Boolean Functions as Models for Quantified Boolean Formulas

In this paper, we introduce the notion of models for quantified Boolean formulas. For various classes of quantified Boolean formulas and various classes of Boolean functions, we investigate the problem of determining whether a model exists. Furthermore, we show for these classes the complexity of the model checking problem, which is to check whether a given set of Boolean functions is a model for a formula. For classes of Boolean functions, we establish some characterizations in terms of classes of quantified Boolean formulas that have such a model. This research has been supported in part by the Air Force Office of Scientific Research under grant FA9550-06-1-0050. This research has been supported in part by the NSFC under grants 60573011 and 10410638.     

A survey on networking games in telecommunications

In this survey, we summarize different modeling and solution concepts of networking games, as well as a number of different applications in telecommunications that make use of or can make use of networking games. We identify some of the mathematical challenges and methodologies that are involved in these problems. We include here work that has relevance to networking games in telecommunications from other areas, in particular from transportation planning.     

Boolean set operations on non-manifold boundary representation objects

For Boolean operations on geometric models, we have developed an intersection algorithm for non-manifold boundary models with vertices, linear edges, planar faces, and volumetric regions. The algorithm operates by intersecting entities in an ordered manner, from vertex to edge, then to face elements. Singular intersections are systematically handled by determining if an entity in one object is within a tolerance region of the entity in the other object. The algorithm performs Boolean operations between objects of different dimensionality as well as solids. An implementation of the proposed algorithm and the experimental results are briefly discussed.     

A decidable first-order logic for knowledge representation

Decidable first-order logics with reasonable model-theoretic semantics have several benefits for knowledge representation. These logics have the expressive power of standard first order logic along with an inference algorithm that will always terminate, both important considerations for knowledge representation. Knowledge representation systems that include a faithful implementation of one of these logics can also use its model-theoretic semantics to provide meanings for the data they store. One such logic, a variant of a simple type of first-order relevance logic, is developed and its properties described. This logic, although extremely weak, does capture a non-trivial and well-motivated set of inferences that can be entrusted to a knowledge representation system.This is a revised and much extended version of a paper of the same name that appears in the Proceedings of the Ninth International Joint Conference on Artificial Intelligence, Los Angeles, California, 1985.     

Soft cooperation systems and games

A cooperative game for a set of agents establishes a fair allocation of the profit obtained for their cooperation. In order to obtain this allocation, a characteristic function is known. It establishes the profit of each coalition of agents if this coalition decides to act alone. Originally players are considered symmetric and then the allocation only depends on the characteristic function; this paper is about cooperative games with an asymmetric set of agents. We introduced cooperative games with a soft set of agents which explains those parameters determining the asymmetry among them in the cooperation. Now the characteristic function is defined not over the coalitions but over the soft coalitions, namely the profit depends not only on the formed coalition but also on the attributes considered for the players in the coalition. The best known of the allocation rules for cooperative games is the Shapley value. We propose a Shapley kind solution for soft games.     

Reasoning about coalitional games

We develop, investigate, and compare two logic-based knowledge representation formalisms for reasoning about coalitional games. The main constructs of Coalitional Game Logic (cgl) are expressions for representing the ability of coalitions, which may be combined with expressions for representing the preferences that agents have over outcomes. Modal Coalitional Game Logic (mcgl) is a normal modal logic, in which the main construct is a modality for expressing the preferences of groups of agents. For both frameworks, we give complete axiomatisations, and show how they can be used to characterise solution concepts for coalitional games. We show that, while cgl is more expressive than mcgl, the former can only be used to reason about coalitional games with finitely many outcomes, while mcgl can be used to reason also about games with infinitely many outcomes, and is in addition more succinct. We characterise the computational complexity of satisfiability for cgl, and give a tableaux-based decision procedure.     

Solutions and properties of multi-stage stackelberg games

The inducible region concept is used to solve multistage, deterministic Stackelberg games, and to study properties of the solutions. We first delineate the inducible region by using a process similar to dynamic programming. A desired outcome is then selected from the region. To construct a Stackelberg strategy, we move forwards in time to cover various contingent situations. This approach gives a distinct picture about the nature of the problem. In particular, two aspects of the principle of the optimality are discussed. A design procedure is presented to construct a relatively robust Stackelberg strategy. The issue of credibility is also addressed.     

Deontic logic in the representation of law: Towards a methodology

There seems to be no clear consensus in the existing literature about the role of deontic logic in legal knowledge representation — in large part, we argue, because of an apparent misunderstanding of what deontic logic is, and a misplaced preoccupation with the surface formulation of legislative texts. Our aim in this paper is to indicate, first, which aspects of legal reasoning are addressed by deontic logic, and then to sketch out the beginnings of a methodology for its use in the analysis and representation of law.The essential point for which we argue is that deontic logic — in some form or other —needs to be taken seriously whenever it is necessary to make explicit, and then reason about, the distinction between what ought to be the case and what is the case, or as we also say, between the ideal and the actual. We take the library regulations at Imperial College as the main illustration, and small examples from genuinely legal domains to introduce specific points. In conclusion, we touch on the role of deontic logic in the development of the theory of normative positions.Deontic logic and the theory of normative positions are of relevance to legal knowledge representation, but also to the analysis and. representation of normative systems generally. The emphasis of the paper is on legal knowledge representation, but we seek to place the discussion within the context of a broader range of issues concerning the role of deontic logic in Computer Science.     

Compactly representing utility functions using weighted goals and the max aggregator

Weighted propositional formulas can be used to model preferences over combinatorial domains: each formula represents a goal we would like to see satisfied, the weight of a formula represents the importance of the goal in question, and to assess the desirability of a given alternative we aggregate the weights of the goals satisfied by that alternative. One of several options is to aggregate by using the maximum of the weights of the satisfied goals. This approach gives rise to a family of preference representation languages, one for each of a range of possible restrictions we can impose on either formulas or weights. We analyze the properties of these languages and establish results regarding their expressivity, and absolute and relative succinctness. We also study the computational complexity of the problem of finding the best and the worst alternative for a given set of weighted goals, and of finding an alternative that is optimal for a group of agents, for a range of different notions of collective optimality proposed in social choice theory and welfare economics.     

Belief representation in a deductivist type-free doxastic logic

Konolige's technical notion of belief based on deduction structures is briefly reviewed and its usefulness for the design of artificial agents with limited representational and deductive capacities is pointed out. The design of artificial agents with more sophisticated representational and deductive capacities is then taken into account. Extended representational capacities require in the first place a solution to the intensional context problems. As an alternative to Konolige's modal first-order language, an approach based on type-free property theory is proposed. It considers often neglected issues, such as the need for a more general account of thede dicto-de re distinction, and quasi-indicators. Extended deductive capacities require a subdivision of Konolige's notion of belief into two distinct technical notions,potential anddispositional belief. The former has to do with what an artificial agent could in principle come to actively believe, given enough time and its specific logical competence; the latter with what an agent can be assumed to believe with respect to a specific goal to be fulfilled.     

双边多问题自治协商的发展研究

自治多问题协商是现实应用领域中比较重要而有价值的研究领域,特别是在电子商务领域。通过协商可以得到“双赢”的结果。本文总结了双边多问题自治协商的研究现状。从经济学角度分析了合作环境和非合作环境的协商各自特点和适用范围;从人工智能角度给出了主要研究方向及研究手段,并且专门对协商中应用的两种协商技术:偏好和多原则决策进行讨论。最后给出了未来自治协商的研究方向和展望。     

Extended Semantics and Optimization Algorithms for CP-Networks

Preference elicitation is a serious bottleneck in many decision support applications and agent specification tasks. Ceteris paribus (CP)-nets were designed to make the process of preference elicitation simpler and more intuitive for lay users by graphically structuring a set of CP preference statements—preference statements that most people find natural and intuitive. Beside their usefulness in the process of preference elicitation, CP-nets support efficient optimization algorithms that are crucial in most applications (e.g., the selection of the best action to execute or the best product configuration). In various contexts, CP-nets with an underlying cyclic structure emerge naturally. Often, they are inconsistent according to the current semantics, and the user is required to revise them. In this paper, we show how optimization queries can be meaningfully answered in many "inconsistent" networks without troubling the user with requests for revisions. In addition, we describe a method for focusing the user's revision process when revisions are truly needed. In the process, we provide a formal semantics that justifies our approach and new techniques for computing optimal outcomes. Some of the methods we use are based on a reduction to the problem of computing stable models for nonmonotonic logic programs, and we explore this relationship closely.     

Matrix games with interval data

The conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. In the real world, sometimes the payoffs are not known and have to be estimated, and sometimes the payoffs are only approximately known. This paper develops a solution method for the two-person zero-sum game where the payoffs are imprecise and are represented by interval data. Since the payoffs are imprecise, the value of the game should be imprecise as well. A pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the value of the game. Based on the duality theorem and by applying a variable substitution technique, the pair of two-level mathematical programs is transformed to a pair of ordinary one-level linear programs. Solving the pair of linear programs produces the interval of the value of the game. It is shown that the two players in the game have the same upper bound and lower bound for the value of the imprecise game. An example illustrates the whole idea and sheds some light on imprecise game.     

Search in games with incomplete information: a case study using Bridge card play

We examine search algorithms in games with incomplete information, formalising a best defence model of such games based on the assumptions typically made when incomplete information problems are analysed in expert texts. We show that equilibrium point strategies for optimal play exist for this model, and define an algorithm capable of computing such strategies. Using this algorithm as a reference we then analyse search architectures that have been proposed for the incomplete information game of Bridge. These architectures select strategies by analysing some statistically significant collection of complete information sub-games. Our model allows us to clearly state the limitations of such architectures in producing expert analysis, and to precisely formalise and distinguish the problems that lead to sub-optimality. We illustrate these problems with simple game trees and with actual play situations from Bridge itself.     

Analyzing the dynamics of stigmergetic interactions through pheromone games

The concept of stigmergy provides a simple framework for interaction and coordination in multi-agent systems. However, determining the global system behavior that will arise from local stigmergetic interactions is a complex problem. In this paper we propose to use Game Theory to analyze stigmergetic interactions. We show that a system where agents coordinate by sharing local pheromone information can be approximated by a limiting pheromone game in which different pheromone vectors represent player strategies. This game view allows us to use established methods and solution concepts from game theory to describe the properties of stigmergy based systems. Our goal is to provide a new framework to aid in the understanding and design of pheromone interactions. We demonstrate how we can use this system to determine the long term system behavior of a simple pheromone model, by analyzing the convergence properties of the pheromone update rule in the approximating game. We also apply this model to cases where multiple colonies of agents concurrently optimize different objectives. In this case a limiting colony game can be linked to colony level interactions to characterize the global system behavior.     

棋牌游戏与事件对策

博弈的原意便是下棋,博弈论的概念也源于棋类游戏．而博弈论的现有成果还难以描述和处理棋牌游戏这一类复杂的动态过程．为此．在分析棋牌游戏特点的基础上．指出它们属于离散事件的动态过程;在阐述离散事件动态系统（DEDS）特点与方法的基础上,应用DEDS的有关理论为象棋博弈过程建模,并提出了事件对策的概念与形式框架．探讨了事件对策理论在战争模拟中的应用,为迅速发展的机器博弈研究创造了良好的理论条件．     

Embedding defaults into terminological knowledge representation formalisms

We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of first-order logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter's semantics. On the algorithmic side, we show that this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are applied only to individuals that are explicitly present in the knowledge base. In this semantics it is possible to compute all extensions of a finite terminological default theory, which means that this type of default reasoning is decidable. We describe an algorithm for computing extensions and show how the inference procedures of terminological systems can be modified to give optimal support to this algorithm.This is a revised and extended version of a paper presented at the3rd International Conference on Principles of Knowledge Representation and Reasoning, October 1992, Cambridge, MA.