支持索引式的PPTL定理证明器的实现

定理证明是目前主流的形式化验证方法,拥有强大的抽象和逻辑表达能力,且不存在状态空间爆炸问题,可用于有穷和无穷状态系统,但其不能完全自动化,并且要求用户掌握较强的数学知识.含索引式的命题投影时序逻辑(PPTL)是一种具有完全正则表达能力,并且包含LTL的时序逻辑,具有较强的建模和性质描述能力.目前,一个可靠完备的含索引式的PPTL公理系统已被构建,然而基于该公理系统的定理证明尚未得到良好工具的支持,存在证明自动化程度较低以及证明冗长易错的问题.鉴于此,首先设计了支持索引式的PPTL定理证明器的实现框架,包括公理系统的形式化与交互式定理证明;然后,在Coq中形式化定义了含索引式的PPTL公式、公理与推理规则,完成了框架中公理系统的实现;最后,通过两个实例的交互式证明验证了该定理证明器的可用性.     

基于MK的实数公理系统相容性和范畴性的Coq形式化

数学定理机器证明是人工智能基础理论的深刻体现. 实数理论是数学分析的基础, 实数公理系统是建立实数理论的重要方法. Morse-Kelley公理化集合论(MK)作为现代数学的基础, 也为实数构建提供了严谨的数学框架和工具. 本文使用定理证明器Coq, 基于MK对实数公理系统进行了深入探索. 在优化了MK形式化代码的基础上, 形式化构建了完整的实数公理系统, 并通过形式化Landau《分析基础》中的实数模型, 证明其相对于MK相容, 此外, 还形式化证明了实数公理系统所有模型在同构意义下是唯一的, 验证了实数公理系统的范畴性. 本文全部定理无例外地给出Coq的机器证明代码, 所有形式化过程已被Coq验证, 并在计算机上运行通过, 充分体现了基于Coq的数学定理机器证明具有可读性、交互性和智能性的特点, 其证明过程规范、严谨、可靠. 该系统可方便地应用于拓扑学和代数学理论的形式化构建. 谨以此文庆祝我国著名控制系统专家秦化淑研究员九十华诞!     

有穷时间投影时序逻辑的完备公理系统

为采用定理证明的方法对并发及交互式系统进行验证,研究了有穷论域下有穷时间一阶投影时序逻辑(projection temporal logic,简称PTL)的一个完备公理系统.在介绍PTL的语法、语义并给出公理系统后,提出了PTL公式的正则形(normal form,简称NF)和正则图(normal form graph,简称NFG).基于NF给出了NFG的构造算法,并利用NFG可描述公式模型的性质证明PTL公式的可满足性判定定理和公理系统的完备性.最后,结合实例展示了PTL及其公理系统在系统验证中的应用.结果表明,基于PTL的定理证明方法可方便用于并发系统的建模与验证.     

针对教学场景的ZFC集合论Coq形式化

离散数学是计算机类专业的基础课程之一,命题逻辑、一阶逻辑与公理集合论是其重要组成部分.教学实践表明,初学者准确理解语法、语义、推理系统等抽象概念是有一定难度的.近年来,已有一些学者开始在教学中引入交互式定理证明工具,以帮助学生构造形式化证明,更透彻地理解逻辑系统.然而,现有的定理证明器有较高上手门槛,直接使用会增加学生的学习负担.鉴于此,在Coq中开发了针对教学场景的ZFC公理集合论证明器.首先,形式化了一阶逻辑推理系统和ZFC公理集合论;之后,开发了数条自动化推理规则证明策略.学生可以在与教科书风格相同的简洁证明环境中使用自动化证明策略完成定理的形式化证明.该工具被用在了大一新生离散数学课程的教学中,没有定理证明经验的学生使用该工具可以快速完成数学归纳法和皮亚诺算术系统等定理的形式化证明,验证了该工具的实际效果.     

命题编码中公理的组合与设计

近年来,基于可满足性的规划方法研究逐渐成为智能规划研究领域中的热点。提出3种基于Graphplan的编码方式中公理的改进:动作互斥的部分放松、动作互斥的完全放松方法、添加框架公理。基于SATPLAN2006规划系统分别实现上述3种改进的编码方式,并对国际规划竞赛中选用的标准后勤域与积木世界域的问题样例予以测试,分析不同编码方式的编码规模与求解效率,验证了基于Graphplan编码方式的改进在绝大多数情况下是有效的。最后,实现基于状态的编码方式,并对上述两个域进行测试,比较约简动作与约简状态这两种极端方式的求解效率和编码规模。实验结果表明,在后勤域的某些问题上基于状态的编码方式比基于动作的编码方式有效得多。上述的改进策略表明,可根据问题域的特性等来考虑该问题最适宜哪些公理组合的编码方式,而不固定使用某种特定的编码方式。     

基于命题可满足性的经典最优规划方法

基于Graphplan的编码方式是2006年国际规划竞赛中著名的最优规划系统SATPLAN2006采用的编码方式。首先给出与编码相关的概念与性质,在基于Graphplan的编码方式的基础上,设计一种新的编码方式:基于FA的编码方式,并从理论上证明该编码方式的有效性。设计并实现对应的规划系统FA-SP,利用国际规划竞赛选用的Benchmark问题予以测试。实验结果表明,与SATPLAN2006相比,FA-SP对于所测两类规划域编码规模均有所压缩,除个别问题外求解效率都有一定程度的提高;对于顺序规划域Blocks World,编码规模平均压缩了40%,求解效率平均提高了2倍;对于并发规划域Logistics,带有小于5%的框架公理的FA编码规模平均压缩了75%,求解效率也有不同程度的提高。     

一种约简动作变元的命题规划编码方式

基于动作的编码方式是2006年国际规划竞赛中著名的最优规划系统SATPLAN2006采用的一种基于约简状态变元的命题规划编码方式.依据基于动作的编码方式,提出一种基于约简动作变元的自动命题规划编码方式:基于命题的编码方式.首先分析构造新编码方式的理论依据,提出基于命题的编码方式的编码组成,证明其有效性,并描述某些公理的具体实现细节,最后分析其与已有几种编码方式的不同之处.在SATPLAN2006中实现了基于命题的编码方式,利用国际规划竞赛选用的标准测试问题予以测试,并分析其与基于动作的编码方式等两种极端编码方式的求解特性.实验结果表明:对于顺序规划问题域,基于命题的编码方式更有效,而对于并发规划问题域,基于动作的编码方式更有效.     

基于推理信息的本体模块化方法

本体模块化在本体推理和复用等应用中有着极为重要的作用.怎么样将本体划分成小的模块是最基本的问题,目前本体模块化的工作主要集中在本体复用的目的上.在这篇文章中,我们提出了一种基于推理信息的本体模块化方法,该方法以提高推理的性能为目的.在基于同一最小推理集合内的公理之间内聚性将会增强的合理假设下,我们的模块化方法通过分析每次推理的过程,得到推理的最小推理集合,然后增强最小推理集合内公理1之间的内聚度,最后根据内聚度将本体划分成模块.在评估阶段,我们首先使用训练公理划分本体,然后通过测试公理来调查本体推理性能提高的程度.根据训练公理和测试公理所属范围的不同,我们使用了三组实验:训练公理和测试公理限定在同一较小范围,训练公理和测试公理不限定范围,训练公理和测试公理的范围实现三次不同的改变.实验的结果尤其是符合实际应用情况的实验三的结果证明了基于推理信息的本体模块化方法的有效性.     

任意公理系统的依赖基

形式化定义了值依赖的公理、公理系统及依赖基。严格证明了任何公理系统对任何背景都具有依赖基,给出 了对任意一个公理系统求任意背景依赖基的方法,并证明了每个公理系统的依赖基不唯一。进而还提出了一种诱导 背景,通过诱导背景可把这个证明过程及依赖基的计算过程形象地反映出来。     

强表达描述逻辑本体的后继式公理定位研究

公理定位能够挖掘描述逻辑中可解释的缺陷,并为逻辑蕴含结果寻找隐藏的理由,因此在描述逻辑研究中引起了广泛的关注.平衡描述逻辑表达能力和推理机求解效率问题一直是公理定位研究的重点内容.本文基于一种后继式判定算法,从白盒和黑盒两个角度将其用于公理定位.白盒方法利用修正的后继式规则（即定位规则）来追踪推理的具体过程,并引入定位公式的概念建立子句的布尔公式标签与逻辑蕴含的所有极小公理集之间的对应关系.黑盒方法则直接调用基于未修正的后继式规则的推理机,并进一步利用碰集树方法求得逻辑蕴含的所有理由.最后,基于这样的两种面向强表达描述逻辑本体的公理定位算法设计推理工具,从理论和实验两方面验证其可行性,并与已有的推理工具比较求解性能.     

State agnostic planning graphs: deterministic,non-deterministic,and probabilistic planning

Planning graphs have been shown to be a rich source of heuristic information for many kinds of planners. In many cases, planners must compute a planning graph for each element of a set of states, and the naive technique enumerates the graphs individually. This is equivalent to solving a multiple-source shortest path problem by iterating a single-source algorithm over each source.We introduce a data-structure, the state agnostic planning graph, that directly solves the multiple-source problem for the relaxation introduced by planning graphs. The technique can also be characterized as exploiting the overlap present in sets of planning graphs. For the purpose of exposition, we first present the technique in deterministic (classical) planning to capture a set of planning graphs used in forward chaining search. A more prominent application of this technique is in conformant and conditional planning (i.e., search in belief state space), where each search node utilizes a set of planning graphs; an optimization to exploit state overlap between belief states collapses the set of sets of planning graphs to a single set. We describe another extension in conformant probabilistic planning that reuses planning graph samples of probabilistic action outcomes across search nodes to otherwise curb the inherent prediction cost associated with handling probabilistic actions. Finally, we show how to extract a state agnostic relaxed plan that implicitly solves the relaxed planning problem in each of the planning graphs represented by the state agnostic planning graph and reduces each heuristic evaluation to counting the relevant actions in the state agnostic relaxed plan. Our experimental evaluation (using many existing International Planning Competition problems from classical and non-deterministic conformant tracks) quantifies each of these performance boosts, and demonstrates that heuristic belief state space progression planning using our technique is competitive with the state of the art.     

Conformant planning via heuristic forward search: A new approach

Conformant planning is the task of generating plans given uncertainty about the initial state and action effects, and without any sensing capabilities during plan execution. The plan should be successful regardless of which particular initial world we start from. It is well known that conformant planning can be transformed into a search problem in belief space, the space whose elements are sets of possible worlds. We introduce a new representation of that search space, replacing the need to store sets of possible worlds with a need to reason about the effects of action sequences. The reasoning is done by implication tests on propositional formulas in conjunctive normal form (CNF) that capture the action sequence semantics. Based on this approach, we extend the classical heuristic forward-search planning system FF to the conformant setting. The key to this extension is an appropriate extension of the relaxation that underlies FF's heuristic function, and of FF's machinery for solving relaxed planning problems: the extended machinery includes a stronger form of the CNF implication tests that we use to reason about the effects of action sequences. Our experimental evaluation shows the resulting planning system to be superior to the state-of-the-art conformant planners MBP, KACMBP, and GPT in a variety of benchmark domains.     

一致性规划中互斥常量合成方法研究

为压缩一致性规划的状态空间,并加快一致性规划的求解速度,将常量引入到一致性规划中,定义一致性规划中的常量,形成新的知识表示"多值一致性规划任务",定义多值一致性规划动作模型,提出一致性规划常量合成方法,给出一致性规划常量合成算法.该方法利用常量的特性在所有初始世界状态和所有实例动作中猜测、验证常量.理论分析和实验结果表明该算法能合成正确的一致性规划常量,生成多值一致性规划任务.为说明一致性规划常量的应用效果,把生成的多值一致性规划任务与规划解重用启发式结合求一致性规划解,并与规划系统CFF进行对比实验.实验结果表明求解质量和效率较高.     

Landmark-based heuristic online contingent planning

In contingent planning problems, agents have partial information about their state and use sensing actions to learn the value of some variables. When sensing and actuation are separated, plans for such problems can often be viewed as a tree of sensing actions, separated by conformant plans consisting of non-sensing actions that enable the execution of the next sensing action. We propose a heuristic, online method for contingent planning which focuses on identifying the next useful sensing action. We select the next sensing action based on a landmark heuristic, adapted from classical planning. We discuss landmarks for plan trees, providing several alternative definitions and discussing their merits. The key part of our planner is the novel landmarks-based heuristic, together with a projection method that uses classical planning to solve the intermediate conformant planning problems. The resulting heuristic contingent planner solves many more problems than state-of-the-art, translation-based online contingent planners, and in most cases, much faster, up to 3 times faster on simple problems, and 200 times faster on non-simple domains.     

一致性规划研究

针对一致性规划的高度求解复杂度,分析主流一致性规划器的求解策略,给出影响一致性规划器性能的主要因素：启发信息的有效性,信念状态表示方法的紧凑性和最终问题求解机制的效率。分析信念状态的表示方法和相应的求解机制,并比较不同表示方法在不同条件下的优劣。讨论一致性规划的未来研究方向和发展趋势。     

一种优化的一致性规划状态变量选择算法

研究了一致性规划任务信念状态空间的表示方法。针对一致性有限域表示(CPT-FDR)算法在任务生成阶段选择状态变量的不足,提出了一种基于初始状态中文字相容互斥的状态变量选择算法——MECV算法。CPT-FDR未考虑初始信念状态中文字的互斥性,产生冗余的编码信息,降低了编码的效率。MECV算法利用有用正负文字构造新的未覆盖事实集,提取初始信念状态中处于不同世界状态的文字组成互斥组,再编码状态变量。实验结果表明该算法能有效地压缩信念状态空间。     

Sequential Monte Carlo in reachability heuristics for probabilistic planning

Some of the current best conformant probabilistic planners focus on finding a fixed length plan with maximal probability. While these approaches can find optimal solutions, they often do not scale for large problems or plan lengths. As has been shown in classical planning, heuristic search outperforms bounded length search (especially when an appropriate plan length is not given a priori). The problem with applying heuristic search in probabilistic planning is that effective heuristics are as yet lacking.In this work, we apply heuristic search to conformant probabilistic planning by adapting planning graph heuristics developed for non-deterministic planning. We evaluate a straight-forward application of these planning graph techniques, which amounts to exactly computing a distribution over many relaxed planning graphs (one planning graph for each joint outcome of uncertain actions at each time step). Computing this distribution is costly, so we apply Sequential Monte Carlo (SMC) to approximate it. One important issue that we explore in this work is how to automatically determine the number of samples required for effective heuristic computation. We empirically demonstrate on several domains how our efficient, but sometimes suboptimal, approach enables our planner to solve much larger problems than an existing optimal bounded length probabilistic planner and still find reasonable quality solutions.     

Conformant plans and beyond: Principles and complexity

Conformant planning is used to refer to planning for unobservable problems whose solutions, like classical planning, are linear sequences of operators called linear plans. The term ‘conformant’ is automatically associated with both the unobservable planning model and with linear plans, mainly because the only possible solutions for unobservable problems are linear plans. In this paper we show that linear plans are not only meaningful for unobservable problems but also for partially-observable problems. In such case, the execution of a linear plan generates observations from the environment which must be collected by the agent during the execution of the plan and used at the end in order to determine whether the goal had been achieved or not; this is the typical case in problems of diagnosis in which all the actions are knowledge-gathering actions.Thus, there are substantial differences about linear plans for the case of unobservable or fully-observable problems, and for the case of partially-observable problems: while linear plans for the former model must conform with properties in state space, linear plans for partially-observable problems must conform with properties in belief space. This differences surface when the problems are allowed to express epistemic goals and conditions using modal logic, and place the plan-existence decision problem in different complexity classes.Linear plans is one extreme point in a discrete spectrum of solution forms for planning problems. The other extreme point is contingent plans in which there is a branch point for every possible observation at each time step, and thus the number of branch points is not bounded a priori. In the middle of the spectrum, there are plans with a bounded number of branch points. Thus, linear plans are plans with zero branch points and contingent plans are plans with unbounded number of branch points.In this work, we lay down foundations and principles for the general treatment of linear plans and plans of bounded branching, and provide exact complexity results for novel decision problems. We also show that linear plans for partially-observable problems are not only of theoretical interest since some challenging real-life problems can be dealt with them.     

PPDDL一致性规划任务的有限域转换方法

给出了PPDDL一致性规划任务和有限域一致性规划任务的定义,扩展了非确定动作等相关语义,并在此基础上提出了一种将PPDDL表示的一致性规划任务转换为有限域表示的一致性规划任务的CFDR方法,实现了经典规划的FDR转换算法在一致性规划中的扩展。相比MCPT算法,主要改进了其中的合成不变量方法和任务生成方法,此外还增加了对于非确定动作效果的表示和处理。通过在标准的一致性规划域上的实验,证明了CFDR的适用性和有效性。     

基于缩减信念状态的Conformant 规划方法

Conformant 规划问题通常转化为信念状态空间的搜索问题来求解.提出了通过降低信念状态的不确定性来提高规划求解效率的方法.首先给出缩减信念状态的增强爬山算法,在此基础上,提出了基于缩减信念状态的Conformant 规划方法,设计了CFF-Lite 规划系统.该规划器的求解过程包括两次增强爬山过程,分别用于缩减信念状态和搜索目标.首先对初始信念状态作最大程度的缩减,提高启发函数的准确性;然后从缩减后的信念状态开始执行启发式搜索.实验结果表明,CFF-Lite 规划系统通过快速缩减信念状态降低了问题的求解难度,在大多数问题上,求解效率和规划解质量与Conformant-FF 相比,都有显著的提高.