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).     

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。     

The effect of reasoning logics on real-time decision making

The advent of satellite tracking and communications technology has motivated organizations to investigate centralized real-time support for remote and mobile units and operations. Transportation companies have begun to use satellite tracking systems, production and energy plants are employing intelligent monitoring systems, and on-site emergency managers are being supported by headquarters in their assessment and decision making process. Although different reasoning logics have been proposed for real-time decision making, little attention has been given to the comparative assessment of these approaches. This paper presents empirical evidence on the impact of alternative reasoning logics on individual decision making in real-time. Following the definition of the decision tasks for hazardous operations, commonly used reasoning logics are discussed. Then, results of an empirical comparison of different reasoning approaches are presented. The data were gathered during an experiment with experienced operators. The conclusions of this research are that the selection of the appropriate reasoning logic in support of real-time decision making is crucial     

Resolution theorem proving in reified modal logics

This paper is concerned with the application of the resolution theorem proving method to reified logics. The logical systems treated include the branching temporal logics and logics of belief based on K and its extensions. Two important problems concerning the application of the resolution rule to reified systems are identified. The first is the redundancy in the representation of truth functional relationships and the second is the axiomatic reasoning about modal structure. Both cause an unnecessary expansion in the search space. We present solutions to both problems which allow the axioms defining the reified logic to be eliminated from the database during theorem proving hence reducing the search space while retaining completeness. We describe three theorem proving methods which embody our solutions and support our analysis with empirical results.Much of the research reported in this paper was supported by DTI IED SERC grant No. GR/F 35968, and was carried out whilst Han Reichgelt was at the University of Nottingham.     

The Propositional Formula Checker HeerHugo

HeerHugo is a propositional formula checker that determines whether a given formula is satisfiable or not. The underlying algorithm is based on a specific breadth-first search procedure, with several enhancements including unit resolution and 2-satisfiability tests. Its main ingredient is the branch/merge rule inspired by an algorithm proposed by Stållmarck, which is protected by a software patent. In this paper, the main elements of the algorithm are discussed, and its remarkable effectiveness is illustrated with some examples and computational results.