智能主体的信念认知时态子结构逻辑模型*

智能主体获取信念的途径主要有两种：一种为他省,通过外界交互,从其他主体获取信息;另一种为自省,通过自己的历史数据库获取相关知识。对于主体信念的描述与刻画,两种途径缺一不可,但当前的BDI理论模型中较多地为他省系统,没有做到两者相结合。其次,在当前的许多理论模型中,通常使用的是二值逻辑、经典模态逻辑或其变形系统,使得相应的逻辑系统普遍存在逻辑全知和粗精度刻画等问题。针对上述问题进行了相关研究,采用了认知时态子结构逻辑建模的方法,表达了智能主体获得“双省”信念的方式,针对其建立了相应的逻辑系统BSoET。     

Preferential belief change using generalized epistemic entrenchment

A sentence A is epistemically less entrenched in a belief state K than a sentence B if and only if a person in belief state K who is forced to give up either A or B will give up A and hold on to B. This is the fundamental idea of epistemic entrenchment as introduced by Gärdenfors (1988) and elaborated by Gärdenfors and Makinson (1988). Another distinguishing feature of relations of epistemic entrenchment is that they permit particularly simple and elegant construction recipes for minimal changes of belief states. These relations, however, are required to satisfy rather demanding conditions. In the present paper we liberalize the concept of epistemic entrenchment by removing connectivity, minimality and maximality conditions. Correspondingly, we achieve a liberalization of the concept of rational belief change that does no longer presuppose the postulates of success and rational monotony. We show that the central results of Gärdenfors and Makinson are preserved in our more flexible setting. Moreover, the generalized concept of epistemic entrenchment turns out to be applicable also to relational and iterated belief changes.     

Persistence and minimality in epistemic logic

We give a general approach to characterizing minimal information in a modal context. Our modal treatment can be used for many applications, but is especially relevant under epistemic interpretations of the operator □. Relative to an arbitrary modal system, we give three characterizations of minimal information and provide conditions under which these characterizations are equivalent. We then study information orders based on bisimulations and Ehrenfeucht–Fraïssé games. Moving to the area of epistemic logics, we show that for one of these orders almost all systems trivialize the notion of minimal information. Another order which we present is much more promising as it permits to minimize with respect to positive knowledge. In S5, the resulting notion of minimal knowledge coincides with well‐established proposals. For S4 we compare the two orders.     

An epistemic model of logic programming

If we view an ordinary logic program as a set of beliefs of animplicit agent about a world, then acompletely epistemic logical view of logic programming would yield a further extension that allows us to reasonexplicitly about beliefs and non-beliefs of any agents. In particular, such a view will accommodate nested beliefs, introspective reasoning of self-beliefs and meta-reasoning of others’ beliefs. In this paper, we present the logical foundation of such a view by developing acomputational logic ofquantified epistemic notions. The semantics of the logic is an extension of Kripke’spossible-worlds semantics with variable domains to capture theintensional imputation problem in epistemic notions. A syntactical characterization of this semantics is developed to yield a clausal form of the logic. An efficient resolution mechanisation of this form is described. It is achieved by augmenting Konolige’sB-resolution with a semi-set-of-support strategy with linear resolution. Further refinements on a Horn clausal form of the logic with negation as failure are also discussed.     

Set-theoretic completeness for epistemic and conditional logic

The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of formulas in the language (the semantics), a collection of axioms and rules of inference characterizing reasoning (the proof theory), and then relate the proof theory to the semantics via soundness and completeness results. Here we consider an approach that is more common in the economics literature, which works purely at the semantic, set-theoretic level. We provide set-theoretic completeness results for a number of epistemic and conditional logics, and contrast the expressive power of the syntactic and set-theoretic approaches. This revised version was published online in June 2006 with corrections to the Cover Date.     

Iterative belief revision in extended logic programming

Extended logic programming augments conventional logic programming with both default and explicit negation. Several semantics for extended logic programs have been proposed that extend the well-founded semantics for logic programs with default negation (called normal programs). We show that two of these extended semantics are intractable; both Dung's grounded argumentation semantics and the well-founded semantics of Alferes et al. are NP-hard. Nevertheless, we also show that these two semantics have a common core, a more restricted form of the grounded semantics, which is tractable and can be computed iteratively in quadratic time. Moreover, this semantics is a representative of a rich class of tractable semantics based on a notion of iterative belief revision.     

带逆角色的认知描述逻辑研究

针对认知角色不能表达个体间双向关系的问题,在描述逻辑ALCK中加入逆角色得到ALCIK,以扩充其表达能力,在能够捕获最小知识和实现自省推理的同时可以更加方便地对实际问题建模,给出了ALCIK的语法和语义,并且在Tbox为空集,Abox中无K算子的情况下,设计了ALCIK概念的查询表算法,根据概念结构归纳证明了表算法的可靠性和完备性,并且一定会停机,最后讨论了复杂度。理论分析表明,此时认知查询问题是可判定的,并且计算复杂度为PSpace-hard。     

On compositional reasoning about anonymity and privacy in epistemic logic

In this paper, we exploit epistemic logic (or the modal logic of knowledge) for multiagent systems to discuss the compositionality of several privacy-related information-hiding/disclosure properties. The properties considered here are anonymity, privacy, onymity, and identity. Our initial observation reveals that anonymity/privacy properties are not necessarily sequentially compositional. This means that even though a system comprising several sequential phases satisfies a certain unlinkability property in each phase, the entire system does not always enjoy a desired unlinkability property. We show that the compositionality can be guaranteed provided that the phases of the system satisfy what we call independence assumptions. More specifically, we develop a series of theoretical case studies of what assumptions are sufficient to guarantee the sequential compositionality of various degrees of anonymity, privacy, onymity, and/or identity properties. Similar results for parallel composition are also discussed. Further, we use the probabilistic extension of epistemic logic to consider the compositionality of probabilistic anonymity/privacy. We show that the compositionality can also be guaranteed in the probabilistic setting, provided that the phases of the system satisfy a probabilistic independence assumption.     

Dynamic belief revision operators

The AGM approach to belief change is not geared to provide a decent account of iterated belief change. Darwiche and Pearl have sought to extend the AGM proposal in an interesting way to deal with this problem. We show that the original Darwiche-Pearl approach is, on the one hand excessively strong and, on the other rather limited in scope. The later Darwiche-Pearl approach, we argue, although it addresses the first problem, still remains rather permissive. We address both these issues by (1) assuming a dynamic revision operator that changes to a new revision operator after each instance of belief change, and (2) strengthening the Darwiche-Pearl proposal. Moreover, we provide constructions of this dynamic revision operator via entrenchment kinematics as well as a simple form of lexicographic revision, and prove representation results connecting these accounts.     

A survey of belief revision and updating in classical logic

This paper summarizes and analyzes the technical aspects of some significant approaches to belief change where beliefs are expressed in classical logic. First, proposals which have played an important role in the elaboration of the problem are considered. Then, we turn to the analysis of various forms of preference relations which are central for the understanding of the difficulties of the problem. © 1994 John Wiley & Sons, Inc.     

Probabilistic Belief Logic and Its Probabilistic Aumann Semantics

In this paper, we present a logic system for probabilistic belief named PBL,which expands the language of belief logic by introducing probabilistic belief. Furthermore, we give the probabilistic Aumann semantics of PBL. We also list some valid properties of belief and probabilistic belief, which form the deduction system of PBL. Finally, we prove the soundness and completeness of these properties with respect to probabilistic Aumann semantics.     

Believing change and changing belief

We present a first-order logic of time, chance, and probability that is capable of expressing the four types of higher-order probability sentences relating subjective probability and objective chance at different times. We define a causal notion of objective chance and show how it can be used in conjunction with subjective probability to distinguish between causal and evidential correlation by distinguishing between conditions, events, and actions that: 1) influence the agent's belief in chance; and 2) the agent believes to influence chance. Furthermore, the semantics of the logic captures some common sense inferences concerning objective chance and causality. We show that an agent's subjective probability is the expected value of its beliefs concerning objective chance. We also prove that an agent using this representation believes with certainty that the past cannot be causally influenced     

Iterated belief change in the situation calculus

John McCarthy's situation calculus has left an enduring mark on artificial intelligence research. This simple yet elegant formalism for modelling and reasoning about dynamic systems is still in common use more than forty years since it was first proposed. The ability to reason about action and change has long been considered a necessary component for any intelligent system. The situation calculus and its numerous extensions as well as the many competing proposals that it has inspired deal with this problem to some extent. In this paper, we offer a new approach to belief change associated with performing actions that addresses some of the shortcomings of these approaches. In particular, our approach is based on a well-developed theory of action in the situation calculus extended to deal with belief. Moreover, by augmenting this approach with a notion of plausibility over situations, our account handles nested belief, belief introspection, mistaken belief, and handles belief revision and belief update together with iterated belief change.     

Hierarchical representation of legal knowledge with metaprogramming in logic

We present an application of metaprogramming in logic that, unlike most metaprogramming applications, is not primarily concerned with controlling the execution of logic programs. Metalevel computation is used to define theories from schemata that were either given explicitly or obtained by abstraction from other theories. Our main application is a representation of legal knowledge in a metalogic programming language. We argue that legal knowledge is multilayered and therefore a single level representation language lacks the needed expressiveness. We show that legal rules can be partitioned into primary, secondary, tertiary, quaternary, and higher level rules. Our classification enables us to define a multilevel model of legal knowledge and a one-to-one correspondence with levels of metaprogramming in logic. We show that this framework has a potential for capturing important legal interpretation principles such as analogia legis, lex specialis legi generali derogat, etc. We have a running example from commercial law that utilizes rules up to the tertiary level, emphasizing analogia legis. The example is expressed in a multilevel metalogic programming language that provides a naming convention and employs reflection between levels.     

Reasoning about ignorance and contradiction: many-valued logics versus epistemic logic

This paper tries to reinterpret three- and four-valued logics of partial ignorance and contradiction in the light of epistemic logic. First, we try to cast Kleene three-valued logic in the setting of a simplified form of epistemic logic. It is a two-tiered logic that embeds propositional logic into another propositional setting. The use of modalities enables Kleene truth values to be expressed at the syntactic level. Kleene logic is then a fragment of the simplified epistemic logic where modalities are in front of literals only. Kleene truth-tables can then be retrieved, while preserving tautologies of classical logic. Kleene logic connectives can be seen as set-valued extensions of Boolean logic ones, but the compositionality of Kleene logic leads to a lack of expressiveness and inferential power compared to the proposed epistemic logic. This methodology is then extended to Belnap four-valued logic, which is tailored to the handling of inconsistent information from various sources. A non-regular modal setting for reasoning about contradiction is obtained, where the adjunction law does not hold. It is a special case of a fragment of the monotonic modal logic EMN.     

Inconsistency tolerance in P2P data integration: An epistemic logic approach

We study peer-to-peer (P2P) data integration, where each peer models an autonomous system that exports data in terms of its own schema, and data interoperation is achieved by means of mappings among the peer schemas, rather than through a unique global schema. We propose a multi-modal epistemic logical formalization based on the idea that each peer is conceived as a rational agent that exchanges knowledge/belief with other peers, thus nicely modeling the modular structure of the system. We then address the issue of dealing with possible inconsistencies, and distinguish between two types of inconsistencies, called local and P2P, respectively. We define a nonmonotonic extension of our logic that is able to reason on the beliefs of peers under both local and P2P inconsistency tolerance. Tolerance to local inconsistency essentially means that the presence of inconsistency within one peer does not affect the consistency of the whole system. Tolerance to P2P inconsistency means being able to resolve inconsistencies arising from the interaction between peers. We study query answering in the new nonmonotonic logic, with the main goal of establishing its decidability and its computational complexity. Indeed, we show that, under reasonable assumptions on peer schemas, query answering is decidable, and is coNP-complete with respect to data complexity, i.e., the size of the data stored at the peers.     

Interventions and belief change in possibilistic graphical models

Causality and belief change play an important role in many applications. This paper focuses on the main issues of causality and interventions in possibilistic graphical models. We show that interventions, which are very useful for representing causal relations between events, can be naturally viewed as a belief change process. In particular, interventions can be handled using a possibilistic counterpart of Jeffrey's rule of conditioning under uncertain inputs. This paper also addresses new issues that are arisen in the revision of graphical models when handling interventions. We first argue that the order in which observations and interventions are introduced is very important. Then we show that in order to correctly handle sequences of observations and interventions, one needs to change the structure of possibilistic networks. Lastly, an efficient procedure for revising possibilistic causal trees is provided.     

Double preference relations for generalised belief change

Many belief change formalisms employ plausibility orderings over the set of possible worlds to determine how the beliefs of an agent ought to be modified after the receipt of a new epistemic input. While most such possible world semantics rely on a single ordering, we investigate the use of an additional preference ordering—representing, for instance, the epistemic context the agent finds itself in—to guide the process of belief change. We show that the resultant formalism provides a unifying semantics for a wide variety of belief change operators. By varying the conditions placed on the second ordering, different families of known belief change operators can be captured, including AGM belief contraction and revision, Rott and Pagnucco's severe withdrawal, the systematic withdrawal of Meyer et al., as well as the linear liberation and σ-liberation operators of Booth et al. Our approach also identifies novel classes of belief change operators worthy of further investigation.     

Axiomatic characterization of the AGM theory of belief revision in a temporal logic

Since belief revision deals with the interaction of belief and information over time, branching-time temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the next-time temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatic characterization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiomatic characterization of the full set of AGM postulates.