A Fibred Tableau Calculus for Modal Logics of Agents

In previous works we showed how to combine propositional multimodal logics using Gabbay's \emph{fibring} methodology. In this paper we extend the above mentioned works by providing a tableau-based proof technique for the combined/fibred logics. To achieve this end we first make a comparison between two types of tableau proof systems, (\emph{graph} $\&$ \emph{path}), with the help of a scenario (The Friend's Puzzle). Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system \KEM. We conclude with a discussion on \KEM's features

A Fibred Tableau Calculus for BDI Logics

In [12,16] we showed how to combine propositional BDI logics using Gabbay's fibring methodology. In this paper we extend the above mentioned works by providing a tableau-based decision procedure for the combined/fibred logics. To achieve this end we first outline with an example two types of tableau systems, (graph and path), and discuss why both are inadequate in the case of fibring. Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system KEM

Modal tableaux for verifying stream authentication protocols

To develop theories to specify and reason about various aspects of multi-agent systems, many researchers have proposed the use of modal logics such as belief logics, logics of knowledge, and logics of norms. As multi-agent systems operate in dynamic environments, there is also a need to model the evolution of multi-agent systems through time. In order to introduce a temporal dimension to a belief logic, we combine it with a linear-time temporal logic using a powerful technique called fibring for combining logics. We describe a labelled modal tableaux system for the resulting fibred belief logic (FL) which can be used to automatically verify correctness of inter-agent stream authentication protocols. With the resulting fibred belief logic and its associated modal tableaux, one is able to build theories of trust for the description of, and reasoning about, multi-agent systems operating in dynamic environments

Modal Tableaux for Verifying Security Protocols

To develop theories to specify and reason about various aspects of multi-agent systems, many researchers have proposed the use of modal logics such as belief logics, logics of knowledge, and logics of norms. As multi-agent systems operate in dynamic environments, there is also a need to model the evolution of multi-agent systems through time. In order to introduce a temporal dimension to a belief logic, we combine it with a linear-time temporal logic using a powerful technique called fibring for combining logics. We describe a labelled modal tableaux system for a fibred belief logic (FL) which can be used to automatically verify correctness of inter-agent stream authentication protocols. With the resulting fibred belief logic and its associated modal tableaux, one is able to build theories of trust for the description of, and reasoning about, multi-agent systems operating in dynamic environments

Labelled Modal Tableaux

Labelled tableaux are extensions of semantic tableaux with annotations (labels, indices) whose main function is to enrich the modal object language with semantic elements. This paper consists of three parts. In the first part we consider some options for labels: simple constant labels vs labels with free variables, logic depended inference rules vs labels manipulation based on a label algebra. In the second and third part we concentrate on a particular labelled tableaux system called KEM using free variable and a specialised label algebra. Specifically in the second part we show how labelled tableaux (KEM) can account for different types of logics (e.g., non-normal modal logics and conditional logics). In the third and final part we investigate the relative complexity of labelled tableaux systems and we show that the uses of KEM's label algebra can lead to speed up on proofs

LDS - Labelled Deductive Systems: Volume 1 - Foundations

Traditional logics manipulate formulas. The message of this book is to manipulate pairs; formulas and labels. The labels annotate the formulas. This sounds very simple but it turned out to be a big step, which makes a serious difference, like the difference between using one hand only or allowing for the coordinated use of two hands. Of course the idea has to be made precise, and its advantages and limitations clearly demonstrated. `Precise' means a good mathematical definition and `advantages demonstrated' means case studies and applications in pure logic and in AI. To achieve that we need to address the following: \begin{enumerate} \item Define the notion of {\em LDS}, its proof theory and semantics and relate it to traditional logics. \item Explain what form the traditional concepts of cut elimination, deduction theorem, negation, inconsistency, update, etc.\ take in {\em LDS}. \item Formulate major known logics in {\em LDS}. For example, modal and temporal logics, substructural logics, default, nonmonotonic logics, etc. \item Show new results and solve long-standing problems using {\em LDS}. \item Demonstrate practical applications. \end{enumerate} This is what I am trying to do in this book. Part I of the book is an intuitive presentation of {\em LDS} in the context of traditional current views of monotonic and nonmonotonic logics. It is less oriented towards the pure logician and more towards the practical consumer of logic. It has two tasks, addressed in two chapters. These are: \begin{itemlist}{Chapter 1:} \item [Chapter1:] Formally motivate {\em LDS} by starting from the traditional notion of `What is a logical system' and slowly adding features to it until it becomes essentially an {\em LDS}. \item [Chapter 2:] Intuitively motivate {\em LDS} by showing many examples where labels are used, as well as some case studies of familiar logics (e.g.\ modal logic) formulated as an {\em LDS}. \end{itemlist} The second part of the book presents the formal theory of {\em LDS} for the formal logician. I have tried to avoid the style of definition-lemma-theorem and put in some explanations. What is basically needed here is the formulation of the mathematical machinery capable of doing the following. \begin{itemize} \item Define {\em LDS} algebra, proof theory and semantics. \item Show how an arbitrary (or fairly general) logic, presented traditionally, say as a Hilbert system or as a Gentzen system, can be turned into an {\em LDS} formulation. \item Show how to obtain a traditional formulations (e.g.\ Hilbert) for an arbitrary {\em LDS} presented logic. \item Define and study major logical concepts intrinsic to {\em LDS} formalisms. \item Give detailed study of the {\em LDS} formulation of some major known logics (e.g.\ modal logics, resource logics) and demonstrate its advantages. \item Translate {\em LDS} into classical logic (reduce the `new' to the `old'), and explain {\em LDS} in the context of classical logic (two sorted logic, metalevel aspects, etc). \end{itemize} \begin{itemlist}{Chapter 1:} \item [Chapter 3:] Give fairly general definitions of some basic concepts of {\em LDS} theory, mainly to cater for the needs of the practical consumer of logic who may wish to apply it, with a detailed study of the metabox system. The presentation of Chapter 3 is a bit tricky. It may be too formal for the intuitive reader, but not sufficiently clear and elegant for the mathematical logician. I would be very grateful for comments from the readers for the next draft. \item [Chapter 4:] Presents the basic notions of algebraic {\em LDS}. The reader may wonder how come we introduce algebraic {\em LDS} in chapter 3 and then again in chapter 4. Our aim in chapter 3 is to give a general definition and formal machinery for the applied consumer of logic. Chapter 4 on the other hand studies {\em LDS} as formal logics. It turns out that to formulate an arbitrary logic as an {\em LDS} one needs some specific labelling algebras and these need to be studied in detail (chapter 4). For general applications it is more convenient to have general labelling algebras and possibly mathematically redundant formulations (chapter 3). In a sense chapter 4 continues the topic of the second section of chapter 3. \item [Chapter 5:] Present the full theory of {\em LDS} where labels can be databases from possibly another {\em LDS}. It also presents Fibred Semantics for {\em LDS}. \item [Chapter 6:] Presents a theory of quantifers for {\em LDS}. The material for this chapter is still under research. \item [Chapter 7:] Studies structured consequence relations. These are logical system swhere the structure is not described through labels but through some geometry like lists, multisets, trees, etc. Thus the label of a wff $A$ is implicit, given by the place of $A$ in the structure. \item [Chapter 8:] Deals with metalevel features of {\em LDS} and its translation into two sorted classical logic. \end{itemlist} Parts 3 and 4 of the book deals in detail with some specific families of logics. Chapters 9--11 essentailly deal with substructural logics and their variants. \begin{itemlist}{Chapter10:} \item [Chapter 9:] Studies resource and substructural logics in general. \item [Chapter 10:] Develops detailed proof theory for some systems as well as studying particular features such as negation. \item [Chapter 11:] Deals with many valued logics. \item [Chapter 12:] Studies the Curry Howard formula as type view and how it compres with labelling. \item [Chapter 13:] Deals with modal and temporal logics. \end{itemlist} Part 5 of the book deals with {\em LDS} metatheory. \begin{itemlist}{Chapter15:} \item [Chapter 14:] Deals with labelled tableaux. \item [Chapter 15:] Deals with combining logics. \item [Chapter 16:] Deals with abduction. \end{itemlist

Model and Proof Theory of Constructive ALC, Constructive Description Logics

Description logics (DLs) represent a widely studied logical formalism with a significant impact in the field of knowledge representation and the Semantic Web. However, they are equipped with a classical descriptive semantics that is characterised by a platonic notion of truth, being insufficiently expressive to deal with evolving and incomplete information, as from data streams or ongoing processes. Such partially determined and incomplete knowledge can be expressed by relying on a constructive semantics. This thesis investigates the model and proof theory of a constructive variant of the basic description logic ALC, called cALC. The semantic dimension of constructive DLs is investigated by replacing the classical binary truth interpretation of ALC with a constructive notion of truth. This semantic characterisation is crucial to represent applications with partial information adequately, and to achieve both consistency under abstraction as well as robustness under refinement, and on the other hand is compatible with the Curry-Howard isomorphism in order to form the cornerstone for a DL-based type theory. The proof theory of cALC is investigated by giving a sound and complete Hilbert-style axiomatisation, a Gentzen-style sequent calculus and a labelled tableau calculus showing finite model property and decidability. Moreover, cALC can be strengthened towards normal intuitionistic modal logics and classical ALC in terms of sound and complete extensions and hereby forms a starting point for the systematic investigation of a constructive correspondence theory.Beschreibungslogiken (BLen) stellen einen vieluntersuchten logischen Formalismus dar, der den Bereich der Wissensrepräsentation und das Semantic Web signifikant geprägt hat. Allerdings basieren BLen meist auf einer klassischen deskriptiven Semantik, die gekennzeichnet ist durch einen idealisierten Wahrheitsbegriff nach Platons Ideenlehre, weshalb diese unzureichend ausdrucksstark sind, um in Entwicklung befindliches und unvollständiges Wissen zu repräsentieren, wie es beispielsweise durch Datenströme oder fortlaufende Prozesse generiert wird. Derartiges partiell festgelegtes und unvollständiges Wissen lässt sich auf der Basis einer konstruktiven Semantik ausdrücken. Diese Arbeit untersucht die Model- und Beweistheorie einer konstruktiven Variante der Basis-BL ALC, die im Folgenden als cALC bezeichnet wird. Die Semantik dieser konstruktiven Beschreibungslogik resultiert daraus, die traditionelle zweiwertige Interpretation logischer Aussagen des Systems ALC durch einen konstruktiven Wahrheitsbegriff zu ersetzen. Eine derartige Interpretation ist die Voraussetzung dafür, um einerseits Anwendungen mit partiellem Wissen angemessen zu repräsentieren, und sowohl die Konsistenz logischer Aussagen unter Abstraktion als auch ihre Robustheit unter Verfeinerung zu gewährleisten, und andererseits um den Grundstein für eine Beschreibungslogik-basierte Typentheorie gemäß dem Curry-Howard Isomorphismus zu legen. Die Ergebnisse der Untersuchung der Beweistheorie von cALC umfassen eine vollständige und korrekte Hilbert Axiomatisierung, einen Gentzen Sequenzenkalkül, und ein semantisches Tableaukalkül, sowie Beweise zur endlichen Modelleigenschaft und Entscheidbarkeit. Darüber hinaus kann cALC zu normaler intuitionistischer Modallogik und klassischem ALC durch vollständige und korrekte Erweiterungen ausgebaut werden, und bildet damit einen Startpunkt für die systematische Untersuchung einer konstruktiven Korrespondenztheorie

Extensions of modal logic KTB and other topics

This thesis covers four topics. They are the extensions of the modal logic KTB, the use of normal forms in modal logic, automated reasoning in the modal logic S4 and the problem of unavoidable words. Extensions of KTB: The modal logic KTB is the logic of reflexive and symmetric frames. Dually, KTB-algebras have a unary (normal) operator f that satisfies the identities f (x){u2265}x and {u231D}x{u2264}f ({u231D}f(x)). Extensions of KTB are subvarieties of the algebra KTB. Both of these form a lattice, and we investigate the structure of the bottom of the lattice of subvarieties. The unique atom is known to correspond to the modal logic whose frame is a single reflexive point. Yutaka demonstrated that this atom has a unique cover, corresponding to the frame of the two element chain. We construct covers of this element, and so demonstrate that there are a continuum of such covers. Normal Forms in Modal Logic: Fine proposed the use of normal forms as an alternative to traditional methods of determining Kripke completeness. We expand on this paper and demonstrate the application of normal forms to a number of traditional modal logics, and define new terms needed to apply normal forms in this situation. Automated reasoning in 84: History based methods for automated reasoning are well understood and accepted. Pliu{u0161}kevi{u010D}ius & Pliu{u0161}kevi{u010D}ien{u0117} propose a new, potentially revolutionary method of applying marks and indices to sequents. We show that the method is flawed, and empirically compare a different mark/index based method to the traditional methods instead. Unavoidable words: The unavoidable words problem is concerned with repetition in strings of symbols. There are two main ways to identify a word as unavoidable, one based on generalised pattern matching and one from an algorithm. Both methods are in NP, but do not appear to be in P. We define the simple unavoidable words as a subset of the standard unavoidable words that can be identified by the algorithm in P-time. We define depth separating IX x homomorphisms as an easy way to generate a subset of the unavoidable words using the pattern matching method. We then show that the two simpler problems are equivalent to each other

IaaS-cloud security enhancement: an intelligent attribute-based access control model and implementation

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. [Continues.