基于上下文的知识表示和推理--人工智能的观点

本文中,我们从知识表示和推理(KRR)的角度概括地阐述了上下文推理的概念和基本原理。首先阐述了上下文的概念;然后介绍了上下文推理的三种基本形式和上下文理论的两个基本原理,也就是局部性原理和一致性原理;接着讨论了上下文推理的形式化问题;最后通过对一个叫“魔术盒问题”的求解来展示如何利用多上下文系统MCS对问题进行形式化表示和求解。     

A multicontext architecture for formalizing complex reasoning

We propose multicontext systems (MC systems) as a formal framework for the specification of complex reasoning. MC systems provide the ability to structure the specification of “global” reasoning in terms of “local” reasoning subpatterns. Each subpattern is modeled as a deduction in a context, formally defined as an axiomatic formal system. the global reasoning pattern is modeled as a concatenation of contextual deductions via bridge rules, i.e., inference rules that infer a fact in one context from facts asserted in other contexts. Besides the formal framework, in this article we propose a three-layer architecture designed to specify and automatize complex reasoning. At the first level we have object-level contexts (called s-contexts) for domain specifications. Problem-solving principles and, more in general, meta-level knowledge about the application domain is specified in a distinct context, called Problem-Solving Context (PSC). On top of s-contexts and PSC, we have a further context, called MT, where it is possible to specify strategies to control multicontext reasoning spanning through s-contexts and PSC. We show how GETFOL can be used as a computer tool for the implementation of MC systems and for the automatization of multicontext deductions. © 1995 John Wiley & Sons, Inc.     

Analogical proportions

Analogy-making is at the core of human and artificial intelligence and creativity with applications to such diverse tasks as proving mathematical theorems and building mathematical theories, common sense reasoning, learning, language acquisition, and story telling. This paper introduces from first principles an abstract algebraic framework of analogical proportions of the form ‘a is to b what c is to d’ in the general setting of universal algebra. This enables us to compare mathematical objects possibly across different domains in a uniform way which is crucial for AI-systems. It turns out that our notion of analogical proportions has appealing mathematical properties. As we construct our model from first principles using only elementary concepts of universal algebra, and since our model questions some basic properties of analogical proportions presupposed in the literature, to convince the reader of the plausibility of our model we show that it can be naturally embedded into first-order logic via model-theoretic types and prove from that perspective that analogical proportions are compatible with structure-preserving mappings. This provides conceptual evidence for its applicability. In a broader sense, this paper is a first step towards a theory of analogical reasoning and learning systems with potential applications to fundamental AI-problems like common sense reasoning and computational learning and creativity.

     

Default logic and specification of nonmonotonic reasoning

In this paper constructions leading to the formation of belief sets by agents are studied. The focus is on the situation when possible belief sets are built incrementally in stages. An infinite sequence of theories that represents such a process is called a reasoning trace. A set of reasoning traces describing all possible reasoning scenarios for the agent is called a reasoning frame. Default logic by Reiter is not powerful enough to represent reasoning frames. In the paper a generalization of default logic of Reiter is introduced by allowing infinite sets of justifications. This formalism is called infinitary default logic. In the main result of the paper it is shown that every reasoning frame can be represented by an infinitary default theory. A similar representability result for antichains of theories (belief frames) is also presented.     

Practical Reflection for Sequent Logics

It is well-known that adding reflective reasoning can tremendously increase the power of a proof assistant. In order for this theoretical increase of power to become accessible to users in practice, the proof assistant needs to provide a great deal of infrastructure to support reflective reasoning. In this paper we explore the problem of creating a practical implementation of such a support layer.Our implementation takes a specification of a logical theory (which is identical to how it would be specified if we were simply going to reason within this logical theory, instead of reflecting it) and automatically generates the necessary definitions, lemmas, and proofs that are needed to enable the reflected meta-reasoning in the provided theory.One of the key features of our approach is that the structure of a logic is preserved when it is reflected. In particular, all variables, including meta-variables, are preserved in the reflected representation. This also allows the preservation of proof automation—there is a structure-preserving one-to-one map from proof steps in the original logic to proof step in the reflected logic.To enable reasoning about terms with sequent context variables, we develop a principle for context induction, called teleportation.This work is fully implemented in the MetaPRL theorem prover.     

人工智能中的上下文推理

对上下文推理的原理和形式进行了阐述,讨论了上下文推理的形式化问题,并给出一个利用MCS对问题进行形式化表示和求解的实例。     

NO Revision and NO Contraction

One goal of normative multi-agent system theory is to formulate principles for normative system change that maintain the rule-like structure of norms and preserve links between norms and individual agent obligations. A central question raised by this problem is whether there is a framework for norm change that is at once specific enough to capture this rule-like behavior of norms, yet general enough to support a full battery of norm and obligation change operators. In this paper we propose an answer to this question by developing a bimodal logic for norms and obligations called NO. A key to our approach is that norms are treated as propositional formulas, and we provide some independent reasons for adopting this stance. Then we define norm change operations for a wide class of modal systems, including the class of NO systems, by constructing a class of modal revision operators that satisfy all the AGM postulates for revision, and constructing a class of modal contraction operators that satisfy all the AGM postulates for contraction. More generally, our approach yields an easily extendable framework within which to work out principles for a theory of normative system change.     

Hybrid

Combining higher-order abstract syntax and (co)-induction in a logical framework is well known to be problematic. We describe the theory and the practice of a tool called Hybrid, within Isabelle/HOL and Coq, which aims to address many of these difficulties. It allows object logics to be represented using higher-order abstract syntax, and reasoned about using tactical theorem proving and principles of (co)induction. Moreover, it is definitional, which guarantees consistency within a classical type theory. The idea is to have a de Bruijn representation of λ-terms providing a definitional layer that allows the user to represent object languages using higher-order abstract syntax, while offering tools for reasoning about them at the higher level. In this paper we describe how to use Hybrid in a multi-level reasoning fashion, similar in spirit to other systems such as Twelf and Abella. By explicitly referencing provability in a middle layer called a specification logic, we solve the problem of reasoning by (co)induction in the presence of non-stratifiable hypothetical judgments, which allow very elegant and succinct specifications of object logic inference rules. We first demonstrate the method on a simple example, formally proving type soundness (subject reduction) for a fragment of a pure functional language, using a minimal intuitionistic logic as the specification logic. We then prove an analogous result for a continuation-machine presentation of the operational semantics of the same language, encoded this time in an ordered linear logic that serves as the specification layer. This example demonstrates the ease with which we can incorporate new specification logics, and also illustrates a significantly more complex object logic whose encoding is elegantly expressed using features of the new specification logic.     

On the evaluation of argumentation formalisms

Argumentation theory has become an important topic in the field of AI. The basic idea is to construct arguments in favor and against a statement, to select the “acceptable” ones and, finally, to determine whether the original statement can be accepted or not. Several argumentation systems have been proposed in the literature. Some of them, the so-called rule-based systems, use a particular logical language with strict and defeasible rules. While these systems are useful in different domains (e.g. legal reasoning), they unfortunately lead to very unintuitive results, as is discussed in this paper. In order to avoid such anomalies, in this paper we are interested in defining principles, called rationality postulates, that can be used to judge the quality of a rule-based argumentation system. In particular, we define two important rationality postulates that should be satisfied: the consistency and the closure of the results returned by that system. We then provide a relatively easy way in which these rationality postulates can be warranted for a particular rule-based argumentation system developed within a European project on argumentation.     

Automated assume-guarantee reasoning for omega-regular systems and specifications

We develop a learning-based automated assume-guarantee (AG) reasoning framework for verifying ω-regular properties of concurrent systems. We study the applicability of non-circular (AG-NC) and circular (AG-C) AG proof rules in the context of systems with infinite behaviors. In particular, we show that AG-NC is incomplete when assumptions are restricted to strictly infinite behaviors, while AG-C remains complete. We present a general formalization, called LAG, of the learning based automated AG paradigm. We show how existing approaches for automated AG reasoning are special instances of LAG. We develop two learning algorithms for a class of systems, called ∞-regular systems, that combine finite and infinite behaviors. We show that for ∞-regular systems, both AG-NC and AG-C are sound and complete. Finally, we show how to instantiate LAG to do automated AG reasoning for ∞-regular, and ω-regular, systems using both AG-NC and AG-C as proof rules.     

The role of context in case-based legal reasoning: teleological, temporal, and procedural

Computational models of relevance in case-based legal reasoning have traditionallybeen based on algorithms for comparing the facts and substantive legal issues of aprior case to those of a new case. In this paper we argue that robust models ofcase-based legal reasoning must also consider the broader social and jurisprudentialcontext in which legal precedents are decided. We analyze three aspects of legalcontext: the teleological relations that connect legal precedents to the socialvalues and policies they serve, the temporal relations between prior andsubsequent cases in a legal domain, and the procedural posture of legal cases,which defines the scope of their precedential relevance. Using real examples drawnfrom appellate courts of New York and Massachusetts, we show with the courts' ownarguments that the doctrine of stare decisis (i.e., similar facts should lead to similar results) is subject to contextual constraints and influences. For each of the three aspects of legal context, we outline an expanded computational framework for case-based legal reasoning that encompasses the reasoning of the examples, and provides a foundation for generating a more robust set of legal arguments.     

A logic for reasoning about probabilities

We consider a language for reasoning about probability which allows us to make statements such as “the probability of E₁ is less than ” and “the probability of E₁ is at least twice the probability of E₂,” where E₁ and E₂ are arbitrary events. We consider the case where all events are measurable (i.e., represent measurable sets) and the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the propositional fragment of) Nilsson's probabilistic logic. As we show elsewhere, the general (nonmeasurable) case corresponds precisely to replacing probability measures by Dempster-Shafer belief functions. In both cases, we provide a complete axiomatization and show that the problem of deciding satisfiability is NP-complete, no worse than that of propositional logic. As a tool for proving our complete axiomatizations, we give a complete axiomatization for reasoning about Boolean combinations of linear inequalities, which is of independent interest. This proof and others make crucial use of results from the theory of linear programming. We then extend the language to allow reasoning about conditional probability and show that the resulting logic is decidable and completely axiomatizable, by making use of the theory of real closed fields.     

Using Abstract Resources to Control Reasoning

Many formalisms for reasoning about knowing commit an agent to be logically omniscient. Logical omniscience is an unrealistic principle for us to use to build a real-world agent, since it commits the agent to knowing infinitely many things. A number of formalizations of knowledge have been developed that do not ascribe logical omniscience to agents. With few exceptions, these approaches are modifications of the possible-worlds semantics. In this paper we use a combination of several general techniques for building non-omniscient reasoners. First we provide for the explicit representation of notions such as problems, solutions, and problem solving activities, notions which are usually left implicit in the discussions of autonomous agents. A second technique is to take explicitly into account the notion of resource when we formalize reasoning principles. We use the notion of resource to describe interesting principles of reasoning that are used for ascribing knowledge to agents. For us, resources are abstract objects. We make extensive use of ordering and inaccessibility relations on resources, but we do not find it necessary to define a metric. Using principles about resources without using a metric is one of the strengths of our approach.We describe the architecture of a reasoner, built from a finite number of components, who solves a puzzle, involving reasoning about knowing, by explicitly using the notion of resource. Our approach allows the use of axioms about belief ordinarily used in problem solving – such as axiom K of modal logic – without being forced to attribute logical omniscience to any agent. In particular we address the issue of how we can use resource-unbounded (e.g., logically omniscient) reasoning to attribute knowledge to others without introducing contradictions. We do this by showing how omniscient reasoning can be introduced as a conservative extension over resource-bounded reasoning.     

Probabilistic Default Reasoning with Conditional Constraints

We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of z-, lexicographic, and conditional entailment for conditional constraints, which are probabilistic generalizations of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment, respectively. We show that the new formalisms have nice properties. In particular, they show a similar behavior as reference-class reasoning in a number of uncontroversial examples. The new formalisms, however, also avoid many drawbacks of reference-class reasoning. More precisely, they can handle complex scenarios and even purely probabilistic subjective knowledge as input. Moreover, conclusions are drawn in a global way from all the available knowledge as a whole. We then show that the new formalisms also have nice general nonmonotonic properties. In detail, the new notions of z-, lexicographic, and conditional entailment have similar properties as their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of z- and lexicographic entailment satisfy the property of rational monotonicity. Furthermore, the new notions of z-, lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints. Finally, we provide algorithms for reasoning under the new formalisms, and we analyze its computational complexity.     

Applying the persistent set approach in temporal reasoning

Since Hanks and McDermott raised the problem of temporal projection (e.g. the Yale shooting problem) and showed that classical nonmonotonic logics failed to solve it, many solutions have been proposed. However, as indicated by some researchers, most of them are not completely satisfactory. In Zhang and Foo [22], we presented a theory of actions called thepersistent set approach (PSA). In this paper, we extend our previous work to deal with temporal reasoning. Different from those minimality-based approaches, we propose a persistence-based formalization of actions within the situation calculus framework, and show that this gives natural and intuitive solutions to the problem of temporal projection in many cases. Explanations of some of the differences between persistence and minimality are given. We show that our approach also provides a unified framework for representing actions with disjunctive effects, while most of the current methods are inappropriate for dealing with these actions in the general case.     

On the soundness,completeness and applicability of the logic of knowledge and communicative commitments in multi-agent systems

Benthem’s correspondence theory is one of the most important tools of the theory of modal logics developed in the last three decades. Correspondence theory, a subfield of the model theory, reflects a systematic study of relations between classes of frames and modal language. In this paper, we use correspondence theory for modal logics to solve a problem not addressed yet in the literature, namely the soundness and completeness of a logic combining two different, yet related modalities: agents’ knowledge and commitments. The paper proves the soundness and completeness of this logic called CTLKC⁺. This work is highly significant as it proves that combining the two agents’ modalities resulted in a consistent logic that can be used to design reliable systems. The methodology is as follows: we develop a set of reasoning postulates (axioms) that reflect the interaction between agents’ knowledge and social commitments in multi-agent system (MAS) using the CTLKC⁺ logic and correspond them to certain classes of frames. In particular, we first give a name, formalization and meaning for each postulate. Then, we correspond the postulates to certain classes of frames and provide the required proofs. Thereafter, we present a discussion that illustrates the importance of the proposed postulates in MASs using a concrete application example called the NetBill protocol taken from the business domain. Finally, we show how the postulates were addressed in the literature. The existence of such a correspondence allows us to prove that the logic generated by any subset of these postulates is sound and complete with respect to models that are based on the corresponding frames. The ultimate goal of this paper is to further assess the logic of knowledge and commitments (CTLKC⁺) from a new perspective (i.e., the soundness and completeness). Consequently, this work advances the literature of logics in MASs and closes a gap that has not been explored before.     

On Logical Foundations of Multilevel Secure Databases

It is envisaged that the application of the multilevel security (MLS) scheme will enhance flexibility and effectiveness of authorization policies in shared enterprise databases and will replace cumbersome authorization enforcement practices through complicated view definitions on a per user basis. However, the critical problem with the current model is that the belief at a higher security level is cluttered with irrelevant or inconsistent data as no mechanism for attenuation is supported. Critics also argue that it is imperative for MLS database users to theorize about the belief of others, perhaps at different security levels, an apparatus that is currently missing and the absence of which is seriously felt.The impetus for our current research is the need to provide an adequate framework for belief reasoning in MLS databases. In this paper, we show that these concepts can be captured in a F-logic style declarative query language, called MultiLog, for MLS deductive databases for which a proof theoretic, model theoretic and fixpoint semantics exist. This development is significant from a database perspective as it now enables us to compute the semantics of MultiLog databases in a bottom-up fashion. We also define a bottom-up procedure to compute unique models of stratified MultiLog databases. Finally, we establish the equivalence of MultiLog's three logical characterizations—model theory, fixpoint theory and proof theory.     

Case studies of Z-module reasoning: Proving benchmark theorems from ring theory

A new method, called Z-module reasoning, was formulated for proving and discovering theorems from ring theory. In a case study, the ZMR system designed to implement this method was used to prove the benchmark x ³ ring theorem from associative ring theory. The system proved the theorem quite efficiently. The system was then used to prove the x ⁴ ring theorem from associative ring theory. Again, a proof was produced easily. These proofs, together with the successes in proving other difficult theorems from ring theory suggest that the Z-module reasoning method is useful for solving a class of problems relying on equality reasoning. This paper illustrates the Z-module reasoning method, and analyzes the computer proof of the x ³ ring theorem.This reasearch was supported in part by the Applied Mathematical Sciences subprogram of the office of Energy Research, U.S. Department of Energy, under contract W-31-109-Eng-38.     

Transposition based contextual insertion on linear DNA strands with deletion precedence

Insertion and deletion operations are two most important operations in molecular computation, and recently these two operations gained interest in the context of molecular computation. In the proposed system, single contextual insertion and usual (with two contexts) contextual deletions are used. In addition, it is assumed that the deletion operation has higher precedence than insertions, if both are possible at a moment. Given a word t, called a context, and the single contextual insertion is performed as follows. For each occurrence of the context t in the given string y, the word t is replaced as txt. In practice, this can be achieved by a replicative transposition process. Similarly, given a pair of words (u, v), called a context, the (u, v)-contextual deletion removes the word in between u and v. Finally, the power of this system and some closure properties are studied.     

Cooperation of Background Reasoners in Theory Reasoning by Residue Sharing

We propose a general way of combining background reasoners in theory reasoning. Using a restricted version of the Craig interpolation lemma, we show that background reasoner cooperation can be achieved as a form of constraint propagation, much in the spirit of existing combination methods for decision procedures. In this case, constraint information is propagated across reasoners eexchanging residues that are, in essence, disjunctions of ground literals over a common signature. As an application of our approach, we describe a multitheory version of the semantic tableau calculus, and we prove it sound and complete.