The Complexity of Synthesizing Uniform Strategies

We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable. Typically, we can state that a strategy is observation-based. We propose a formal language to specify uniformity properties, interpreted over two-player turn-based arenas equipped with a binary relation between plays. This way, we capture e.g. games with winning conditions expressible in epistemic temporal logic, whose underlying equivalence relation between plays reflects the observational capabilities of agents (for example, synchronous perfect recall). Our framework naturally generalizes many other situations from the literature. We establish that the problem of synthesizing strategies under uniformity constraints based on regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007

Cognitive context and arguments from ontologies for learning

The deployment of learning resources on the web by different experts has resulted in the accessibility of multiple viewpoints about the same topics. In this work we assume that learning resources are underpinned by ontologies. Different formalizations of domains may result from different contexts, different use of terminology, incomplete knowledge or conflicting knowledge. We define the notion of cognitive learning context which describes the cognitive context of an agent who refers to multiple and possibly inconsistent ontologies to determine the truth of a proposition. In particular we describe the cognitive states of ambiguity and inconsistency resulting from incomplete and conflicting ontologies respectively. Conflicts between ontologies can be identified through the derivation of conflicting arguments about a particular point of view. Arguments can be used to detect inconsistencies between ontologies. They can also be used in a dialogue between a human learner and a software tutor in order to enable the learner to justify her views and detect inconsistencies between her beliefs and the tutor’s own. Two types of arguments are discussed, namely: arguments inferred directly from taxonomic relations between concepts, and arguments about the necessary an

Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility

State-of-the-art on evolution and reactivity

This report starts by, in Chapter 1, outlining aspects of querying and updating resources on the Web and on the Semantic Web, including the development of query and update languages to be carried out within the Rewerse project. From this outline, it becomes clear that several existing research areas and topics are of interest for this work in Rewerse. In the remainder of this report we further present state of the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs; in Chapter 4 event-condition-action rules, both in the context of active database systems and in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks

Refinement Modal Logic

In this paper we present {\em refinement modal logic}. A refinement is like a bisimulation, except that from the three relational requirements only `atoms' and `back' need to be satisfied. Our logic contains a new operator 'all' in addition to the standard modalities 'box' for each agent. The operator 'all' acts as a quantifier over the set of all refinements of a given model. As a variation on a bisimulation quantifier, this refinement operator or refinement quantifier 'all' can be seen as quantifying over a variable not occurring in the formula bound by it. The logic combines the simplicity of multi-agent modal logic with some powers of monadic second-order quantification. We present a sound and complete axiomatization of multi-agent refinement modal logic. We also present an extension of the logic to the modal mu-calculus, and an axiomatization for the single-agent version of this logic. Examples and applications are also discussed: to software verification and design (the set of agents can also be seen as a set of actions), and to dynamic epistemic logic. We further give detailed results on the complexity of satisfiability, and on succinctness

Calculus for decision systems

The conceptualization of the term system has become highly dependent on the application domain. What a physicist means by the term system might be different than what a sociologist means by the same term. In 1956, Bertalanffy [1] defined a system as a set of units with relationships among them . This and many other definitions of system share the idea of a system as a black box that has parts or elements interacting between each other. This means that at some level of abstraction all systems are similar, what eventually differentiates one system from another is the set of underlining equations which describe how these parts interact within the system. ^ In this dissertation we develop a framework that allows us to characterize systems from an interaction level, i.e., a framework that gives us the capability to capture how/when the elements of the system interact. This framework is a process algebra called Calculus for Decision Systems (CDS). This calculus provides means to create mathematical expressions that capture how the systems interact and react to different stimuli. It also provides the ability to formulate procedures to analyze these interactions and to further derive other interesting insights of the system. ^ After defining the syntax and reduction rules of the CDS, we develop a notion of behavioral equivalence for decision systems. This equivalence, called bisimulation, allows us to compare decision systems from the behavioral standpoint. We apply our results to games in extensive form, some physical systems, and cyber-physical systems. ^ Using the CDS for the study of games in extensive form we were able to define the concept of subgame perfect equilibrium for a two-person game with perfect information. Then, we investigate the behavior of two games played in parallel by one of the players. We also explore different couplings between games, and compare - using bisimulation - the behavior of two games that are the result of two different couplings. The results showed that, with some probability, the behavior of playing a game as first player, or second player, could be irrelevant. ^ Decision systems can be comprised by multiple decision makers. We show that in the case where two decision makers interact, we can use extensive games to represent the conflict resolution. For the case where there are more than two decision makers, we presented how to characterize the interactions between elements within an organizational structure. Organizational structures can be perceived as multiple players interacting in a game. In the context of organizational structures, we use the CDS as an information sharing mechanism to transfer the inputs and outputs from one extensive game to another. We show the suitability of our calculus for the analysis of organizational structures, and point out some potential research extensions for the analysis of organizational structures. ^ The other general area we investigate using the CDS is cyber-physical systems. Cyber-physical systems or CPS is a class of systems that are characterized by a tight relationship between systems (or processes) in the areas of computing, communication and physics. We use the CDS to describe the interaction between elements in some simple mechanical system, as well as a particular case of the generalized railroad crossing (GRC) problem, which is a typical case of CPS. We show two approaches to the solution of the GRC problem. ^ This dissertation does not intend to develop new methods to solve game theoretical problems or equations of motion of a physical system, it aims to be a seminal work towards the creation of a general framework to study systems and equivalence of systems from a formal standpoint, and to increase the applications of formal methods to real-world problems