This thesis studies the use of dynamic epistemic logics for the sake of information privacy. The core of the work is the synthesis of three approaches: security logics from A. Hommersom, plausibility frames and communication logic from A. Baltag and S. Smets, and studies concerning the so called Russian cards protocol. Thereafter we present a program, made in the NetLogo environment, in order to demonstrate the workings of the basic ideas.

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.

Software product line engineering is a common method for designing complex software systems. Feature modeling is the most common approach to specify product lines. A feature model is a feature diagram (a special tree of features) plus some crosscutting constraints. Feature modeling languages are grouped into basic and cardinality-based models. The common understanding of the semantics of feature models is a Boolean semantics. We discuss a major deficiency of this semantics and fix it by applying, in turn, modal logic, the theory of multisets, and formal language theory. In order to adequately represent the semantics of basic models, we propose a Kripke semantics and show that basic feature modeling needs a modal rather than Boolean logic. We propose two multiset based theories for cardinality-based feature diagrams, called flat and hierarchical semantics. We show that the hierarchical semantics of a given cardinality-based diagram captures all information in the diagram. We also charac- terize sets of multisets, which can provide a hierarchical semantics of some diagrams. We provide three different reduction processes going from a cardinality-based diagram to an appropriate regular expression. As for crosscutting constraints, we propose a formal language interpretation of them. We also characterize some existing analysis operations over feature models in terms of operations on the corresponding languages and discuss the relevant decidability problems. / Thesis / Doctor of Philosophy (PhD)

Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics - which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics. / This report has also appeared as Report No. 03-03, Department of Computer Science, The University of Iowa.

<p>Many computer systems in our daily life require highly available applications (such as medical equipment) and some others run on difficult to access places (such as satellites). These systems are subject to a variety of potential failures that may degrade their performance. Therefore, being able to reason about faults and their impact on systems is gaining considerable attention. Existing work on fault tolerance is mostly focused on addressing faults at the programming language level. In the recent past, significant efforts have been made to use formal methods to specify and verify fault tolerant systems to provide more reliable software. Related with this, some researchers have pointed out that Deontic Logic is useful for reasoning about fault tolerant systems due to its expressive nature in relation to defining norms, used to describe expected behaviour and prescribing what happens when these norms are violated.</p> <p>In this thesis, we demonstrate how Deontic Logic can be used to model an existing real world problem concerning fault tolerance mechanisms. We consider different situations that a vehicle faces on the road and the consequent reactions of the driver or vehicle based on good and bad behaviour. We got the idea and motivation for this case study from the SASPENCE sub-project, conducted under the European Integrated Project PReVENT. This sub-project focuses on a vehicle’s behaviour in maintaining safe speed and safe distance on the road. As our first modelling attempt, we use a Propositional Deontic Logic approach, to justify to what extent we can apply this Logical approach to model a real world problem. Subsequently, we use a First Order Deontic Logic approach, as it can incorporate the use of parameters and quantification over them, which is more useful to model real world scenarios.</p> <p>We state and prove some interesting expected properties of the models using a First Order proof system. Based on these modelling exercises, we acquired different engineering ideas and lessons, and present them in this thesis in order to aid modelling of future fault tolerant systems.</p> / Master of Science (MSc)

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.

Pushdown systems equip a finite state system with an unbounded stack memory, and are thus infinite state. By recording the call history on the stack, these systems provide a natural model for recursive procedure calls. Model-checking for pushdown systems has been well-studied. Tools implementing pushdown model-checking (e.g. Moped) are an essential back-end component of high-profile software model checkers such as SLAM, Blast and Terminator. Higher-order pushdown systems define a more complex memory structure: a higher-order stack is a stack of lower-order stacks. These systems form a robust hierarchy closely related to the Caucal hierarchy and higher-order recursion schemes. This latter connection demonstrates their importance as models for programs with higher-order functions. We study the global model-checking problem for (higher-order) pushdown systems. In particular, we present a new algorithm for computing the winning regions of a parity game played over an order-1 pushdown system. We then show how to compute the winning regions of two-player reachability games over order-n pushdown systems. These algorithms extend the saturation methods of Bouajjani, Esparza and Maler for order-1 pushdown systems, and Bouajjani and Meyer for higher-order pushdown systems with a single control state. These techniques begin with an automaton recognising (higher-order) stacks, and iteratively add new transitions until the automaton becomes saturated. The reachability result, presented at FoSSaCS 2007 and in the LMCS journal, is the main contribution of the thesis. We break the saturation paradigm by adding new states to the automaton during the iteration. We identify the fixed points required for termination by tracking the updates that are applied, rather than by observing the transition structure. We give a number of applications of this result to LTL model-checking, branching-time model-checking, non-emptiness of higher-order pushdown automata and Büchi games. Our second major contribution is the first application of the saturation technique to parity games. We begin with a mu-calculus characterisation of the winning region. This formula alternates greatest and least fixed point operators over a kind of reachability formula. Hence, we can use a version of our reachability algorithm, and modifications of the Büchi techniques, to compute the required result. The main advantages of this approach compared to existing techniques due to Cachat, Serre and Vardi et al. are that it is direct and that it is not immediately exponential in the number of control states, although the worst-case complexity remains the same.

This thesis presents TransLucid, a low-level, purely declarative, intensional programming language. Built on a simple algebra and with just a small number of primitives, TransLucid programs define arbitrary dimensional infinite data structures, which are then queried to produce results. The formal foundations of TransLucid come from the work in intensional logic by Montague and Scott. The background chapters give a history of intensional logic and its predecessors in the Western world, as well as a history of intensional programming and Lucid, the first intensional programming language. The semantics of TransLucid are fully specified in the form of operational semantics. Three levels of semantics are given, in increasing order of efficiency, with the sequential warehouse semantics, the most efficient, being presented together with a proof that any expression will be evaluated by only examining relevant dimensions in the current context. The language is then extended in three important ways, by adding versioned identifiers, (declarative) side-effects and timestamped equations and demands. Adding versioned identifiers to TransLucid enriches the expressiveness of the language and allows the encoding of a variety of programming paradigms, ranging from manipulating large data-cubes to pattern-matching. Adding side-effects supports one of the main reasons for TransLucid: namely, to provide a target language, together with a methodology, for translating the main programming paradigms, thus creating a uniform end platform that can be the focus for optimisation and program verification. A translation of imperative programs into TransLucid is given. Timestamped equations and demands enable TransLucid to become a language for synchronous programming in real-time systems, as well as allowing runtime updates to a program's equations. The language TransLucid represents a decisive advance in declarative programming. It has applications in many fields of computer science and opens up exciting new avenues of research.

This dissertation is focused on an algebraic approach of some many-valued generalizations of modal logics. The starting point is the definition of the [0,1]-valued and the Ł_n-valued Kripke models, where [0,1] denotes the well known MV-algebra and Ł_n its finite subalgebra {0, 1/n, ... , (n-1)/n,1} for any positive integer n. Two types of structures are used to define validity of formulas: the class of L-frames and the class of Ł_n-valued L-frames. The latter structures are L-frames in which we specify in each world u the set Ł_m (where m is a divisor of n) of the possible truth values of the formulas in u. These two classes of structures define two distinct notions of validity. We use these notions to study the problem of definability of classes of structures with modal formulas. We obtain for these two classes an equivalent of the Goldblatt-Thomason theorem. We are able to consider completeness problems with respect to these relational semantics thanks to the connections between relational and algebraic semantics. Our strongest results are about Ł_n-valued logics. We are indeed able to apply and develop algebraic tools (namely, canonical and strong canonical extensions) that allow to generate complete Ł_n-valued logics. / Nous consacrons cette dissertation à une étude algébrique de certaines généralisations multivaluées des logiques modales. Notre point de départ est la définition des modèle de Kripke [0,1]-valués et Ł_n-valués, où [0,1] désigne la MV-algèbre bien connue et Ł_n sa sous-algèbre {0, 1/n, ... , (n-1)/n,1} pour tout naturel non nul n. Nous utilisons deux types de structures pour définir une relation de validité: la classe des L-structures et celles des L-structures Ł_n-valuées. Ces dernières sont des L-structures dans lesquelles nous précisons pour chaque monde u l'ensemble Ł_m (où m est un diviseur de n) des valeurs de vérité que les formules sont autorisées à prendre en u. Ces deux classes de structures définissent deux notions distinctes de validité. Nous les utilisons pour étudier le problème de la définissabilité des classes de structures à l'aide du langage modal. Nous obtenons dans les deux cas l'équivalent du théorème de Goldblatt-Thomason. Nous considérons aussi les problèmes de complétude vis-à-vis de ces sémantiques relationnelles à l'aide des liens qui les lient à la sémantique algébrique. Les résultats les plus forts que nous obtenons concernent les logiques modales Ł_n-valuées. En effet, dans ce cas, nous pouvons appliquer et développer des outils algébriques (à savoir, les extensions canoniques et les extensions canoniques fortes) qui permettent de générer des logiques complètes.

In this thesis, the main focus is on deontic logic as a tool for formal representation of moral reasoning in natural language. The simple standard system of deontic logic (SDL), i.e. the minimal Kripkean modal logic extended with the deontic axiom, stating that necessity (interpreted as obligation) implies possibility (interpreted as permission), has often been considered inadequate for this aim, due to different problems, e.g. the so-called deontic paradoxes. A general survey of deontic logic and the problems with SDL is made in chapter 1. In chapter 2, a system denoted Classical Deontic-Modal logic (CDM1) is defined. In this system, there is a primary obligation operator indexed to sets of possible worlds, and a secondary requirement operator, defined in terms of strictly necessary conditions for fulfilling an obligation. This secondary operator has most of the properties of the necessity operator in SDL. In chapters 3 and 4, it is argued that CDM1 is able to handle the SDL problems presented in chapter 1 in an adequate way, and the treatment of these problems in CDM1 is also compared with their treatment in some other well-known deontic systems. In chapter 5, it is argued that even though the problems related to quantification in modal contexts are relevant to deontic logic, these issues are not specific to deontic logic. In chapter 6, the relations between some controversial features of moral reasoning, such as moral dilemmas and “non-standard” deontic categories like supererogation, and deontic logic are discussed. It is shown how CDM1 can be modified in order to accommodate these features.