Fuzzy region connection calculus in finite discrete space domains

Many practical applications involving spatial aspects work with finite discrete space domains, e.g. map grids, railways track layouts and road networks. Such space domains are computationally tractable and often include specialised forms of spatial reasoning. Moreover, in such applications, the spatial information naturally includes various forms of approximation, uncertainty or inexactness. Fuzzy representations are then appropriate. In this paper, we reformulate the region connection calculus (RCC) framework for finite, discrete space domains in simple set-theoretical terms. We generalise RCC framework and develop several fuzzy spatial concepts like fuzzy regions, fuzzy directions, fuzzy named distances. We propose a fuzzification of standard spatial relations in RCC. For this purpose, we enhance the fuzzy set theory to include fuzzy definitions for membership, subset and set equality crisp binary relations between sets (fuzzy or crisp). We illustrate the approach using a discrete finite two-dimensional map grid as the space domain.     

A fuzzy sets theoretic approach to approximate spatial reasoning

Relational composition-based reasoning has become the most prevalent method for qualitative reasoning since Allen's 1983 work on temporal intervals. Underlying this reasoning technique is the concept of a jointly exhaustive and pairwise disjoint set of relations. Systems of relations such as RCC5 and RCC8 were originally developed for ideal regions, not subject to imperfections such as vagueness or fuzziness which are found in many applications in geographic analysis and image understanding. This paper, however, presents a general method for classifying binary topological relations involving fuzzy regions using the RCC5 or the RCC8 theory. Our approach is based on fuzzy set theory and the theory of consonant random set. Some complete classifications of topological relations between fuzzy regions are also given. Furthermore, two composition operators on spatial relations between fuzzy regions are introduced in this paper. These composition operators provide reasonable relational composition-based reasoning engine for spatial reasoning involving fuzzy regions.     

A condensed semantics for qualitative spatial reasoning about oriented straight line segments

More than 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. However, it turned out to be difficult to establish a sound constraint calculus based on these relations. In this paper, we present the results of a new investigation into dipole constraint calculi which uses algebraic methods to derive sound results on the composition of relations of dipole calculi. This new method, which we call condensed semantics, is based on an abstract symbolic model of a specific fragment of our domain. It is based on the fact that qualitative dipole relations are invariant under orientation preserving affine transformations.The dipole calculi allow for a straightforward representation of prototypical reasoning tasks for spatial agents. As an example, we show how to generate survey knowledge from local observations in a street network. The example illustrates the fast constraint-based reasoning capabilities of dipole calculi. We integrate our results into two reasoning tools which are publicly available.     

Property persistence in the situation calculus

We develop a new automated reasoning technique for the situation calculus that can handle a class of queries containing universal quantification over situation terms. Although such queries arise naturally in many important reasoning tasks, they are difficult to automate in the situation calculus due to the presence of a second-order induction axiom. We show how to reduce queries about property persistence, a common type of universally-quantified query, to an equivalent form that does not quantify over situations and so is amenable to existing reasoning techniques. Our algorithm replaces induction with a meta-level fixpoint calculation; crucially, this calculation uses only first-order reasoning with a limited set of axioms. The result is a powerful new tool for verifying sophisticated domain properties in the situation calculus.     

基于结合空间拓扑和方向关系信息的空间推理

结合了定性空间推理中著名的区域连接演算（region connection calculus,RCC）和基于区域的方向关系演算（cardinal direction calculus,CDC）,并且给出两个演算在两个方向上的交互表,即RCC8-To-CDC和CDC-To-RCC8．给出了结合RCC8和CDC知识的约束满足问题的路径一致算法（path consistency algorithm）（该算法是对Allen著名的路径一致算法的修改）,并且采用两个队列实现了该算法,采用这种结构可以实现并行计算．在该算法中,基于以上两个交互表的交互操作被嵌入到算法里面来保证整个约束满足问题的一致性．算法的计算复杂性证明是多项式的,     

Reasoning about reasoning in a meta-level architecture

In this paper we discuss reasoning about reasoning in a multiple agent scenario. We consider agents that are perfect reasoners, loyal, and that can take advantage of both the knowledge and ignorance of other agents. The knowledge representation formalism we use is (full) first order predicate calculus, where different agents are represented by different theories, and reasoning about reasoning is realized via a meta-level representation of knowledge and reasoning. The framework we provide is pretty general: we illustrate it by showing a machine checked solution to the three wisemen puzzle. The agents' knowledge is organized into units: the agent's own knowledge about the world and its knowledge about other agents are units containing object-level knowledge; a unit containing meta-level knowledge embodies the reasoning about reasoning and realizes the link among units. In the paper we illustrate the meta-level architecture we propose for problem solving in a multi-agent scenario; we discuss our approach in relation to the modal one and we compare it with other meta-level architectures based on logic. Finally, we look at a class of applications that can be effectively modeled by exploiting the meta-level approach to reasoning about knowledge and reasoning.     

An approach to fuzzy default reasoning for function approximation

This paper discusses fuzzy reasoning for approximately realizing nonlinear functions by a small number of fuzzy if-then rules with different specificity levels. Our fuzzy rule base is a mixture of general and specific rules, which overlap with each other in the input space. General rules work as default rules in our fuzzy rule base. First, we briefly describe existing approaches to the handling of default rules in the framework of possibility theory. Next, we show that standard interpolation-based fuzzy reasoning leads to counterintuitive results when general rules include specific rules with different consequents. Then, we demonstrate that intuitively acceptable results are obtained from a non-standard inclusion-based fuzzy reasoning method. Our approach is based on the preference for more specific rules, which is a commonly used idea in the field of default reasoning. When a general rule includes a specific rule and they are both compatible with an input vector, the weight of the general rule is discounted in fuzzy reasoning. We also discuss the case where general rules do not perfectly but partially include specific rules. Then we propose a genetics-based machine learning (GBML) algorithm for extracting a small number of fuzzy if-then rules with different specificity levels from numerical data using our inclusion-based fuzzy reasoning method. Finally, we describe how our approach can be applied to the approximate realization of fuzzy number-valued nonlinear functions     

Reasoning with Qualitative Positional Information for Domestic Domains in the Situation Calculus

In this paper, we present a thorough integration of qualitative representations and reasoning for positional information for domestic service robotics domains into our high-level robot control. In domestic settings for service robots like in the RoboCup@Home competitions, complex tasks such as “get the cup from the kitchen and bring it to the living room” or “find me this and that object in the apartment” have to be accomplished. At these competitions the robots may only be instructed by natural language. As humans use qualitative concepts such as “near” or “far”, the robot needs to cope with them, too. For our domestic robot, we use the robot programming and plan language Readylog, our variant of Golog. In previous work we extended the action language Golog, which was developed for the high-level control of agents and robots, with fuzzy set-based qualitative concepts. We now extend our framework to positional fuzzy fluents with an associated positional context called frames. With that and our underlying reasoning mechanism we can transform qualitative positional information from one context to another to account for changes in context such as the point of view or the scale. We demonstrate how qualitative positional fluents based on a fuzzy set semantics can be deployed in domestic domains and showcase how reasoning with these qualitative notions can seamlessly be applied to a fetch-and-carry task in a RoboCup@Home scenario.     

Reasoning of fuzzy relational databases with fuzzy ontologies

A significant interest developed regarding the problem of describing databases with expressive knowledge representation techniques in recent years, so that database reasoning may be handled intelligently. Therefore, it is possible and meaningful to investigate how to reason on fuzzy relational databases (FRDBs) with fuzzy ontologies. In this paper, we first propose a formal approach and an automated tool for constructing fuzzy ontologies from FRDBs, and then we study how to reason on FRDBs with constructed fuzzy ontologies. First, we give their respective formal definitions of FRDBs and fuzzy Web Ontology Language (OWL) ontologies. On the basis of this, we propose a formal approach that can directly transform an FRDB (including its schema and data information) into a fuzzy OWL ontology (consisting of the fuzzy ontology structure and instance). Furthermore, following the proposed approach, we implement a prototype construction tool called FRDB2FOnto. Finally, based on the constructed fuzzy OWL ontologies, we investigate how to reason on FRDBs (e.g., consistency, satisfiability, subsumption, and redundancy) through the reasoning mechanism of fuzzy OWL ontologies, so that the reasoning of FRDBs may be done automatically by means of the existing fuzzy ontology reasoner.© 2012 Wiley Periodicals, Inc.     

Fuzzifying Allen's Temporal Interval Relations

When the time span of an event is imprecise, it can be represented by a fuzzy set, called a fuzzy time interval. In this paper, we propose a framework to represent, compute, and reason about temporal relationships between such events. Since our model is based on fuzzy orderings of time points, it is not only suitable to express precise relationships between imprecise events (ldquoRoosevelt died before the beginning of the Cold Warrdquo) but also imprecise relationships (ldquoRoosevelt died just before the beginning of the Cold Warrdquo). We show that, unlike previous models, our model is a generalization that preserves many of the properties of the 13 relations Allen introduced for crisp time intervals. Furthermore, we show how our model can be used for efficient fuzzy temporal reasoning by means of a transitivity table. Finally, we illustrate its use in the context of question answering systems.     

A framework for specifying and monitoring user tasks

Interrupting users engaged in tasks typically has negative effects on their task completion time, error rate, and affective state. Empirical research has shown that these negative effects can be mitigated by deferring interruptions until more opportune moments in a user’s task sequence. However, existing systems that reason about when to interrupt do not have access to models of user tasks that would allow for such finer-grained temporal reasoning. To enable this reasoning, we have developed an integrated framework for specifying and monitoring user tasks. For task specification, our framework provides a language that supports expressive specification of tasks using a concise notation. For task monitoring, our framework provides an event database and handler that manages events from any instrumented application and a task monitor that observes a user’s progress through specified tasks. We describe the design and implementation of our framework, showing how it can be used to specify and monitor practical, representative user tasks. We also report results from two user studies measuring the effectiveness of our existing implementation. The use of our framework will enable attention aware systems to consider a user’s position in a task when reasoning about when to interrupt.     

Reasoning with propositional knowledge based on fuzzy neural logic

In this article, a new kind of reasoning for propositional knowledge, which is based on the fuzzy neural logic initialed by Teh, is introduced. A fundamental theorem is presented showing that any fuzzy neural logic network can be represented by operations: bounded sum, complement, and scalar product. Propositional calculus of fuzzy neural logic is also investigated. Linear programming problems risen from the propositional calculus of fuzzy neural logic show a great advantage in applying fuzzy neural logic to answer imprecise questions in knowledge-based systems. An example is reconsidered here to illustrate the theory. © 1996 John Wiley & Sons, Inc.     

Specifying and computing preferred plans

In this paper, we address the problem of specifying and computing preferred plans using rich, qualitative, user preferences. We propose a logical language for specifying preferences over the evolution of states and actions associated with a plan. We provide a semantics for our first-order preference language in the situation calculus, and prove that progression of our preference formulae preserves this semantics. This leads to the development of PPlan, a bounded best-first search planner that computes preferred plans. Our preference language is amenable to integration with many existing planners, and beyond planning, can be used to support a diversity of dynamical reasoning tasks that employ preferences.     

FUZZY REASONING IN A MULTIAGENT SYSTEM OF SURVEILLANCE SENSORS TO MANAGE COOPERATIVELY THE SENSOR-TO-TASK ASSIGNMENT PROBLEM

In this work, a surveillance network composed of a set of sensors and a fusion center is designed as a multiagent system. Negotiation among sensors (agents) is proposed to solve the task-to-sensor assignment problem (the allocation of tasks to sensors), addressing several aspects. First, the fusion center determines the tasks (system tasks) to be performed by the network at each management cycle. To do that, a fuzzy reasoning system determines the priorities of these system tasks by means of a symbolic inference process using the fused data received from all sensors. In addition, a fuzzy reasoning process, similar to that performed in the fusion center, is proposed to evaluate the priority of local tasks (sensor tasks) now executed by each sensor. The network coordination procedure will be based on the system-task priorities, computed in the fusion center, and on the local priorities evaluated in each sensor. Priority values for system and sensor tasks will be the basis to guide a negotiation process among sensors in the multiagent system. The validity of the fuzzy reasoning approach is supported by the fact that it has been able to manage environmental situations in a similar way as experienced human operators do. Included results illustrate how the negotiation scheme, based on task priority and measured through their time-variant priority, allows the adaption of sensor operation to changing situations.     

A neural network model of causality

This paper proposes a model for commonsense causal reasoning, based on the basic idea of neural networks. After an analysis of the advantages and limitations of existing accounts of causality, a fuzzy logic based formalism FEL is proposed that takes into account the inexactness and the cumulative evidentiality of commonsense causal reasoning, overcoming the limitations of existing accounts. Analyses concerning how FEL handles various aspects of commonsense causal reasoning are performed, in an abstract way. FEL can be implemented (naturally) in a neural (connectionist) network. This work also serves to link rule-based reasoning with neural network models, in that a rule-encoding scheme (FEL) is equated directly to a neural network model.     

A logic-based model of intention formation and action for multi-agent subcontracting

We present a formalism for representing the formation of intentions by agents engaged in cooperative activity. We use a syntactic approach presenting a formal logical calculus that can be regarded as a meta-logic that describes the reasoning and activities of the agents. Our central focus is on the evolving intentions of agents over time, and the conditions under which an agent can adopt and maintain an intention. In particular, the reasoning time and the time taken to subcontract are modeled explicitly in the logic. We axiomatize the concept of agent interactions in the meta-language, show that the meta-theory is consistent and describe the unique intended model of the meta-theory. In this context we deal both with subcontracting between agents and the presence of multiple recipes, that is, multiple ways of accomplishing tasks. We show that under various initial conditions and known facts about agent beliefs and abilities, the meta-theory representation yields good results.