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.     

多视点间不一致性的认知推理

需求工程可以认为是一个知识表示,知识获取和知识分析的过程.多视点需求工程就是希望复杂系统中的不同参与者分别从自己的角度出发对预期系统进行描述,从而形成更完备的需求规约.由于多视点方法的这种特性,导致多个涉众有可能对同一问题进行描述,从而形成重叠的需求.这些重叠的需求就是涉众之间的公共知识,对公共知识的不同解释是导致需求规约中不一致问题的根源.本文对基于问题域的多视点需求建模框架进行基于时序认知逻辑的解释和推理,期望达到以下目的:1)使用户陈述的需求更加结构化;2)使用形式化的方法帮助涉众发现那些重叠的需求.     

Epistemic Logic for Rule-Based Agents

The logical omniscience problem, whereby standard models of epistemic logic treat an agent as believing all consequences of its beliefs and knowing whatever follows from what else it knows, has received plenty of attention in the literature. But many attempted solutions focus on a fairly narrow specification of the problem: avoiding the closure of belief or knowledge, rather than showing how the proposed logic is of philosophical interest or of use in computer science or artificial intelligence. Sentential epistemic logics, as opposed to traditional possible worlds approaches, do not suffer from the problems of logical omniscience but are often thought to lack interesting epistemic properties. In this paper, I focus on the case of rule-based agents, which play a key role in contemporary AI research but have been neglected in the logical literature. I develop a framework for modelling monotonic, nonmonotonic and introspective rule-based reasoners which have limited cognitive resources and prove that the resulting models have a number of interesting properties. An axiomatization of the resulting logic is given, together with completeness, decidability and complexity results.     

Temporal Languages for Epistemic Programs

This paper adds temporal logic to public announcement logic (PAL) and dynamic epistemic logic (DEL). By adding a previous-time operator to PAL, we express in the language statements concerning the muddy children puzzle and sum and product. We also express a true statement that an agent’s beliefs about another agent’s knowledge flipped twice, and use a sound proof system to prove this statement. Adding a next-time operator to PAL, we provide formulas that express that belief revision does not take place in PAL. We also discuss relationships between announcements and the new knowledge agents thus acquire; such relationships are related to learning and to Fitch’s paradox. We also show how inverse programs and hybrid logic each can be used to help determine whether or not an arbitrary structure represents the play of a game. We then add a past-time operator to DEL, and discuss the importance of adding yet another component to the language in order to prove completeness.     

自动机,逻辑与博弈

讨论了特定的自动机、自动机的识别能力、逻辑的表达能力和博弈思想的关系。使用博弈思想可以比较容易地证明一元二阶逻辑(S1S和S2S)的可决定性。主要考虑线性时间(linear time)与分支时间(branch time)两种情况，通过这些逻辑与别的时态逻辑的表达能力的等价性可以证明其它逻辑也具有决定性，可以设计相应的自动机去解决模型检查(Model Checking)问题。     

Temporalizing Epistemic Default Logic

We present an epistemic default logic, based on the metaphore of a meta-level architecture. Upward reflection is formalized by a nonmonotonic entailment relation, based on the objective facts that are either known or unknown at the object level. Then, the meta (monotonic) reasoning process generates a number of default-beliefs of object-level formulas. We extend this framework by proposing a mechanism to reflect these defaults down. Such a reflection is seen as essentially having a temporal flavour: defaults derived at the meta-level are projected as facts in a next object level state. In this way, we obtain temporal models for default reasoning in meta-level formalisms which can be conceived as labeled branching trees. Thus, descending the tree corresponds to shifts in time that model downward reflection, whereas the branching of the tree corresponds to ways of combining possible defaults. All together, this yields an operational or procedural semantics of reasoning by default, which admits one to reason about it by means of branching-time temporal logic. Finally, we define sceptical and credulous entailment relations based on these temporal models and we characterize Reiter extensions in our semantics.     

Probabilistic Dynamic Epistemic Logic

In this paper I combine the dynamic epistemic logic ofGerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1994). The resultis a new probabilistic dynamic epistemic logic, a logic for reasoning aboutprobability, information, and information change that takes higher orderinformation into account. Probabilistic epistemic models are defined, and away to build them for applications is given. Semantics and a proof systemis presented and a number of examples are discussed, including the MontyHall Dilemma.     

Updating Epistemic Logic Programs

We consider the problem of updating non-monotonic knowledgebases represented by epistemic logic programs where disjunctiveinformation and notions of knowledge and belief can be explicitlyexpressed. We propose a formulation for epistemic logic programupdate based on a principle called minimal change and maximalcoherence. The central feature of our approach is that duringan update or a sequence of updates, contradictory informationis removed on a basis of minimal change under the semanticsof epistemic logic programs and then coherent information ismaximally retained in the update result. Through various updatescenarios, we show that our approach provides both semanticand syntactic characterizations for an update problem. We alsoinvestigate essential semantic properties of epistemic logicprogram update.     

Self-Referential Justifications in Epistemic Logic

This paper is devoted to the study of self-referential proofs and/or justifications, i.e., valid proofs that prove statements about these same proofs. The goal is to investigate whether such self-referential justifications are present in the reasoning described by standard modal epistemic logics such as  $\mathsf{S4}$ . We argue that the modal language by itself is too coarse to capture this concept of self-referentiality and that the language of justification logic can serve as an adequate refinement. We consider well-known modal logics of knowledge/belief and show, using explicit justifications, that $\mathsf{S4}$ , $\mathsf{D4}$ , $\mathsf{K4}$ , and  $\mathsf{T}$ with their respective justification counterparts  $\mathsf{LP}$ , $\mathsf{JD4}$ , $\mathsf{J4}$ , and  $\mathsf{JT}$ describe knowledge that is self-referential in some strong sense. We also demonstrate that self-referentiality can be avoided for  $\mathsf{K}$ and  $\mathsf{D}$ . In order to prove the former result, we develop a machinery of minimal evidence functions used to effectively build models for justification logics. We observe that the calculus used to construct the minimal functions axiomatizes the reflected fragments of justification logics. We also discuss difficulties that result from an introduction of negative introspection.     

实时时序逻辑语言XYZ/RE到时间自动机的映射

时间自动机是一种重要的实时系统建模工具。本文建立了实时时序逻辑语言XYZ/RE到时间自动机的一种映射机制,将XYZ/RE所描述的系统进程直接转换为时间自动机,这样不但可以准确捕获实时系统功能和控制行为,还可以利用基于时间自动机的验证工具UPPAAL对XYZ/RE描述的系统正确性进行检测。最后本文通过一个实例的描述与检测,验证了映射机制的有效性。     

Bisimulations for Temporal Logic

We define bisimulations for temporal logic with Since and Until. This new notion is compared to existing notions of bisimulations, and then used to develop the basic model theory of temporal logic with Since and Until. Our results concern both invariance and definability. We conclude with a brief discussion of the wider applicability of our ideas.     

Dynamic Epistemic Logic for Implicit and Explicit Beliefs

Epistemic logic with its possible worlds semantic model is a powerful framework that allows us to represent an agent’s information not only about propositional facts, but also about her own information. Nevertheless, agents represented in this framework are logically omniscient: their information is closed under logical consequence. This property, useful in some applications, is an unrealistic idealisation in some others. Many proposals to solve this problem focus on weakening the properties of the agent’s information, but some authors have argued that solutions of this kind are not completely adequate because they do not look at the heart of the matter: the actions that allow the agent to reach such omniscient state. Recent works have explored how acts of observation, inference, consideration and forgetting affect an agent’s implicit and explicit knowledge; the present work focuses on acts that affect an agent’s implicit and explicit beliefs. It starts by proposing a framework in which these two notions can be represented, and then it looks into their dynamics, first by reviewing the existing notion of belief revision, and then by introducing a rich framework for representing diverse forms of inference that involve both knowledge and beliefs.     

Multi-weighted Automata and MSO Logic

Weighted automata are non-deterministic automata where the transitions are equipped with weights. They can model quantitative aspects of systems like costs or energy consumption. The value of a run can be computed, for example, as the maximum, average, or discounted sum of transition weights. In multi-weighted automata, transitions carry several weights and can model, for example, the ratio between rewards and costs, or the efficiency of use of a primary resource under some upper bound constraint on a secondary resource. Here, we introduce a general model for multi-weighted automata as well as a multi-weighted MSO logic. In our main results, we show that this multi-weighted MSO logic and multi-weighted auto-mata are expressively equivalent both for finite and infinite words. The translation process is effective, leading to decidability results for our multi-weighted MSO logic.     

一种带传递关系的认知描述逻辑研究

描述逻辑是语义Web的逻辑基础,它是形式化表达领域知识的一种工具.描述逻辑是一阶逻辑的可判定子集,适合对领域知识的概念术语进行建模.因为某些应用程序的需要和领域知识难以完全描述的因素,Web上有大量的不完全知识.描述逻辑基于开放世界假设,只能表达单调推理,不能处理不完全知识.在描述逻辑中加入认知运算符K可以得到认知描述逻辑.认知描述逻辑因其非单调特性和良好的时间复杂度等特点在处理不完全知识方面有较好的优势.在认知描述逻辑ALCK的基础上加入传递关系属性提出了新的认知描述逻辑语言ALCKR+,保留了描述逻辑原有的优点,增强了表达能力并通过认知查询拥有了非单调推理的能力.设计了ALCKR+的语法、语义以及表算法,给出了表算法的正确性以及可判定性证明,证明表算法的时间复杂度为PSPACE-tomplete.     

Implicit Epistemic Aspects of Constructive Logic

In the present paper I wish to regard constructivelogic as a self-contained system for the treatment ofepistemological issues; the explanations of theconstructivist logical notions are cast in anepistemological mold already from the outset. Thediscussion offered here intends to make explicit thisimplicit epistemic character of constructivism.Particular attention will be given to the intendedinterpretation laid down by Heyting. This interpretation, especially as refined in the type-theoretical work of Per Martin-Löf, puts thesystem on par with the early efforts of Frege andWhitehead-Russell. This quite recent work, however,has proved valuable not only in the philosophy andfoundations of mathematics, but has also foundpractical application in computer science, where thelanguage of constructivism serves as an implementableprogramming language, and within the philosophy oflanguage.\footnote{Nordstr\"{o}m et al. (1990) give an overview of the work in computerscience, whereas Ranta (1995) provides an impressiveconstructivist alternative to Montague Grammar usingthe richer type structure of Martin-L\"{o}f in placeof the simple classical type theory of Church.} Mypresentation will be carried out through a contrastwith standard metamathematical work.\footnote{Troelstra and van Dalen (1988) give an encyclopedictreatment of the metamathematics of constructivism.}In the course of the development I have occasion tooffer some novel considerations (in Sections~6 and 8) on thenature of proof and inference(-acts).     

First-Order Logic with Two Variables and Unary Temporal Logic

We investigate the power of first-order logic with only two variables over ω-words and finite words, a logic denoted by FO². We prove that FO² can express precisely the same properties as linear temporal logic with only the unary temporal operators: “next,” “previously,” “sometime in the future,” and “sometime in the past,” a logic we denote by unary-TL Moreover, our translation from FO² to unary-TL converts every FO² formula to an equivalent unary-TL formula that is at most exponentially larger and whose operator depth is at most twice the quantifier depth of the first-order formula. We show that this translation is essentially optimal. While satisfiability for full linear temporal logic, as well as for unary-TL, is known to be PSPACE-complete, we prove that satisfiability for FO² is NEXP-complete, in sharp contrast to the fact that satisfiability for FO³ has nonelementary computational complexity. Our NEXP upper bound for FO² satisfiability has the advantage of being in terms of the quantifier depth of the input formula. It is obtained using a small model property for FO² of independent interest, namely, a satisfiable FO² formula has a model whose size is at most exponential in the quantifier depth of the formula. Using our translation from FO² to unary-TL we derive this small model property from a corresponding small model property for unary-TL. Our proof of the small model property for unary-TL is based on an analysis of unary-TL types.     

Concurrent Logic and Automata Combined: A Semantics for Components

In this paper, we describe a true-concurrent hierarchical logic interpreted over concurrent automata. Concurrent automata constitute a special kind of asynchronous transition system (ATS) used for modelling the behaviour of components as understood in component-based software development. Here, a component-based system consists of several interacting components whereby each component manages calls to and from the component using ports to ensure encapsulation. Further, a component can be complex and made of several simpler interacting components. When a complex component receives a request through one of its ports, the port delegates the request to an internal component. Our logic allows us to describe the different views we can have on the system. For example, the overall component interactions, whether they occur sequentially, simultaneously or in parallel, and how each component internally manages the received requests (possibly expressed at different levels of detail). Using concurrent automata as an underlying formalism we guarantee that the expressiveness of the logic is preserved in the model. In future work, we plan to integrate our truly-concurrent approach into the Edinburgh Concurrency Workbench.