This thesis investigates logical formalizations of Castelfranchi and Falcone's (C&F) theory of trust [9, 10, 11, 12]. The C&F theory of trust defines trust as an essentially mental notion, making the theory particularly well suited for formalizations in multi-modal logics of beliefs, goals, intentions, actions, and time. Three different multi-modal logical formalisms intended for multi-agent systems are compared and evaluated along two lines of inquiry. First, I propose formal definitions of key concepts of the C&F theory of trust and prove some important properties of these definitions. The proven properties are then compared to the informal characterisation of the C&F theory. Second, the logics are used to formalize a case study involving an Internet forum, and their performances in the case study constitute grounds for a comparison. The comparison indicates that an accurate modelling of time, and the interaction of time and goals in particular, is integral for formal reasoning about trust. Finally, I propose a Horn fragment of the logic of Herzig, Lorini, Hubner, and Vercouter [25]. The Horn fragment is shown to be too restrictive to accurately express the considered case study.

Neste trabalho, estudamos algumas formas de combinar sistemas de Lógica Modal, analisando quando a combinação preserva propriedades como correção, completude e decidibilidade. Estendemos um estudo já realizado sobre combinações de sistemas de Lógica Modal Normal para sistemas de Lógica Modal Não-normal. O principal resultado deste trabalho é a preservação de completude da aplicação externa de um sistema de Lógica Modal Não-normal M em um sistema lógico L. Outro resultado importante é um exemplo de interação forte na combinação independente, ou fusão, de dois sistemas de Lógica Modal Não-normal. / In this work, we study a few ways of combining Modal Logic systems, analysing when the combination preserves properties like soundness, completeness and decidability. We extend a study of the combination of Normal Modal Logic systems to Non-normal Modal Logic systems. The main result of this work is the completeness preservation in the external application of a Non-normal Modal Logic system M to a logic system L. Another important result is an example of strong interations arising in the fusion of two Non-normal Modal Logic system.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Truth preservation is an important topic in model theory. However a brief examination of the models for a logic often show that isomorphism is needlessly restrictive as a truth preserving construction. In the case of modal logics with Kripke semantics the notions of simulation and bisimulation prove far more practical and interesting than isomorphism. We present and study these various notions, followed by a discussion of Shehtman’s frame product as semantics for certain many-dimensional modal logics. We show how simulations and bisimulations can be interpreted inside models over frame products. This is followed by a discussion on a category-theoretic setting for frame products, where the arrows may run between frames with different types. / AFRIKAANSE OPSOMMING: Die behou van waarheid is ’n prominente onderwerp in modelteorie. ’n Vlugtige ondersoek van die modelle vir ’n besondere logika wys egter dat isomorfisme onnodig beperkend as waarheid-behoudende konstruksie is. In die geval van modale logika met Kripke se semantiek is simulasie en bisimulasie heelwat meer prakties en interessant as isomorfisme. Na die bekendstel en studie van hierdie onderskeie begrippe bespreek ons Shehtman se raamproduk as semantiek vir sekere meer-dimensionele modale logikas. Ons wys ons hoe simulasies en bisimulasies binne modelle oor sulke raamprodukte geïnterpreteer kan word. Daarna bespreek ons ’n kategorie-teoretiese konteks vir raamprodukte, waar die pyle tussen rame met verskillende tipes mag loop.

We consider the problem of answering conjunctive queries over description logic knowledge bases via query rewriting. Given a conjunctive query Q and a TBox T, we compute a new query Q′ that incorporates the semantic consequences of T such that, for any ABox A, evaluating Q over T and A can be done by evaluating the new query Q′ over A alone. We present RQR—a novel resolution-based rewriting algorithm for the description logic ELHIO¬ that generalizes and extends existing approaches. RQR not only handles a spectrum of logics ranging from DL-Lite_core up to ELHIO¬, but it is worst-case optimal with respect to data complexity for all of these logics; moreover, given the form of the rewritten queries, their evaluation can be delegated to off-the-shelf (deductive) database systems. We use RQR to derive the novel complexity results that conjunctive query answering for ELHIO¬ and DL-Lite+ are, respectively, PTime and NLogSpace complete with respect to data complexity. In order to show the practicality of our approach, we present the results of an empirical evaluation. Our evaluation suggests that RQR, enhanced with various straightforward optimizations, can be successfully used in conjunction with a (deductive) database system in order to answer queries over knowledge bases in practice. Moreover, in spite of being a more general procedure, RQR will often produce significantly smaller rewritings than the standard query rewriting algorithm for the DL-Lite family of logics.

This thesis describes a decision and minimization procedure for modal logic. The decision procedure answers the question of whether there exists a satisfying pointed model for a formula which obeys user-specified first-order conditions on the underlying frame. Then the minimization procedure produces a minimal model with respect to the number of worlds that satisfies the desired formula while obeying the requisite conditions on the underlying frame. A proof of correctness for the decision and minimization procedures is supplied, as well as a description of an implementation built upon the Enfragmo model expansion solver. / Graduate / 0984 / 0318 / wbkboyer@gmail.com

No description available.

The modal logic S5 gives us a simple technical tool to analyze some main notions from philosophy (e.g. metaphysical necessity and epistemological concepts such as knowledge and belief). Although S5 can be axiomatized by some simple rules, this logic shows some puzzling properties. For example, an interpolation result holds for the propositional version, but this same result fails when we add first-order quantifiers to this logic. In this dissertation, we study the failure of the Definability and Interpolation Theorems for first-order S5. At the same time, we combine the results of justification logic and we investigate the quantified justification counterpart of S5 (first-order JT45). In this way we explore the relationship between justification logic and modal logic to see if justification logic can contribute to the literature concerning the restoration of the Interpolation Theorem. / A lógica modal S5 nos oferece um ferramental técnico para analizar algumas noções filosóficas centrais (por exemplo, necessidade metafísica e certos conceitos epistemológicos como conhecimento e crença). Apesar de ser axiomatizada por princípios simples, esta lógica apresenta algumas propriedades peculiares. Uma das mais notórias é a seguinte: podemos provar o Teorema da Interpolação para a versão proposicional, mas esse mesmo teorema não pode ser provado quando adicionamos quantificadores de primeira ordem a essa lógica. Nesta dissertação vamos estudar a falha dos Teoremas da Definibilidade e da Interpolação para a versão quantificada de S5. Ao mesmo tempo, vamos combinar os resultados da lógica da justificação e investigar a contraparte da versão quantificada de S5 na lógica da justificação (a lógica chamada JT45 de primeira ordem). Desse modo, vamos explorar a relação entre lógica modal e lógica da justificação para ver se a lógica da justificação pode contribuir para a restauração do Teorema da Interpolação.

The cloud computing paradigm introduces an efficient utilisation of huge computing resources by multiple users with minimal expense and deployment effort compared to traditional computing facilities. Although cloud computing has incredible benefits, some governments and enterprises remain hesitant to transfer their computing technology to the cloud as a consequence of the associated security challenges. Security is, therefore, a significant factor in cloud computing adoption. Cloud services consist of three layers: Software as a Service (SaaS), Platform as a Service (PaaS), and Infrastructure as a Service (IaaS). Cloud computing services are accessed through network connections and utilised by multi-users who can share the resources through virtualisation technology. Accordingly, an efficient access control system is crucial to prevent unauthorised access. This thesis mainly investigates the IaaS security enhancement from an access control point of view.

Ted Sider writes that "many are impressed with the utility of possible worlds in linguistics and philosophy", and this is true, in particular, of those with an interest in modal logic. However, in the midst of the marvelous milieu brought on by the development of possible world semantics, some have stopped to ask just what it is that possible worlds are. They certainly seem useful, and we seem to understand how to use them and talk about them, but what precisely is it that we're talking about when we talk of possible worlds? In this thesis, I will attempt to outline the most significant and well-recognized view in this debate: that of David Lewis. Through my discussion of him, I will find occasion to discuss some alternative views that have arisen. After finishing my presentation of Lewis, I will discuss where people have begun to take this debate and address the question of whether progress can be made towards a substantive answer. In Chapter I, I begin by presenting the motivation of the question of possible worlds found in the study of modal logic. I then present the major approaches taken to answering the questions that were raised, leading into my discussion of David Lewis's famous and robust account. I present key features of Lewis's view and then move into his criticisms of the other major responses. This much should suffice as a relatively thorough treatment of the answers that have come before. In Chapter II, I discuss the current state of the debate. I begin by mentioning several problems that can be spotted in Lewis's views in particular. I then move to Menzel's account, which tries to answer the question of possible worlds from a new angle, jettisoning the direction taken by Lewis and his contemporaries. I explain why Menzel has taken this new approach, and then move into another new approach, this time given by Stephen Yablo. I discuss how these two approaches can help serve each other in helpful ways. But, at last, I present several hurdles these two views would have to overcome in order to play together nicely.

Disertacijoje nagrinėjamos žinių logikos su centrinio agento sąveikos aksioma. Tyrimas apima multimodalines logikas Kn, Tn, K4n ir S4n. Disertacijos tikslas – baigtinės išvedimo paieškos sekvenciniai skaičiavimai minėtoms logikoms. Darbe pristatomas naujas išvedimo paieškos baigtinumą užtikrinantis metodas, kuris yra pritaikomas minėtoms logikoms, o taip pat monomodalinėms logikoms K4 ir S4. / In the dissertation epistemic logics with central agent interaction axiom are analysed. The research covers multimodal logics Kn, Tn, K4n and S4n. The aim of the work is finite derivation search sequent calculi for the mentioned logics. A new method to obtain the termination of derivation search is presented in the thesis and this method is applied to the mentioned logics as well as to monomodal logics K4 and S4.