Alternating Transition Systems Research Articles

States, goals and values: Revisiting practical reasoning

In this paper we address some limitations with proposals concerning an argumentation scheme for practical reasoning grounded on action-based alternating transition systems augmented with values. In particular, we extend the machinery to enable the proper representation of, and ability to reason with, goals. This allows the more satisfactory representation of certain critical questions, and the means to explicitly record differences between agents as to what will count as the fulfillment of goals and the promotion of values. It also allows us to express desires in terms of values, and to make plain the relation between a change in circumstances and the promotion and demotion of values. Three detailed examples are used to illustrate the additional kinds of problem the extensions allow us to consider.

A modal characterization of alternating approximate bisimilarity

Recently, alternating transition systems are adopted to describe control systems with disturbances and their finite abstract systems. In order to capture the equivalence relation between these systems, a notion of alternating approximate bisimilarity is introduced. This paper aims to establish a modal characterization for alternating approximate bisimilarity. Based on this result, we provide a link between specifications satisfied by the samples of control systems with disturbances and their finite abstractions. Moreover, a simple example is given to illustrate the application of such link in the design of controller of control systems.

Did he jump or was he pushed?

In this paper, we present a particular role for abductive reasoning in law by applying it in the context of an argumentation scheme for practical reasoning. We present a particular scheme, based on an established scheme for practical reasoning, that can be used to reason abductively about how an agent might have acted to reach a particular scenario, and the motivations for doing so. Plausibility here depends on a satisfactory explanation of why this particular agent followed these motivations in the particular situation. The scheme is given a formal grounding in terms of action-based alternating transition systems and we illustrate the approach with a running legal example.

On the Expressiveness and Complexity of ATL

ATL is a temporal logic geared towards the specification and verification of properties in multi-agents systems. It allows to reason on the existence of strategies for coalitions of agents in order to enforce a given property. In this paper, we first precisely characterize the complexity of ATL model-checking over Alternating Transition Systems and Concurrent Game Structures when the number of agents is not fixed. We prove that it is \Delta^P_2 - and \Delta^P_?_3-complete, depending on the underlying multi-agent model (ATS and CGS resp.). We also consider the same problems for some extensions of ATL. We then consider expressiveness issues. We show how ATS and CGS are related and provide translations between these models w.r.t. alternating bisimulation. We also prove that the standard definition of ATL (built on modalities "Next", "Always" and "Until") cannot express the duals of its modalities: it is necessary to explicitely add the modality "Release".

Model Checking Abilities of Agents: A Closer Look

Alternating-time temporal logic (atl) is a logic for reasoning about open computational systems and multi-agent systems. It is well known that atl model checking is linear in the size of the model. We point out, however, that the size of an atl model is usually exponential in the number of agents. When the size of models is defined in terms of states and agents rather than transitions, it turns out that the problem is (1) Δ3P-complete for concurrent game structures, and (2) Δ2P-complete for alternating transition systems. Moreover, for “Positive atl” that allows for negation only on the level of propositions, model checking is (1) Σ2P-complete for concurrent game structures, and (2) NP-complete for alternating transition systems. We show a nondeterministic polynomial reduction from checking arbitrary alternating transition systems to checking turn-based transition systems, We also discuss the determinism assumption in alternating transition systems, and show that it can be easily removed. In the second part of the paper, we study the model checking complexity for formulae of atlwith imperfect information (atlir). We show that the problem is Δ2P-complete in the number of transitions and the length of the formula (thereby closing a gap in previous work of Schobbens in Electron. Notes Theor. Comput. Sci. 85(2), 2004). Then, we take a closer look and use the same fine structure complexity measure as we did for atl with perfect information. We get the surprising result that checking formulae of atlir is also Δ3P-complete in the general case, and Σ2P-complete for “Positive atlir”. Thus, model checking agents’ abilities for both perfect and imperfect information systems belongs to the same complexity class when a finer-grained analysis is used.

Modeling software product lines using color-blind transition systems

Families of embedded discrete finite state programs are modeled using input-enabled alternating transition systems. One model describes all functionality, while each variant is defined by an environment, describing its possible uses. The environments show both the inputs that a system can receive and indicate which of the system’s responses are relevant for the environment. The latter trait, called color-blindness, creates new possibilities for system transformations in the specialization process. We demonstrate the use of the framework by applying it to two classes of realistic design languages. An example of a product line of alarm clocks is used throughout the article.

Addressing moral problems through practical reasoning

In this paper, following the work of Hare, we consider moral reasoning not as the application of moral norms and principles, but as reasoning about what ought to be done in a particular situation, with moral norms perhaps emerging from this reasoning. We model this situated reasoning drawing on our previous work on argumentation schemes, here set in the context of Action-Based Alternating Transition Systems. We distinguish what prudentially ought to be done from what morally ought to be done, consider what legislation might be appropriate and characterise the differences between morally correct, morally praiseworthy and morally excusable actions. We also describe an implementation which simulates this reasoning and discuss some issues arising from the simulation.

Practical reasoning as presumptive argumentation using action based alternating transition systems

In this paper we describe an approach to practical reasoning, reasoning about what it is best for a particular agent to do in a given situation, based on presumptive justifications of action through the instantiation of an argument scheme, which is then subject to examination through a series of critical questions. We identify three particular aspects of practical reasoning which distinguish it from theoretical reasoning. We next provide an argument scheme and an associated set of critical questions which is able to capture these features. In order that both the argument scheme and the critical questions can be given precise interpretations we use the semantic structure of an Action-Based Alternating Transition System as the basis for their definition. We then work through a detailed example to show how this approach to practical reasoning can be applied to a problem solving situation, and briefly describe some other previous applications of the general approach. In a second example we relate our account to the social laws paradigm for co-ordinating multi-agent systems. The contribution of the paper is to provide firm foundations for an approach to practical reasoning based on presumptive argument in terms of a well-known model for representing the effects of actions of a group of agents.

Comparing Semantics of Logics eor Multi-Agent Systems

We draw parallels between several closely related logics that combine – in different proportions – elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly in 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der Hoek and Wooldridge (2002). In particular, we establish some subsumption and equivalence results for their semantics, as well as interpretation of the alternating-time temporal epistemic logic into ATL. The focus in this paper is on models: alternating transition systems, multi-player game models (alias concurrent game structures) and coalition effectivity models turn out to be intimately related, while alternating epistemic transition systems share much of their philosophical and formal apparatus. Our approach is constructive: we present ways to transform between different types of models and languages.

A game-based verification of non-repudiation and fair exchange protocols1

In this paper, we report on a recent work for the verification of non-repudiation protocols. We propose a verification method based on the idea that non-repudiation protocols are best modeled as games. To formalize this idea, we use alternating transition systems, a game based model, to model protocols and alternating temporal logic, a game based logic, to express requirements that the protocols must ensure. This method is automated by using the model-checker MOCHA, a model-checker that supports the alternating transition systems and the alternating temporal logic. Several optimistic protocols are analyzed using MOCHA.