物件導向軟體之架構(Object-Oriented Software Construction)探討

What is modal logic

The B Book

/pdf/introduction-to-boolean-algebras-3fm27i4jtx.pdf

Introduction to Boolean algebras

First‐order logic

Deontic action logic, atomic boolean algebras and fault-tolerance

In this paper we present a propositional deontic logic, with the goal of using it to specify fault-tolerant systems, and an axiomatization of it. We prove several results about this logic: completeness, soundness, compactness and decidability. The main technique used during the completeness proof is based on standard techniques for modal logics, but it has some new characteristics introduced for dealing with this logic. In addition, the logic provides several operators which appear useful for use in practice, in particular to model fault-tolerant systems and to reason about their fault tolerance properties.

A complete and compact propositional deontic logic

In [1] and [2] we have introduced a novel deontic action logic for reasoning about fault-tolerance In this paper we present a tableaux method for this logic; this proof system is sound and complete, and because the logic has the usual boolean operators on actions, it also allows us to deal successfully with action complement and parallel execution of actions Finally, we describe an example of application of this proof system which shows how the tableaux system can be used to obtain (counter-) models of specifications

A Tableaux System for Deontic Action Logic

Dynamic reconfiguration, understood as the ability to manage at run time the live components and how these interact in a system, is a feature that is crucial in various languages and computing paradigms, in particular in object orientation. In this paper, we study a categorical approach for characterising dynamic reconfiguration in a logical specification language. The approach is based on the notion of institution, which enables us to work in an abstract, logic independent, setting. Furthermore, our formalisation makes use of representation maps in order to relate the generic specification of components (e.g., as specified through classes) to the behaviour of actual instances in a dynamic environment. We present the essential characteristics for dealing with dynamic reconfiguration in a logical specification language, indicating their technical and practical motivations. As a motivational example, we use a temporal logic, component based formalism, but the analysis is general enough to be applied to other logics. Moreover, the use of representation maps in the formalisation allows for the combination of different logics for different purposes in the specification. We illustrate the ideas with a simple specification of a Producer-Consumer component based system.

Towards managing dynamic reconfiguration of software systems in a categorical setting

In goal-oriented requirements engineering approaches, conflict analysis has been proposed as an abstraction for risk analysis. Intuitively, given a set of expected goals to be achieved by the system-to-be, a conflict represents a subtle situation that makes goals diverge, i.e., not be satisfiable as a whole. Conflict analysis is typically driven by the identify-assess-control cycle, aimed at identifying, assessing and resolving conflicts that may obstruct the satisfaction of the expected goals. In particular, the assessment step is concerned with evaluating how likely the identified conflicts are, and how likely and severe are their consequences. So far, existing assessment approaches restrict their analysis to obstacles (conflicts that prevent the satisfaction of a single goal), and assume that certain probabilistic information on the domain is provided, that needs to be previously elicited from experienced users, statistical data or simulations. In this paper, we present a novel automated approach to assess how likely a conflict is, that applies to general conflicts (not only obstacles) without requiring probabilistic information on the domain. Intuitively, given the LTL formulation of the domain and of a set of goals to be achieved, we compute goal conflicts, and exploit string model counting techniques to estimate the likelihood of the occurrence of the corresponding conflicting situations and the severity in which these affect the satisfaction of the goals. This information can then be used to prioritize conflicts to be resolved, and suggest which goals to drive attention to for refinements.

Pablo F. Castro

Papers

Deontic action logic, atomic boolean algebras and fault-tolerance

A complete and compact propositional deontic logic

A Tableaux System for Deontic Action Logic

Towards managing dynamic reconfiguration of software systems in a categorical setting

Goal-conflict likelihood assessment based on model counting