiewicz, Gödel, and product modal logics.

Logics for belief functions on MV-algebras

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism. © 2012 Elsevier Inc. All rights reserved.

A syntactic realization theorem for justification logics

Justification logics are refinements of modal logics where modalities are replaced by justification terms. They are connected to modal logics via so-called realization theorems. We present a syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms \$mathsfd\$, \$mathsft\$, \$mathsfb\$, \$mathsf4\$, and \$mathsf5\$ with their justification counterparts. The proof employs cut-free nested sequent systems together with Fitting's realization merging technique. We further strengthen the realization theorem for \$mathsfKB5\$ and \$mathsfS5\$ by showing that the positive introspection operator is superfluous.

Decidability for some justification logics with negative introspection

Justification logics are modal logics that include justifications for the agent's knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specifications.

Modal interpolation via nested sequents

The main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequent-like proof formalisms, such as hypersequents, nested sequents, and labelled sequents. In this paper, we start closing this gap by presenting an algorithm for proving the CIP for modal logics by induction on a nested-sequent derivation. This algorithm is applied to all the logics of the so-called modal cube.

Modelo de arquitectura para gestión cooperativa de sistemas y servicios distribuidos basado en agentes autónomos

La creciente complejidad, heterogeneidad y dinamismo inherente a las redes de telecomunicaciones, los sistemas distribuidos y los servicios avanzados de información y comunicación emergentes, así como el incremento de su criticidad e importancia estratégica, requieren la adopción de tecnologías cada vez más sofisticadas para su gestión, su coordinación y su integración por parte de los operadores de red, los proveedores de servicio y las empresas, como usuarios finales de los mismos, con el fin de garantizar niveles adecuados de funcionalidad, rendimiento y fiabilidad. Las estrategias de gestión adoptadas tradicionalmente adolecen de seguir modelos excesivamente estáticos y centralizados, con un elevado componente de supervisión y difícilmente escalables. La acuciante necesidad por flexibilizar esta gestión y hacerla a la vez más escalable y robusta, ha provocado en los últimos años un considerable interés por desarrollar nuevos paradigmas basados en modelos jerárquicos y distribuidos, como evolución natural de los primeros modelos jerárquicos débilmente distribuidos que sucedieron al paradigma centralizado. Se crean así nuevos modelos como son los basados en Gestión por Delegación, en el paradigma de código móvil, en las tecnologías de objetos distribuidos y en los servicios web. Estas alternativas se han mostrado enormemente robustas, flexibles y escalables frente a las estrategias tradicionales de gestión, pero continúan sin resolver aún muchos problemas. Las líneas actuales de investigación parten del hecho de que muchos problemas de robustez, escalabilidad y flexibilidad continúan sin ser resueltos por el paradigma jerárquico-distribuido, y abogan por la migración hacia un paradigma cooperativo fuertemente distribuido. Estas líneas tienen su germen en la Inteligencia Artificial Distribuida (DAI) y, más concretamente, en el paradigma de agentes autónomos y en los Sistemas Multi-agente (MAS). Todas ellas se perfilan en torno a un conjunto de objetivos que pueden resumirse en alcanzar un mayor grado de autonomía en la funcionalidad de la gestión y una mayor capacidad de autoconfiguración que resuelva los problemas de escalabilidad y la necesidad de supervisión presentes en los sistemas actuales, evolucionar hacia técnicas de control fuertemente distribuido y cooperativo guiado por la meta y dotar de una mayor riqueza semántica a los modelos de información. Cada vez más investigadores están empezando a utilizar agentes para la gestión de redes y sistemas distribuidos. Sin embargo, los límites establecidos en sus trabajos entre agentes móviles (que siguen el paradigma de código móvil) y agentes autónomos (que realmente siguen el paradigma cooperativo) resultan difusos. Muchos de estos trabajos se centran en la utilización de agentes móviles, lo cual, al igual que ocurría con las técnicas de código móvil comentadas anteriormente, les permite dotar de un mayor componente dinámico al concepto tradicional de Gestión por Delegación. Con ello se consigue flexibilizar la gestión, distribuir la lógica de gestión cerca de los datos y distribuir el control. Sin embargo se permanece en el paradigma jerárquico distribuido. Si bien continúa sin definirse aún una arquitectura de gestión fiel al paradigma cooperativo fuertemente distribuido, estas líneas de investigación han puesto de manifiesto serios problemas de adecuación en los modelos de información, comunicación y organizativo de las arquitecturas de gestión existentes. En este contexto, la tesis presenta un modelo de arquitectura para gestión holónica de sistemas y servicios distribuidos mediante sociedades de agentes autónomos, cuyos objetivos fundamentales son el incremento del grado de automatización asociado a las tareas de gestión, el aumento de la escalabilidad de las soluciones de gestión, soporte para delegación tanto por dominios como por macro-tareas, y un alto grado de interoperabilidad en entornos abiertos. A partir de estos objetivos se ha desarrollado un modelo de información formal de tipo semántico, basado en lógica descriptiva que permite un mayor grado de automatización en la gestión en base a la utilización de agentes autónomos racionales, capaces de razonar, inferir e integrar de forma dinámica conocimiento y servicios conceptualizados mediante el modelo CIM y formalizados a nivel semántico mediante lógica descriptiva. El modelo de información incluye además un “mapping” a nivel de meta-modelo de CIM al lenguaje de especificación de ontologías OWL, que supone un significativo avance en el área de la representación y el intercambio basado en XML de modelos y meta-información. A nivel de interacción, el modelo aporta un lenguaje de especificación formal de conversaciones entre agentes basado en la teoría de actos ilocucionales y aporta una semántica operacional para dicho lenguaje que facilita la labor de verificación de propiedades formales asociadas al protocolo de interacción. Se ha desarrollado también un modelo de organización holónico y orientado a roles cuyas principales características están alineadas con las demandadas por los servicios distribuidos emergentes e incluyen la ausencia de control central, capacidades de reestructuración dinámica, capacidades de cooperación, y facilidades de adaptación a diferentes culturas organizativas. El modelo incluye un submodelo normativo adecuado al carácter autónomo de los holones de gestión y basado en las lógicas modales deontológica y de acción.---ABSTRACT---The growing complexity, heterogeneity and dynamism inherent in telecommunications networks, distributed systems and the emerging advanced information and communication services, as well as their increased criticality and strategic importance, calls for the adoption of increasingly more sophisticated technologies for their management, coordination and integration by network operators, service providers and end-user companies to assure adequate levels of functionality, performance and reliability. The management strategies adopted traditionally follow models that are too static and centralised, have a high supervision component and are difficult to scale. The pressing need to flexibilise management and, at the same time, make it more scalable and robust recently led to a lot of interest in developing new paradigms based on hierarchical and distributed models, as a natural evolution from the first weakly distributed hierarchical models that succeeded the centralised paradigm. Thus new models based on management by delegation, the mobile code paradigm, distributed objects and web services came into being. These alternatives have turned out to be enormously robust, flexible and scalable as compared with the traditional management strategies. However, many problems still remain to be solved. Current research lines assume that the distributed hierarchical paradigm has as yet failed to solve many of the problems related to robustness, scalability and flexibility and advocate migration towards a strongly distributed cooperative paradigm. These lines of research were spawned by Distributed Artificial Intelligence (DAI) and, specifically, the autonomous agent paradigm and Multi-Agent Systems (MAS). They all revolve around a series of objectives, which can be summarised as achieving greater management functionality autonomy and a greater self-configuration capability, which solves the problems of scalability and the need for supervision that plague current systems, evolving towards strongly distributed and goal-driven cooperative control techniques and semantically enhancing information models. More and more researchers are starting to use agents for network and distributed systems management. However, the boundaries established in their work between mobile agents (that follow the mobile code paradigm) and autonomous agents (that really follow the cooperative paradigm) are fuzzy. Many of these approximations focus on the use of mobile agents, which, as was the case with the above-mentioned mobile code techniques, means that they can inject more dynamism into the traditional concept of management by delegation. Accordingly, they are able to flexibilise management, distribute management logic about data and distribute control. However, they remain within the distributed hierarchical paradigm. While a management architecture faithful to the strongly distributed cooperative paradigm has yet to be defined, these lines of research have revealed that the information, communication and organisation models of existing management architectures are far from adequate. In this context, this dissertation presents an architectural model for the holonic management of distributed systems and services through autonomous agent societies. The main objectives of this model are to raise the level of management task automation, increase the scalability of management solutions, provide support for delegation by both domains and macro-tasks and achieve a high level of interoperability in open environments. Bearing in mind these objectives, a descriptive logic-based formal semantic information model has been developed, which increases management automation by using rational autonomous agents capable of reasoning, inferring and dynamically integrating knowledge and services conceptualised by means of the CIM model and formalised at the semantic level by means of descriptive logic. The information model also includes a mapping, at the CIM metamodel level, to the OWL ontology specification language, which amounts to a significant advance in the field of XML-based model and metainformation representation and exchange. At the interaction level, the model introduces a formal specification language (ACSL) of conversations between agents based on speech act theory and contributes an operational semantics for this language that eases the task of verifying formal properties associated with the interaction protocol. A role-oriented holonic organisational model has also been developed, whose main features meet the requirements demanded by emerging distributed services, including no centralised control, dynamic restructuring capabilities, cooperative skills and facilities for adaptation to different organisational cultures. The model includes a normative submodel adapted to management holon autonomy and based on the deontic and action modal logics.

A preference-based semantics for CTD reasoning

In [8] the authors developed a logical system based on the definition of a new non-classical connective ⊗ capturing the notion of reparative obligation. The system proved to be appropriate for handling well-known contrary-to-duty paradoxes but no model-theoretic semantics was presented. In this paper we fill the gap and define a suitable possible-world semantics for the system for which we can prove soundness and completeness. The semantics is a preference-based non-normal one extending and generalizing semantics for classical modal logics.

Group Beliefs : Studies on the Nature and Logic of Collective Doxastic Attitudes

This thesis studies the nature and logic of collective doxastic attitudes, or what is referred to in ordinary language as "group beliefs". Beliefs and other intentional attitudes are attributed to groups and collections of people, and such attributions are used to explain and predict the actions of groups. The thesis develops an understanding of group beliefs as voluntarily adopted views or acceptances rather than as ordinary beliefs. Such an understanding can provide new answers to questions concerning collective knowledge and justification of group beliefs, and it allows developing modal logics with collective doxastic and epistemic notions. The thesis consists of six articles. The first three articles are philosophical studies concerned with the nature of group beliefs. The last three articles are logical studies that aim at developing proof-theoretical calculi for reasoning about collective doxastic attitudes.

By indirections find directions out : thinkable worlds in Abbott and Vonnegut

This thesis is concerned with the interaction between literature and abstract thought. More specifically, it studies the epistemological charge of the literary, the type of knowledge that is carried by elements proper to fictional narratives into different disciplines. By concentrating on two different theoretical methods, the creation of thought experiments and the framing of possible worlds, methods which were elaborated and are still used today in spheres as varied as modal logics, analytic philosophy and physics, and by following their reinsertion within literary theory, the research develops the theory that both thought experiments and possible worlds are in fact short narrative stories that inform knowledge through literary means. By using two novels, Abbott’s Flatland and Vonnegut’s The Sirens of Titan, that describe extra-dimensional existence in radically different ways, respectively as a phenomenologically unknowable space and as an outward perspective on time, it becomes clear that literature is constitutive of the way in which worlds, fictive, real or otherwise, are constructed and understood. Thus dimensions, established through extensional analogies as either experimental knowledge or modal possibility for a given world, generate new directions for thought, which can then take part in the inductive/deductive process of scientia. By contrasting the dimensions of narrative with the way that dimensions were historically constituted, the research also establishes that the literary opens up an infinite potential of abstract space-time domains, defined by their specific rules and limits, and that these different experimental folds are themselves partaking in a dimensional process responsible for new forms of understanding. Over against science fiction literary theories of speculation that posit an equation between the fictive and the real, this thesis examines the complex structure of many overlapping possibilities that can organise themselves around larger compossible wholes, thus offering a theory of reading that is both non-mimetic and non-causal. It consequently examines the a dynamic process whereby literature is always reconceived through possibilities actualised by reading while never defining how the reader will ultimately understand the overarching structure. In this context, the thesis argues that a causal story can be construed out of any one interaction with a given narrative—underscoring, for example, the divinatory strength of a particular vision of the future—even as this narrative represents only a fraction of the potential knowledge of any particular literary text. Ultimately, the study concludes by tracing out how novel comprehensions of the literary, framed by the material conditions of their own space and time, endlessly renew themselves through multiple interactions, generating analogies and speculations that facilitate the creation of new knowledge.