An argumentation framework in default logic

This article presents a formal theory about nontrivial reasoning with inconsistent information, applicable, among other things, to defeasible reasoning. The theory, which is inspired by a formal analysis of legal argument, is based on the idea that inconsistency tolerant reasoning is more than revising an unstructural set of premises; rather it should be regarded as constructing and comparing arguments for incompatible conclusions. This point of view gives rise to two important observations, both pointing at some flaws of other theories. The first is that arguments should be compared as they are constructed, viz. step-by-step, while the second observation is that a knowledge representation language is needed with a defeasible conditional, since the material implication gives rise to arguments which are not constructed in actual reasoning. Accordingly, a nonmonotonic logic, default logic, is chosen as the formalism underlying the argumentation framework. The general structure of the framework allows for any standard for comparing pairs of arguments; in this study two such standards are investigated, based on specificity and on orderings of the premises.     

Quantitative logic

In this paper, we introduce the concept of the degree of the truth in the framework of so called many-valued propositional logic systems with the intention of measuring to what extent a given formula is true. Such a concept can indeed induce, in a very natural way, the degree of the similarity as well as to induce a pseudo-metric among formulas as the ‘graded’ version of the notion of the logical equivalence. The basic properties of such induced logic metric space hence are investigated in this paper. We further introduce different concepts of the degree of the divergence and the degree of the consistency in order to grade the extent of the consistency of a logic theory. To the end, all the basic logic notions are graded. Lastly, we propose in this paper three patterns of ‘approximate reasoning’ so far as the many-valued propositional logic systems are concerned. Hence, we can claim that we have laid the foundation for the “quantitative logic”. Since this theory has touched upon several key concepts of similarity, comparison, measurements, etc. in information theory, we are convinced that the theory may have profound impact in contemporary information technology. In addition, quantitative logic can be regarded as a highly representative example of mathematics of uncertainty capable of handling vagueness.     

可能性缺省逻辑及其应用

本文分析了Yager用可能性理论框架来表示缺省知识的形式化方法,并测试了三类不同的应用方案,得到的结果与Reiter的缺省逻辑得到的结果相比较,表明只在具有严格的约束的缺省逻辑下,Yager的形式化方法才与Reiter的缺省逻辑具有一定的相关性,我们指出了它们在一般缺省理论下的不匹配处,并给出了以不动点机制抽改进方来消除这
些不匹配。     

On randomization and discovery

In the first part of this paper, traditional computability theory is extended to prove that the attainable density of knowledge is virtually unbounded. That is, the more bits available for storage, the more information that can be stored, where the density of information per bit cannot be bounded above. In the second part, the paper explains how machine intelligence becomes possible as a result of the capability for creating, storing, and retrieving virtually unlimited information/knowledge. It follows from this theory that there is no such thing as a valid non-trivial proof, which in turn implies the need for heuristic search/proof techniques. Two examples are presented to show how heuristics can be developed, which are randomizations of knowledge - establishing the connection with the first part of the paper. Even more intriguing, it is shown that heuristic proof techniques are to formal proof techniques what fuzzy logic is to classical logic.     

Fuzzy-set-based machine-cell formation in cellular manufacturing

In cellular manufacturing, manufacturing cells are designed based on the assumption that only one machine is used for a particular operation. However, there can be alternative machines to process an operation. In this article, a fuzzy-set-based machine-cell formation algorithm for cellular manufacturing is presented. The fuzzy logic is employed to express the degree of appropriateness when alternative machines are specified to process a part shape. For machine grouping, the similarity-coefficient-based approach is used. The algorithm produces efficient machine cells and part families, which maximize the similarity values. This algorithm can also be used when the intercellular movement costs should be minimized. A numerical example is given to illustrate this approach.     

A Rewriting Logic Approach to Operational Semantics (Extended Abstract)

This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: big-step and small-step structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, and continuation-based semantics. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a one-to-one correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or pre-impose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles.     

A rewriting logic approach to operational semantics

This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: big-step and small-step structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, continuation-based semantics, and the chemical abstract machine. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a one-to-one correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or pre-impose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles.     

Translating Multi-Agent Autoepistemic Logic into Logic Program

In order to develop a proof procedure of multi-agent autoepistemic Logic (MAEL), a natural framework to formalize belief and reasoning including inheritance, persistence, and causality, we introduce a method that translates a MAEL theory into a logic program with integrity constraints. It is proved that there exists one-to-one correspondence between extensions of a MAEL theory and stable models of a logic program translated from it. Our approach has the following advantages: (1) We can obtain all extensions of a MAEL theory if we compute all stable models of the translated logic program. (2) We can fully use efficient techniques or systems for computing stable models of a logic program. We also investigate the properties of reasoning in MAEL through this translation. The fact that the extension computing problem can be reduced to the stable model computing problem implies that there are close relationships between MAEL and other formalizations of nonmonotonic reasoning.     

A Foundation of Solution Methods for Constraint Hierarchies

Constraint hierarchies provide a framework for soft constraints, and have been applied to areas such as artificial intelligence, logic programming, and user interfaces. In this framework, constraints are associated with hierarchical preferences or priorities called strengths, and may be relaxed if they conflict with stronger constraints. To utilize constraint hierarchies, researchers have designed and implemented various practical constraint satisfaction algorithms. Although existing algorithms can be categorized into several approaches, what kinds of algorithms are possible has been unclear from a more general viewpoint. In this paper, we propose a novel theory called generalized local propagation as a foundation of algorithms for solving constraint hierarchies. This theory formalizes a way to express algorithms as constraint scheduling, and presents theorems that support possible approaches. A benefit of this theory is that it covers algorithms using constraint hierarchy solution criteria known as global comparators, for which only a small number of algorithms have been implemented. With this theory, we provide a new classification of solution criteria based on their difficulties in constraint satisfaction. We also discuss how existing algorithms are related to our theory, which will be helpful in designing new algorithms.     

Beyond Transaction Cost Economics: Towards an endogenous theory of Information Technology Outsourcing

In our review, we coded 73 empirical findings from 31 journal articles that applied Transaction Cost Economics (TCE) to study Information Technology Outsourcing (ITO). As Karimi-Alaghehband et al. (2011) note correctly, the empirical results of TCE tests in the context of ITO are mixed. We found that only 49% of the empirical ITO findings supported TCE logic. We found only slightly better support for TCE when it is used as a normative theory (54%) than when it is used as a predictive theory (47%). The main difference between Karimi-Alaghehband et al.’s (2011) contribution and our contribution to the debate focuses upon what to do next. Karimi-Alaghehband et al. (2011) argue that ITO researchers need to apply TCE more faithfully. We argue that we are asking too much of TCE—the ITO phenomenon is more complex than can be accommodated by TCE. We argue that ITO research has matured to the point that we should be building our own endogenous ITO theory. We offer observations and insights on what such a theory might entail. In moving ITO research forward, we first critique TCE assumptions and provide alternative assumptions that seem to fit ITO observations well. We draw on our review of 741 ITO empirical findings (Lacity et al., 2010) to provide a detailed theoretical framework to advance further study that suggests the most promising constructs to use in an endogenous ITO theory.     

Symbolic planning and control of robot motion [Grand Challenges of Robotics]

In this paper, different research trends that use symbolic techniques for robot motion planning and control are illustrated. As it often happens in new research areas, contributions to this topic started at about the same time by different groups with different emphasis, approaches, and notation. This article tries to describe a framework in which many of the current methods and ideas can be placed and to provide a coherent picture of what the authors want to do, what have they got so far, and what the main missing pieces are. Generally speaking, the aim of symbolic control as is envisioned in this article is to enable the usage of methods of formal logic, languages, and automata theory for solving effectively complex planning problems for robots and teams of robots. The results presented in this article can be divided in two groups: top-down approaches, whereby formal logic tools are employed on rather abstract models of robots; and bottom up approaches, whose aim is to provide means by which such abstractions are possible and effective. The two ends do not quite tie as yet, and much work remains to be done in both directions to obtain generally applicable methods. However, the prospects of symbolic control of robots are definitely promising, and the challenging nature of problems to be solved warrants for the interest of a wide community of researchers     

基于泛逻辑学的模糊逻辑关系柔性的研究

模糊逻辑是许多实际应用的逻辑基础,但是其理论基础还不太成熟,不能够实现真正的柔性,这也就影响了它的应用范围.逻辑学正处于第二次革命中,也就是由刚性逻辑到柔性逻辑的转变,泛逻辑学正是由何华灿教授建立的一种新的柔性逻辑体系.只有在泛逻辑学的框架内才能真正实现模糊逻辑关系的柔性化.     

A research programme for object-orientation

The aim of this paper is to identify a research programme for object-orientation according to Lakatos's concepts from the theory of science. This programme will serve as a framework within which research on object-orientation can take place. Today there does not exist a general agreement as to what constitutes the core of object-orientation and a universal object-oriented model has not been defined. Lakatos suggested that scientific progress be viewed in the context of research programmes instead of individual theories. According to post-empiricism every statement is theory-impregnated. Therefore it is not possible to compare different theories objectively. If we view scientific development within the framework of research programmes, this problem is reduced, since theories within the same research programme can be compared. An analysis of the object-oriented approach, starting with a historical view of the development of object-orientation, is presented together with various definitions of what object-orientation means. On this basis a proposal for a hard core for an object-oriented research programme is put forward. This core should constitute the framework for further research. Thereafter a protecting belt is suggested wherein the interesting research topics of the research programme are to be found.     

Robust distributed control of robot formations with parameter uncertainty

This paper discusses robot formations in a distributed framework. The most important contribution is the incorporation of robustness into robot formation systems. When robots carry out tasks in a poor environment, the parameters in their models fluctuate around the nominal values, which may destroy the stability of the formation system. By modeling the group of robots as an interconnected system, we aim to develop a set of robust distributed controllers such that the overall system is robust to external disturbance as well as parameter uncertainty. Based on the graph rigidity theory, we also consider the rotation of a formation that plays an important role in real-time applications. Both simulations and real-time experiments are carried out to validate the effectiveness of the proposed framework.     

Logics and Multi-agents: towards a new symbolic model of cognition

The last edition of CLIMA, held in 2001 in Paphos (Cyprus) ended with a panel session on the role of Computational Logic (CL) in Multi-Agent Systems (MAS).Two dimensions in MAS development were singled out and discussed: on the one hand reactivity vs. rationality, and on the other hand individuals vs. societies. Most of the points discussed aimed at justifying and motivating the application of CL techniques to MAS development: should be logics used to implement the individuals, or the society, or both? should be logics used to model the reactive part, or the pro-active part, or both? what do we want to achieve in terms of properties, openness to integration, etc.?A most intuitive reply to these questions could be that logic should be used for what logic is good at. For instance, logic programming-based techniques such as abductive and inductive logic programming seem suitable for modelling agent hypothetical reasoning and adaptability. Modal logic operators such as those adopted by a BDI agent model [3] could be a powerful and synthetic way to describe the agent behaviour and to put it into relationship with the other agents in a society. Model checking-based techniques can be applied to the verification of agent systems. A combination of multiple approaches, like modal and temporal logics, or abduction and induction in a logic programming framework, could be the key to achieve a more comprehensive agent and agent system architecture. But in this case, to determine which properties of the chosen combinations hold is not an easy task.At the time of this new edition of CLIMA, while the debate about the role of CL in MAS is still open, from within the CL community we are witnessing a growth of interest for Multi-Agent Systems considered per se as an interesting cognitive model. This is due to many reasons, among which, we would say, the need to put “abstract” reasoning in the context of a “concrete” environment, and to use logic not only to solve problems in a virtual world, but in a real arena. The multi-agent metaphor of intelligent individuals that are situated into dynamic and unpredictable environments and that can interact with each other by updating their beliefs, can be regarded then as the basis for a new symbolic model of cognition.     

Deontic logic in the representation of law: Towards a methodology

There seems to be no clear consensus in the existing literature about the role of deontic logic in legal knowledge representation — in large part, we argue, because of an apparent misunderstanding of what deontic logic is, and a misplaced preoccupation with the surface formulation of legislative texts. Our aim in this paper is to indicate, first, which aspects of legal reasoning are addressed by deontic logic, and then to sketch out the beginnings of a methodology for its use in the analysis and representation of law.The essential point for which we argue is that deontic logic — in some form or other —needs to be taken seriously whenever it is necessary to make explicit, and then reason about, the distinction between what ought to be the case and what is the case, or as we also say, between the ideal and the actual. We take the library regulations at Imperial College as the main illustration, and small examples from genuinely legal domains to introduce specific points. In conclusion, we touch on the role of deontic logic in the development of the theory of normative positions.Deontic logic and the theory of normative positions are of relevance to legal knowledge representation, but also to the analysis and. representation of normative systems generally. The emphasis of the paper is on legal knowledge representation, but we seek to place the discussion within the context of a broader range of issues concerning the role of deontic logic in Computer Science.     

From Hilbert’s program to a logic tool box

In this paper I discuss what, according to my long experience, every computer scientists should know from logic. We concentrate on issues of modeling, interpretability and levels of abstraction. We discuss what the minimal toolbox of logic tools should look like for a computer scientist who is involved in designing and analyzing reliable systems. We shall conclude that many classical topics dear to logicians are less important than usually presented, and that less known ideas from logic may be more useful for the working computer scientist.     

Semantic forgetting in answer set programming

The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In this paper, we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting can be entirely captured by classical forgetting. We present several algorithms for computing a representation of the result of forgetting, and provide a characterization of the computational complexity of reasoning from a logic program under forgetting. As applications of our approach, we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs, and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting. The basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency. In particular, we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming.