Sequent calculi for skeptical reasoning in predicate default logic and other nonmonotonic logics

Sequent calculi for skeptical consequence in predicate default logic, predicate stable model logic programming, and infinite autoepistemic theories are presented and proved sound and complete. While skeptical consequence is decidable in the finite propositional case of all three formalisms, the move to predicate or infinite theories increases the complexity of skeptical reasoning to being ₁¹-complete. This implies the need for sequent rules with countably many premises, and such rules are employed. AMS subject classification 03B42, 68N17, 68T27This paper grew directly out of the authors dissertation, written under the direction of Anil Nerode.     

Light logics and optimal reduction: Completeness and complexity

Typing of lambda-terms in elementary and light affine logic (EAL and LAL, respectively) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, respectively) proof-nets admits a guaranteed polynomial (elementary, respectively) bound; on the other hand these terms can also be evaluated by optimal reduction using the abstract version of Lamping’s algorithm. The first reduction is global while the second one is local and asynchronous. We prove that for LAL (EAL, respectively) typed terms, Lamping’s abstract algorithm also admits a polynomial (elementary, respectively) bound. We also give a proof of its soundness and completeness (for EAL and LAL with type fixpoints), by using a simple geometry of interaction model (context semantics).     

基于描述逻辑的组合知识库推理

由于知识库的定义不同,相近领域的知识库不能相互利用已有知识进行推理。为了联合不同的知识库进行推理,通过对描述逻辑的表现形式进行扩展提出一种组合描述逻辑,并基于概念的相似性将不同的领域概念进行关联,给出组合描述逻辑的语法及语义以及相应的Tableau算法。通过实例表明,组合描述逻辑可以利用已有知识进行推理;组合描述逻辑可以将不同的知识库进行结合,为借用不同知识库的知识进行推理提供一条新的途径。     

Using objects to handle complexity in finite element software

Engineering software is becoming ever more complex. Finite element programs have sophisticated graphical input and output facilities, and are increasingly required to be linked to other software such as CAD or databases. The paper shows how an object oriented approach to finite element programming can be used to handle this complexity. This requires an approach that is very different from that adopted in more traditional programming. A foundation finite element class system is developed. This represents the essential data structure of the main finite element classes. It is then shown how this system can be used in a graphical model of two dimensional structures. The finite element system imposed no constraints on the development of the graphical model, yet could still be used easily. An important feature is that the nodes and elements are distributed around the graphical model, rather than being held centrally. For instance nodes may belong to points or lines of the graphical model. This means that the data structure used in the program more closely matches the way that the user of the program is likely to think.     

基于ALCQ(D)的CBR事例修正算法研究

CBR(基于事例推理)是人工智能领域的一个分支,它克服了知识获取的瓶颈问题,事例修正是CBR的关键步骤。以ALC为代表的描述逻辑已被充分应用到CBR中,但目前在基于描述逻辑的CBR中还没有比较有效的算法来判断检索到的相似事例是否需要修正和如何进行修正。ALCQ(D)是在ALC的基础上引入定性数量约束Q和有型域D得到的。提出的算法用ALCQ(D)概念来描述CBR源事例和目标事例,先假定检索到的相似事例能够解决目标问题,即假定目标事例和相似事例同时满足知识库,但这样可能会与知识库产生冲突;接着使用冲突检测机制来查找相似事例概念描述中导致冲突的概念;最后使用概念替换规则在TBox本体库中检索该概念的最相似概念去替换它自己。研究表明,该算法具有界限性、可靠性和完备性。通过一个实例对其进行检验,结果表明,该算法可以准确修正检索到的相似事例,解决目标问题。