超协调限制逻辑的计算复杂性分析

超协调限制逻辑LPc是一种同时具有非单调性和超协调性的非经典逻辑，它可作为在不完全与不协调知识下常识推理的形式化.给出了命题LPc的计算复杂性结果和算法实现，指出LPc是NP完全问题，并给出了将LPc转化为等价的优先限制逻辑的线性时间算法，由于限制逻辑具有实用的实现算法且可用归结方法实现，因而该算法为LPc的实现提供了新的途径.     

A Complexity Dichotomy For Hypergraph Partition Functions

We consider the complexity of counting homomorphisms from an r-uniform hypergraph G to a symmetric r-ary relation H. We give a dichotomy theorem for r > 2, showing for which H this problem is in FP and for which H it is #P-complete. This generalizes a theorem of Dyer and Greenhill (2000) for the case r = 2, which corresponds to counting graph homomorphisms. Our dichotomy theorem extends to the case in which the relation H is weighted, and the goal is to compute the partition function, which is the sum of weights of the homomorphisms. This problem is motivated by statistical physics, where it arises as computing the partition function for particle models in which certain combinations of r sites interact symmetrically. In the weighted case, our dichotomy theorem generalizes a result of Bulatov and Grohe (2005) for graphs, where r = 2. When r = 2, the polynomial time cases of the dichotomy correspond simply to rank-1 weights. Surprisingly, for all r > 2 the polynomial time cases of the dichotomy have rather more structure. It turns out that the weights must be superimposed on a combinatorial structure defined by solutions of an equation over an Abelian group. Our result also gives a dichotomy for a closely related constraint satisfaction problem.     

命题线性时序逻辑的对偶模型问题的复杂性

定义了一个命题线性时序逻辑的对偶模型的概念.一个公式f的对偶模型是指f的满足以下条件的两个模型(即状态的w序列):在每个位置上这两个模型对原子命题的赋值都是对偶的.然后,对于确定一个公式f是否有对偶模型的判定问题(记为DM)和在一个Kripke-结构中确定是否存在从两个给定状态出发的对偶模型满足给定公式f的判定问题(记为KDM)的复杂性进行了研究.证明了以下结果:对于只含有F("Future")算子的命题线性时序逻辑,DM和KDM都是NP完全的;而对于以下命题线性时序逻辑,DM和KDM都是PSPACE完全的:含有F,X ("Next")算子的逻辑、含有U("Until")算子的逻辑、含有U,S,X算子的逻辑以及由Wolper给出的含有正规语言算子的逻辑(一般称为扩展时序逻辑,简称ETL).     

基于一类严格三角范数的命题逻辑

剩余模糊逻辑演算与连续三角范数是紧密相关的,三角范数是合取联结词的真值函数,三角范数的剩余是蕴涵联结词的真值函数. 在这些逻辑中,非运算都是由蕴涵和真值常量0定义的,即(→)P∶P→0-.在本文中,我们引入一种具有对合性质的强非运算联结词"～"和投影联结词"Δ",证明基于严格泛与运算模型T(x,y,h)(h∈(0.75,1))的命题演算逻辑PC(T)系统是基本严格模糊逻辑SBL;PC(T)～是基本严格模糊逻辑SBL的扩张SBL～.     

基于幂零泛与运算模型的命题模糊逻辑

本文讨论了泛与运算模型T(x,y．h)(h∈(o,0．75))的一些性质;证明了泛与运算模型T(x,y,h)(h∈(0,O.75))是一个幂零三角范数;而且泛与运算模型T(x,y．h)(h∈(0,0．75))与泛蕴涵运算模型,(x,y,h)(h∈(0,0.75))是一个伴随对;进一步证明了([0,1].∨,∧．*,→．0,1)作成一个MV-代数。给出了基于幂零泛与运算模型T(x,y,h)(h∈(0,0.75))的模糊命题演算系统PC(T),证明了此命题演算系统与Lukasiewicz逻辑命题演算系统是等价的。     

A Cut-Free Gentzen Formulation of Basic Propositional Calculus

We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination theorem isproved in a syntactic way by modifying Gentzen's method. Thisdual-context style system exemplifies the effectiveness of dual-contextformulation in formalizing various non-classical logics.     

概率命题逻辑是经典命题演算形式系统的随机事件语义

经典命题演算形式系统(CPC)中的公式只是一些形式符号,这些形式符号的意义是由具体的解释给出的.概率逻辑是在标准概率空间上建立的一种逻辑体系,是CPC的随机事件语义,对联结词的解释就是集合运算,对形式公式的解释就是事件函数,对逻辑蕴涵和逻辑等价的解释就是事件(集合)包含和事件相等=.由于不存在处处适用的真值函数(算子),概率逻辑不能在CPC内实现概率演算,但可在CPC内实现事件演算,CPC完全适用于概率命题演算.     

A Dichotomy for Real Weighted Holant Problems

Holant is a framework of counting characterized by local constraints. It is closely related to other well-studied frameworks such as the counting constraint satisfaction problem (#CSP) and graph homomorphism. An effective dichotomy for such frameworks can immediately settle the complexity of all combinatorial problems expressible in that framework. Both #CSP and graph homomorphism can be viewed as subfamilies of Holant with the additional assumption that the equality constraints are always available. Other subfamilies of Holant such as Holant^* and Holant ^c problems, in which we assume some specific sets of constraints to be freely available, were also studied. The Holant framework becomes more expressive and contains more interesting tractable cases with less or no freely available constraint functions, while, on the other hand, it also becomes more challenging to obtain a complete characterization of its time complexity. Recently, a complexity dichotomy for a variety of subfamilies of Holant such as #CSP, graph homomorphism, Holant^*, and Holant ^c for Boolean domain was proved. In this paper, we prove a dichotomy for the general Holant framework where all the constraints are real symmetric functions on Boolean inputs. This setting already captures most of the interesting combinatorial counting problems defined by local constraints, such as (perfect) matching. This is the first time a dichotomy is obtained for general Holant problems without any auxiliary functions. One benefit of working with the Holant framework is some powerful new reduction technique such as the holographic reduction. Along the proof of our dichotomy, we introduce a new reduction technique, namely realizing a constraint function by approximating it. This new technique is employed in our proof in a situation where it seems that all previous reduction techniques fail; thus, this new idea of reduction might also be of independent interest. Besides proving a dichotomy and developing a new technique, we also obtained some interesting by-products. We prove a dichotomy for #CSP, restricting to instances where each variable appears a multiple of d times for any d. We also prove that counting the number of Eulerian orientations on 2k-regular graphs is #P-hard for any \({k \geq 2}\).     

Extended IF逻辑的命题演算系统

Extended IF 逻辑是一阶逻辑的扩张,其主要特点是可表达量词间的相互依赖和独立关系,但其命题部分至今没有得到公理化.基于Cirquent 演算方法,给出了一个关于Cirquent 语义(命题水平)可靠完备的形式系统.该系统能够很好地解释和表达命题联结词间的相互依赖和独立关系,从而使Extended IF 逻辑在命题水平得到了真正意义上的公理化.     

A Dichotomy Theorem for Learning Quantified Boolean Formulas

We consider the following classes of quantified boolean formulas. Fix a finite set of basic boolean functions. Take conjunctions of these basic functions applied to variables and constants in arbitrary ways. Finally quantify existentially or universally some of the variables. We prove the following dichotomy theorem: For any set of basic boolean functions, the resulting set of formulas is either polynomially learnable from equivalence queries alone or else it is not PAC-predictable even with membership queries under cryptographic assumptions. Furthermore, we identify precisely which sets of basic functions are in which of the two cases.     

Reasoning Processes in Propositional Logic

We conducted a computer-based psychological experiment in which a random mix of 40 tautologies and 40 non-tautologies were presented to the participants, who were asked to determine which ones of the formulas were tautologies. The participants were eight university students in computer science who had received tuition in propositional logic. The formulas appeared one by one, a time-limit of 45 s applied to each formula and no aids were allowed. For each formula we recorded the proportion of the participants who classified the formula correctly before timeout (accuracy) and the mean response time among those participants (latency). We propose a new proof formalism for modeling propositional reasoning with bounded cognitive resources. It models declarative memory, visual memory, working memory, and procedural memory according to the memory model of Atkinson and Shiffrin and reasoning processes according to the model of Newell and Simon. We also define two particular proof systems, T and NT, for showing propositional formulas to be tautologies and non-tautologies, respectively. The accuracy was found to be higher for non-tautologies than for tautologies (p < .0001). For tautologies the correlation between latency and minimum proof length in T was .89 and for non-tautologies the correlation between latency and minimum proof length in NT was .87.     

A Complexity Measure

This paper describes a graph-theoretic complexity measure and illustrates how it can be used to manage and control program complexity. The paper first explains how the graph-theory concepts apply and gives an intuitive explanation of the graph concepts in programming terms. The control graphs of several actual Fortran programs are then presented to illustrate the correlation between intuitive complexity and the graph-theoretic complexity. Several properties of the graph-theoretic complexity are then proved which show, for example, that complexity is independent of physical size (adding or subtracting functional statements leaves complexity unchanged) and complexity depends only on the decision structure of a program.     

Axiomatizing the Skew Boolean Propositional Calculus

The skew Boolean propositional calculus () is a generalization of the classical propositional calculus that arises naturally in the study of certain well-known deductive systems. In this article, we consider a candidate presentation of and prove it constitutes a Hilbert-style axiomatization. The problem reduces to establishing that the logic presented by the candidate axiomatization is algebraizable in the sense of Blok and Pigozzi. In turn, this process is equivalent to verifying four particular formulas are derivable from the candidate presentation. Automated deduction methods played a central role in proving these four theorems. In particular, our approach relied heavily on the method of proof sketches.     

On the Hybrid Propositional Encodings of Planning

Recently, casting planning as propositional satisfiability (SAT) has been shown to be an efficient technique of plan synthesis. This article is a response to the recently proposed challenge of developing novel propositional encodings that are based on a combination of different types of plan refinements and characterizing the tradeoffs. We refer to these encodings as hybrid encodings. An investigation of these encodings is important, because this can give insights into what kinds of planning problems can be solved faster with hybrid encodings.
Encodings based on partial–order planning and state–space planning have been reported in previous research. We propose a new type of encoding called a unifying encoding that subsumes these two encodings. We also report on several other hybrid encodings. Next, we show how the satisfiability framework can be extended to incremental planning. State–space encoding is attractive because of its lower size and causal encoding is attractive because of its highest flexibility in reordering steps. We show that hybrid encodings have a higher size and a lower flexibility in step reordering and, thus, do not combine the best of these encodings. We discuss in detail several specific planning scenarios where hybrid encodings are likely to be superior to nonhybrid encodings.     

PH的一种复杂性类分解

本文基于ΔPK-复杂性类给出多项式时间谱系PH的一个分解,并讨论了相关的一些性质。利用该分解给出PH是否只有有限个层次这一重要计算复杂性理论问题的两个充分条件,并证明了NP中稀疏集构成的语言类在LP2∧中。     

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.     

二分思想在计算几何中的应用

简要阐述了计算几何中的二分思想,并通过例题对其进行应用,体现二分在计算几何中简洁高效的优势。     

Propositional logic of reflexive sentences

The author suggests a semantically closed language with Tarski’s truth predicate and variables based on formulas in which reflexive sentences (i.e., referring to themselves) are expressed explicitly (by the reflexivity quantor introduced by the author).