Minimal Belief and Negation as Failure in Multi-Agent Systems

We propose an epistemic, nonmonotonic approach to the formalization of knowledge in a multi-agent setting. From the technical viewpoint, a family of nonmonotonic logics, based on Lifschitz's modal logic of minimal belief and negation as failure, is proposed, which allows for formalizing an agent which is able to reason about both its own knowledge and other agents' knowledge and ignorance. We define a reasoning method for such a logic and characterize the computational complexity of the major reasoning tasks in this formalism. From the practical perspective, we argue that our logical framework is well-suited for representing situations in which an agent cooperates in a team, and each agent is able to communicate his knowledge to other agents in the team. In such a case, in many situations the agent needs nonmonotonic abilities, in order to reason about such a situation based on his own knowledge and the other agents' knowledge and ignorance. Finally, we show the effectiveness of our framework in the robotic soccer application domain.     

Multi-modal nonmonotonic logics of minimal knowledge

In this paper we introduce multi-modal logics of minimal knowledge. Such a family of logics constitutes the first proposal in the field of epistemic nonmonotonic logic in which the three following aspects are simultaneously addressed: (1) the possibility of formalizing multiple agents through multiple modal operators; (2) the possibility of using first-order quantification in the modal language; (3) the possibility of formalizing nonmonotonic reasoning abilities for the agents modeled, based on the principle of minimal knowledge. We illustrate the expressive capabilities of multi-modal logics of minimal knowledge to provide a formal semantics to peer-to-peer data integration systems, which constitute one of the most recent and complex architectures for distributed information systems.      

Reasoning about Minimal Knowledge in Nonmonotonic Modal Logics

We study the problem of embedding Halpern and Moses's modal logic of minimal knowledge states into two families of modal formalism for nonmonotonic reasoning, McDermott and Doyle's nonmonotonic modal logics and ground nonmonotonic modal logics. First, we prove that Halpern and Moses's logic can be embedded into all ground logics; moreover, the translation employed allows for establishing a lower bound (3p) for the problem of skeptical reasoning in all ground logics. Then, we show a translation of Halpern and Moses's logic into a significant subset of McDermott and Doyle's formalisms. Such a translation both indicates the ability of Halpern and Moses's logic of expressing minimal knowledge states in a more compact way than McDermott and Doyle's logics, and allows for a comparison of the epistemological properties of such nonmonotonic modal formalisms.     

A Framework for Automated Reasoning in Multiple-Valued Logics

The language of signed formulas offers a first-order classical logic framework for automated reasoning in multiple-valued logics. It is sufficiently general to include both annotated logics and fuzzy operator logics. Signed resolution unifies the two inference rules of annotated logics, thus enabling the development of an SLD-style proof procedure for annotated logic programs. Signed resolution also captures fuzzy resolution. The logic of signed formulas offers a means of adapting most classical inference techniques to multiple-valued logics.     

基于一阶模态逻辑的模糊推理

研究基于可信度的模糊一阶模态逻辑,给出了基于常域的模糊一阶模态逻辑语义以及推理形式系统描述.为有效进行模糊断言间的推理,考虑了模糊约束的概念.模糊约束是一个表达式,其中既有语法成分又包含意义信息.模糊推理形式系统中的基本对象是模糊约束,针对模糊约束引进可满足性概念,研究模糊约束可满足性相关性质.利用模糊约束的概念,模糊断言间的推理可以直接在语义环境下加以考虑,因此,以模糊约束为基本元素的模糊推理形式系统随之建立.主要分析新产生断言有效性与模糊约束集可满足性之间的关系,并在此基础上给出了模糊推理形式系统的推理规则.进一步的工作可探讨模糊推理形式系统的可靠性与完全性,建立推理过程的能行机制.研究结果可在人工智能和计算机科学等领域得以应用.     

An Interpretation of Default Logic in Minimal Temporal Epistemic Logic

When reasoning about complex domains, where information available is usually only partial, nonmonotonic reasoning can be an important tool. One of the formalisms introduced in this area is Reiter's Default Logic (1980). A characteristic of this formalism is that the applicability of default (inference) rules can only be verified in the future of the reasoning process. We describe an interpretation of default logic in temporal epistemic logic which makes this characteristic explicit. It is shown that this interpretation yields a semantics for default logic based on temporal epistemic models. A comparison between the various semantics for default logic will show the differences and similarities of these approaches and ours.     

经验逻辑：一种非单调逻辑的统一形式

人的常识推理是一种充满经验性知识的累积过程,而经验推理具有非单调性。本文提出一种关于典型与例外的经验逻辑,特别研究它的非单调性,它提供了一个现存的主要非单调逻辑的统一基础,这是通过一种类似的规则把它们翻译成经验逻辑获得的。因此,经验逻辑给出了一类更一般而且直观的非单调推理形式。     

A computationally tractable nonmonotonic logic

Nonmonotonic logic is intended to apply specifically to situations where the initial information is incomplete. Using nonmonotonic reasoning procedures we shall be able to jump to conclusions, but withdraw them later when we gain additional information. A number of nonmonotonic logics have been introduced and widely discussed. Nonmonotonic logics tend to be introduced proof theoretically, and little attention is paid to their semantic characteristics or their computational tractability. We address both of these issues by presenting a nonmonotonic logic for the Herbrand subset of first-order predicate logic. This nonmonotonic logic is shown to be both sound and complete. Theories formulated in this logic can be executed in logic programming fashion     

基于描述逻辑的OntoUML模型的推理研究

作为语义网的逻辑基础,描述逻辑在知识表示与知识推理方面发挥着重要作用。基于描述逻辑的推理系统保证了其推理的合理性和有效性。本文概要介绍基于UFO本体的OntoUML,并探讨OntoUML模型到描述逻辑的形式化表示及推理方法。     

Nonmonotonic logic and temporal projection

Nonmonotonic formal systems have been proposed as an extension to classical first-order logic that will capture the process of human “default reasoning” or “plausible inference” through their inference mechanisms, just as modus ponens provides a model for deductive reasoning. But although the technical properties of these logics have been studied in detail and many examples of human default reasoning have been identified, for the most part these logics have not actually been applied to practical problems to see whether they produce the expected results.We provide axioms for a simple problem in temporal reasoning which has long been identified as a case of default reasoning, thus presumably amenable to representation in nonmonotonic logic. Upon examining the resulting nonmonotonic theories, however, we find that the inferences permitted by the logics are not those we had intended when we wrote the axioms, and in fact are much weaker. This problem is shown to be independent of the logic used; nor does it depend on any particular temporal representation. Upon analyzing the failure we find that the nonmonotonic logics we considered are inherently incapable of representing this kind of default reasoning.The first part of the paper is an expanded version of one that appeared in the 1986 AAAI proceedings. The second part reports on several responses to our result that have appeared since the original paper was published.     

Why nonmonotonic logic?

The motivation for nonmonotonic logic is to produce a machine representation for default reasoning, broadly construed. In this paper we argue that all nonmonotonic logics have (by definition) inference rules that fail to preserve truth, and this fact leads to several undesirable features. In response to these problems, but recognizing the importance of the original motivation for nonmonotonic logic, we propose an alternative to nonmonotonic logic, which achieves nonmonotonicity of reasoning without abandoning in any way truth preserving inferences. This approach is based on a possible worlds framework, which we illustrate with a small Prolog program. Motivating this approach is an important distinction, which we believe the advocates of nonmonotonic logic to be ignoring: that between inferencing and making decisions, or equivalently that between inferencing and theory construction.     

Knowledge-Driven versus Data-Driven Logics

The starting point of this work is the gap between two distinct traditions in information engineering: knowledge representation and data-driven modelling. The first tradition emphasizes logic as a tool for representing beliefs held by an agent. The second tradition claims that the main source of knowledge is made of observed data, and generally does not use logic as a modelling tool. However, the emergence of fuzzy logic has blurred the boundaries between these two traditions by putting forward fuzzy rules as a Janus-faced tool that may represent knowledge, as well as approximate non-linear functions representing data. This paper lays bare logical foundations of data-driven reasoning whereby a set of formulas is understood as a set of observed facts rather than a set of beliefs. Several representation frameworks are considered from this point of view: classical logic, possibility theory, belief functions, epistemic logic, fuzzy rule-based systems. Mamdani's fuzzy rules are recovered as belonging to the data-driven view. In possibility theory a third set-function, different from possibility and necessity plays a key role in the data-driven view, and corresponds to a particular modality in epistemic logic. A bi-modal logic system is presented which handles both beliefs and observations, and for which a completeness theorem is given. Lastly, our results may shed new light in deontic logic and allow for a distinction between explicit and implicit permission that standard deontic modal logics do not often emphasize.     

Propositional Attitudes and Causation

Predicting and explaining the behavior of others in terms of mental states is indispensable for everyday life. It will be equally important for artificial agents. We present an inference system for representing and reasoning about mental states, and use it to provide a formal analysis of the false-belief task. The system allows for the representation of information about events, causation, and perceptual, doxastic, and epistemic states (vision,belief, and knowledge), incorporating ideas from the event calculus and multi-agent epistemic logic. Unlike previous AI formalisms, our focus here is on mechanized proofs and proof programmability, not on metamathematical results. Reasoning is performed via relatively cognitively plausible inference rules, and a degree of automation is achieved by generalpurpose inference methods and by a syntactic embedding of the system in first-order logic.     

Modal nonmonotonic logics demodalized

The study of the relation between default logic and modal nonmonotonic logics has been mostly concerned with the task of translating default logic to autoepistemic or some other modal nonmonotonic logic. Here, we discuss the reverse problem, that is, the possibility of translating modal nonmonotonic logics into default-type systems formulated in the language without modal operators. To this end, we first consider a reformulation of both formalisms in terms of what we call default consequence relations. These consequence relations turn out to be especially suitable for studying default and modal nonmonotonic reasoning. We show, in particular, that different kinds of such reasoning naturally correspond to different structural rules imposed on default consequence relations. Our main results also demonstrate that all modal nonmonotonic objects considered have exact nonmodal counterparts. As an immediate consequence of these results, we obtain a method of reducing common types of modal nonmonotonic reasoning to nonmodal default reasoning.     

一类扩展的动态描述逻辑

作为描述逻辑的扩展,动态描述逻辑为语义Web服务的建模和推理提供了一种有效途径.在将语义Web服务建模为动作之后,动态描述逻辑从动作执行结果的角度提供了丰富的推理机制,但对于动作的执行过程却不能加以处理.借鉴Pratt关于命题动态逻辑的相关研究,一方面,对动态描述逻辑中动作的语义重新进行定义,将每个动作解释为由关于可能世界的序列组成的集合;另一方面,在动态描述逻辑中引入动作过程断言,用来对动作的执行过程加以刻画.在此基础上提出一类扩展的动态描述逻辑EDDL(X),其中的X表示从ALC(attributive language with complements)到SHOIN(D)等具有不同描述能力的描述逻辑.以X为描述逻辑ALCQO(attributive language with complements,qualified number restrictions and nominals)的情况为例,给出了EDDL(ALCQO)的表判定算法,并证明了算法的可终止性、可靠性和完备性.EDDL(X)可以从动作执行过程和动作执行结果两个方面对动作进行全面的刻画和推理,为语义Web服务的建模和推理提供了进一步的逻辑支持.     

The Dynamics of Syntactic Knowledge

The syntactic approach to epistemic logic avoids the logicalomniscience problem by taking knowledge as primary rather thanas defined in terms of possible worlds. In this study, we combinethe syntactic approach with modal logic, using transition systemsto model reasoning. We use two syntactic epistemic modalities:‘knowing at least’ a set of formulae and ‘knowingat most’ a set of formulae. We are particularly interestedin models restricting the set of formulae known by an agentat a point in time to be finite. The resulting systems are investigatedfrom the point of view of axiomatization and complexity. Weshow how these logics can be used to formalise non-omniscientagents who know some inference rules, and study their relationshipto other systems of syntactic epistemic logics, such as Ågotnesand Walicki (2004, Proc. 2nd EUMAS, pp. 1–10), Alechinaet al. (2004, Proc. 3rd AAMAS, pp. 601–613), Duc (1997,J. Logic Comput., 7, 633–648).     

Autoepistemic logic of first order and its expressive power

We study the expressive power of first-order autoepistemic logic. We argue that full introspection of rational agents should be carried out by minimizing positive introspection and maximizing negative introspection. Based on full introspection, we propose the maximal well-founded semantics that characterizes autoepistemic reasoning processes of rational agents, and show that breadth of the semantics covers all theories in autoepistemic logic of first order, Moore's AE logic, and Reiter's default logic. Our study demonstrates that the autoepistemic logic of first order is a very powerful framework for nonmonotonic reasoning, logic programming, deductive databases, and knowledge representation.This research is partially supported by NSERC grant OGP42193.