'Classical' Negation in Nonmonotonic Reasoning and Logic Programming

Gelfond and Lifschitz were the first to point out the need for a symmetric negation in logic programming and they also proposed a specific semantics for such negation for logic programs with the stable semantics, which they called 'classical'. Subsequently, several researchers proposed different, often incompatible, forms of symmetric negation for various semantics of logic programs and deductive databases. To the best of our knowledge, however, no systematic study of symmetric negation in non-monotonic reasoning was ever attempted in the past. In this paper we conduct such a systematic study of symmetric negation. We introduce and discuss two natural, yet different, definitions of symmetric negation: one is called strong negation and the other is called explicit negation. For logic programs with the stable semantics, both symmetric negations coincide with Gelfond–Lifschitz' 'classical negation'. We study properties of strong and explicit negation and their mutual relationship as well as their relationship to default negation 'not', and classical negation '¬'. We show how one can use symmetric negation to provide natural solutions to various knowledge representation problems, such as theory and interpretation update, and belief revision. Rather than to limit our discussion to some narrow class of nonmonotonic theories, such as the class of logic programs with some specific semantics, we conduct our study so that it is applicable to a broad class of non-monotonic formalisms. In order to achieve the desired level of generality, we define the notion of symmetric negation in the knowledge representation framework of AutoEpistemic logic of Beliefs, introduced by Przymusinski.     

Logic Programming and Burden of Proof in Legal Reasoning

In legal reasoning, there are a lot of interesting problems related with techniques of informatics. We propose a research field called juris-informatics to hope that we could make a great success like bio-informatics to introduce various techniques of informatics into legal domain. In this paper, we show our contributions to apply logic programing to formalizing and implementing burden of proof in legal reasoning.     

Reasoning about Solids Using Constraint Logic Programming

The embedding of constraint satisfaction on the domain of discourse into a rule-based programming paradigm like logic programming provides a powerful reasoning tool. We present an application in spatial reasoning that uses this combination to produce a clear, concise, yet very expressive system through its ability to manipulate partial information. Three-dimensional solid objects in constructive solid geometry representation are manipulated, and their spatial relationship with one another, points, or regions is reasoned about. The language used to develop this application is QUAD-CLP(), an experimental constraint logic programming language of our own design, which is equipped with a solver for quadratic and linear arithmetic constraints over the reals.     

Reliable Computing: Special Issue on Dependable Reasoning about Uncertainty

Reliable Computing -     

Informational Logic as a Tool for Automated Reasoning

A logical entropy-based Informational Logic is presented which provides new tools for probabilistic automated reasoning and knowledge representation. Applications in automated theorem proving are examined, and a decision theory for probabilistic theorems is proposed.     

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.     

不确定性推理中确定性的传播

系统行为的确定性在不确定性推理方法中的合理传播是每一种不确定性推理方法均需考虑的问题,系统行为的确定性是控制和决策的一个重要参考信息,也是衡量一种不确定性推理方法发展成熟与否的一个标志.主观Bayes方法、确定性理论和灰色定性仿真是三种考虑了确定性在推理过程中传播,具有代表性的不确定性推理方法,它们的确定性传播方法被介绍,并对其优缺点进行了分析,结果显示灰色定性仿真的传播方法更为合理.     

Multi-Dimensional Modal Logic as a Framework for Spatio-Temporal Reasoning

In this paper we advocate the use of multi-dimensional modal logics as a framework for knowledge representation and, in particular, for representing spatio-temporal information. We construct a two-dimensional logic capable of describing topological relationships that change over time. This logic, called PSTL (Propositional Spatio-Temporal Logic) is the Cartesian product of the well-known temporal logic PTL and the modal logic S4_u, which is the Lewis system S4 augmented with the universal modality. Although it is an open problem whether the full PSTL is decidable, we show that it contains decidable fragments into which various temporal extensions (both point-based and interval based) of the spatial logic RCC-8 can be embedded. We consider known decidability and complexity results that are relevant to computation with multi-dimensional formalisms and discuss possible directions for further research.     

Clausal Logic and Logic Programming in Algebraic Domains

We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introduce a natural declarative semantics and a fixed-point semantics for disjunctive logic programs, and prove their equivalence; finally, we apply our results to give both a syntax and semantics for default logic in any coherent algebraic dcpo.     

语义web中以描述逻辑为本体语言的推理

语义Web是worldwideweb的发展方向,它的实现能有效地提高互联网的智能化程度,进而提高其使用效率。描述逻辑作为语义Web的一个逻辑基础,成为其研究和开发的重要内容。该文讨论了语义Web中以描述逻辑为本体语言的推理方法,并对其应用作了简要的分析。     

Logic Programming and Prolog: A Tutorial

Logic programming offers significant advantages for the massively parallel computer systems of tomorrow. This tutorial examines the potential of Prolog to implement those advantages.     

Reasoning in a Restricted Temporal Logic

We consider RTL, a linear time propositional temporal logic whose only modalities are the [formula] (eventually) operator and its dual [formula] (always). Although less expressive than the full temporal logic, RTL is the fragment of temporal logic that is used most often and in many verification systems. Indeed, many properties of distributed systems discussed in the literature are RTL properties. Another advantage of RTL over the full temporal logic is in the decidability procedure; while deciding satisfiability of a formula in full temporal logic is a PSPACE complete procedure, doing so for an RTL formula is in NP. We characterize the class of ω-regular languages that are definable in RTL and show simple translations between ω-regular sets and RTL formulae that define them. We explore the applications of RTL in reasoning about communication systems. Finally, we relate variants of RTL (when interpreted over a real line segments) to several fragments of Interval Modal Logic and show that the satisfiability problem for RTL when interpreted over a real line is NP-complete.     

Reasoning About Truth in First-Order Logic

First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the aforementioned proof systems when capacity limits are put on the cognitive resources. Finally, we investigate the correlation between a number of mathematical complexity measures defined on graphs and sentences and some psychological complexity measures that were recorded in the experiment.     

产品的相似性推理:一种描述逻辑的方法

采用产品本体理论对设计进行本体标注,得到对应产品设计的形式化概念,在此基础上通过本体的推理——基于描述逻辑的知识推理,对产品进行分类．文中分别就设计的相似性和基于实例的设计中实例间的相似性推理提出了明确的算法,并通过实例进行了说明．