递归程序结构研究

对递归程序的结构进行了较为深入的研究 ,提出了递归树的概念 ,给出了递归程序的一般结构 ,把递归分为简单链结构、树状结构、复杂链结构三种情况 ,据此 ,给出了复杂的递归问题的程序设计方法 ,根据此方法 ,可方便地写出较为复杂的递归问题的递归程序 ,从而提高设计递归程序的效率。     

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.     

Strict completion of Logic Programs

The paper presents a new approach to the problem of completeness of the SLDNF-resolution. We propose a different reference theory that we call strict completion. This new concept of completion (comp^*(P)) is based on a program transformation that given any program transforms it into a strict one (with the same computational behaviour) and the usual notion of program completion. We consider it a reasonable reference theory to discuss program semantics and completeness results. The standard 2-valued logic is used. The new comp^*(P) is always consistent and the completeness of all allowed programs and goals w.r.t. comp^*(P) is proved.     

逻辑程序的事实维护

事实是逻辑程序的重要组成部分,事实维护影响着整个逻辑程序的一致性和完整性,并能够促进和完善规则维护。论文在分析了人工进行维护操作的弊端后,对事实维护中可能出现的情况进行分类分析,提出了事实维护系统的框架,重点描述了预警检测子系统所扮演的核心作用。     

Bounded Nondeterminism of Logic Programs

We introduce the notion of bounded nondeterminism for logic programs and queries. A program and a query have bounded nondeterminism if there are finitely many refutations for them via any selection rule. We offer a declarative characterization of the class of programs and queries that have bounded nondeterminism by defining bounded programs and queries. The characterization is provided in terms of Herbrand interpretations and level mappings, in the style of existing characterizations of universal termination. A direct application of the theoretical framework is concerned with the automatic generation of a terminating control. We present a transformational approach that given a bounded program and a bounded query yields a terminating program and query with the same set of refutations. Concerning the issue of automating the approach, by means of an example we sketch how an automatic method for proving left termination can be adapted to the purpose of inferring boundedness. Such an adaption reveals that the method does not scale up to medium/large sized programs due to scarce modularity of the required proof obligations. We provide then a modular refinement of boundedness for the significant class of well-moded programs and queries.     

Recursive Estimation and Testing of Dynamic Models

Recursive estimates can be useful for diagnostic purposes, but algorithms for estimating dynamic models recursively with autocorrelated perturbations can be computationally complicated. Thus, we propose a Conditional Recursive Least Squares algorithm (CRLS): given initial full-sample consistent estimates obtained from a correctly specified model, the model is linearized to obtain recursive consistent estimators along the full sample. These may in turn be used to compute statistics to test for structural breaks with unknown break dates. This procedure is illustrated with the Gas-Furnace data.     

Logic Programs with Ordered Disjunction

Logic programs with ordered disjunction (LPODs) contain a new connective which allows representing alternative, ranked options for problem solutions in the heads of rules: A × B intuitively means that if possible A , but if A is not possible, then at least B . The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. We show how LPODs can be implemented using answer set solvers for normal programs. The implementation is based on a generator, which produces candidate answer sets and a tester which checks whether a given candidate is maximally preferred and produces a better candidate if it is not. We also discuss the complexity of reasoning tasks based on LPODs and possible applications.     

The Recursive Resolution method for Modal Logic

In this paper a syntactic proof procedure, Recursive Resolution (RR), will be introduced for a Modal Logic system S4. The RR is analogous to Robinson’s resolution method on predicate calculus. In Predicate Calculus, a well-formed-formula (wff) can be transformed to a set of normal forms (clauses) after a skolemization process where skolem functions are introduced. For any two normal forms, the resolution method tells how to find their resolvent if they are resolvable at all. Similarly, for modal logic S4, there is a preliminary step in RR to transform a wff into a set of normal forms (m-clauses) after a skolemization step of the possibility operator □. For any two normal forms (m-clauses), the RR method determines whether they are modal-resolvable. If so, their modal-resolvent(s) (MR) can be computed. Traditionally, we use the semantic tableau or related method to reason on modal logic which is a direct application of the semantic analysis of the concept of possible world. Computationally, these semantic proof procedures involve unnecessary backtracking and so cannot be efficiently implemented in a computer. RR is also justified by and devised according to the semantic analysis of possible worlds. But it avoids explicit construction of possible worlds or reducing modalities by quantified variables and can be implemented by some recursive functions.     

树型结构在递归程序教学中的应用

递归程序可以嵌套调用,因此在运行过程中其运行轨迹较复杂。本文将用数据结构中的树型结构来形象化描述递归程序运行轨迹,使递归程序的运行轨迹更加清晰明了和易于理解。     

描述逻辑程序系统的设计与实现

Eiter等人为语义网提出的回答集程序和描述逻辑相结合的描述逻辑程序,获得了本体上的非单调表达和推理能力。王以松等人证明了描述逻辑程序的完备化和环公式可以精确刻画描述逻辑程序的回答集。在此基础上,进一步证明了若完备化公式的模型不是回答集则一定存在终止环公式反例,它们是多项式时间可计算的。设计并实现了借助SAT求解器MiniSAT以及描述逻辑推理机RacerPro计算描述逻辑强回答集的原型DLP_SAT。实验结果表明,该原型能有效地计算一些熟知的描述逻辑程序的强回答集。     

Quantitative Separation Logic and Programs with Lists

This paper presents an extension of a decidable fragment of Separation Logic for singly-linked lists, defined by Berdine et al. (2004). Our main extension consists in introducing atomic formulae of the form ls ^k (x, y) describing a list segment of length k, stretching from x to y, where k is a logical variable interpreted over positive natural numbers, that may occur further inside Presburger constraints. We study the decidability of the full first-order logic combining unrestricted quantification of arithmetic and location variables. Although the full logic is found to be undecidable, validity of entailments between formulae with the quantifier prefix in the language $^* {$_\mathbbN, "_\mathbbN}^*\exists^* \{\exists_{\bf \mathbb{N}}, \forall_{\bf \mathbb{N}}\}^* is decidable. We provide here a model theoretic method, based on a parametric notion of shape graphs. We have implemented our decision technique, providing a fully automated framework for the verification of quantitative properties expressed as pre- and post-conditions on programs working on lists and integer counters.     

Bayesian Update of Recursive Agent Models

We present a framework for Bayesian updating of beliefs about models of agent(s) based on their observed behavior. We work within the formalism of the Recursive Modeling Method (RMM) that maintains and processes models an agent may use to interact with other agent(s), the models the agent may think the other agent has of the original agent, the models the other agent may think the agent has, and so on. The beliefs about which model is the correct one are incrementally updated based on the observed behavior of the modeled agent and, as the result, the probability of the model that best predicted the observed behavior is increased. Analogously, the models on deeper levels of modeling can be updated; the models that the agent thinks another agent uses to model the original agent are revised based on how the other agent is expected to observe the original agent's behavior, and so on. We have implemented and tested our method in two domains, and the results show a marked improvement in the quality of interactions with the belief update in both domains.     

Partial and Nested Recursive Function Definitions in Higher-order Logic

Based on inductive definitions, we develop a tool that automates the definition of partial recursive functions in higher-order logic (HOL) and provides appropriate proof rules for reasoning about them. Termination is modeled by an inductive domain predicate which follows the structure of the recursion. Since a partial induction rule is available immediately, partial correctness properties can be proved before termination is established. It turns out that this modularity also facilitates termination arguments for total functions, in particular for nested recursions. Our tool is implemented as a definitional package extending Isabelle/HOL. Various extensions provide convenience to the user: pattern matching, default values, tail recursion, mutual recursion and currying.