Abstract: We present some methods, based on the rough set and Boolean reasoning approaches, for extracting laws from decision tables. First we discuss several procedures for decision rules synthesis from decision tables. Next we show how to apply some near-to-functional relations between data to data filtration. Two methods of searching for new classifiers (features) are described: searching for new classifiers in a given set of logical formulas, and searching for some functions approximating near-to-functional relations.

Abstract: Vagueness and uncertainty have attracted the attention of philosophers and logicians for many years. Recently, AI researchers contributed essentially to this area of research. Fuzzy set theory and the theory of evidence are seemingly the most appealing topics. On this note we present a new approach, based on the rough set theory, for looking to these problems. The theory of rough sets seems a suitable mathematical tool for dealing with problems of vagueness and uncertainty. This paper is a modified version of the author's lecture titled An inquiry into vagueness and uncertainty, which was delivered at the AI Conference in Wigry (Poland), 1994.

Abstract: Automated knowledge acquisition is an important research issue in machine learning. Several methods of inductive learning, such as ID3 family and AQ family, have been applied to discover meaningful knowledge from large databases and their usefulness is assured in several aspects. However, since their methods are of a deterministic nature and the reliability of acquired knowledge is not evaluated statistically, these methods are ineffective when applied to domains essentially probabilistic in nature, such as medical domains. Extending concepts of rough set theory to a probabilistic domain, we introduce a new approach to knowledge acquisition, which induces probabilistic rules based on rough set theory (PRIMEROSE) and develop a program that extracts rules for an expert system from a clinical database, using this method. The results show that the derived rules almost correspond to those of the medical experts.

Abstract: The theory of rough sets is a relatively new research direction concerned with the analysis and modeling of classification and decision problems involving vague, imprecise, uncertain, or incomplete information. The methodology stems from the premise that the classifcation of empirical observation and subsequent decision making are fundamental features of intelligent behavior. Consequently, the methodology models observations as classifications and decision problems as sets expressed approximately in terms of lower and upper bounds constructed using the classifications (Pawlak 1991). The rigorous mathematical approach for dealing with such problems formally was originally proposed by Zdzislaw Pawlak and later investigated in detail by logicians, mathematicians, and computer scientists. The theory of rough sets gave rise to new formal approaches to approximate reasoning, digital logic analysis and reduction, control algorithm acquisition, machine learning algorithms, and pattern recognition. One particularly attractive application area for this methodology is in knowledge discovery or database mining. Initiated by Gregory Piatetsky-Shapiro (Piatetsky-Shapiro and Frawley 1991), knowledge discovery has grown into an important research and application subfield within AI. It is concerned with identification of nontrivial data patterns or relationships normally hidden in databases. The relationships typically assume the form of data dependencies, either functional, partially functional, or probabilistic, and their discovery and characterization are possible only by using special software tools. In this context, the existing research results derived from the basic model of rough sets provide a wealth of techniques applicable to the knowledge discovery problem. In particular, the theory of rough sets is used to model and analyze the data at various levels of abstraction to better expose the data regularities; it provides techniques to analyze data dependencies, to identify fundamental factors, and to discover rules, both deterministic and nondeterministic, from data. This special issue represents a spectra of research results in both rough sets and knowledge discovery areas, with particular emphasis on applications. The applications described in this issue fall into the following categories: medical research, data preprocessing and reduction for neural networks, control algorithm acquisition, database systems, and machine learning. The more theoretical articles deal with such problems as the representation of uncertain information and formal reasoning with such information, concept formation and database storage, and retrieval of vague or imprecise information. Almost all the articles in this collection were chosen from the fifty papers presented at the International Workshop on Rough Sets and Knowledge Discovery held in Banff, Canada, in October 1993. The workshop was organized by the Department of Computir Science at the University of Regina in Regina, Saskatchewan, Canada.

Abstract: In this paper we focus on the temporal constraints between causes and effects of causal relations, and, to deal correctly with such relations, we stress the importance of analyzing the action-types (aspectual category) of causes and effects. In particular, we propose a domain-independent ontology in which the distinctions between action-types (e.g., the distinction between durative and punctual situations) are dealt with, and different types of causal relations are distinguished, on the basis of (i) the temporal constraints they impose between causes and effects (these constraints are expressed in a temporal formalism that extends Vilain's point interval algebra) and (ii) the action-types of their causes and effects. Our ontology allows one to capture precisely the temporal constraints imposed by causation and the action-types of the related situations. Moreover, in case the user has no accurate knowledge about the action-types of some situations and/or the types of some causal connections to be dealt with, our formalism allows the user to leave the descriptions underspecified, and more specific pieces of information may be inferred. Inferences provide a flow of information about action-types to information about temporal constraints in causation and vice versa, and demonstrate that a deep integration of time and causation is provided also at the inferential level.

Abstract: We propose a procedure for estimating DBLEARN's potential for knowledge discovery, given a relational database and concept hierarchies. This procedure is most useful for evaluating alternative concept hierarchies for the same database. The DBLEARN knowledge discovery program uses an attribute-oriented inductive-inference method to discover potentially significant high-level relationships in a database. A concept forest, with at most one concept hierarchy for each attribute, defines the possible generalizations that DBLEARN can make for a database. The potential for discovery in a database is estimated by examining the complexity of the corresponding concept forest. Two heuristic measures are defined based on the number, depth, and height of the interior nodes. Higher values for these measures indicate more complex concept forests and arguably more potential for discovery. Experimental results using a variety of concept forests and four commercial databases show that in practice both measures permit quite reliable decisions to be made; thus, the simplest may be most appropriate.

Abstract: The inverted pendulum poses serious problems for qualitative modeling methods, so it is a good benchmark to test their performance. This paper shows how a new data analysis method known as rough set theory can be utilized to swing up and stabilize the pendulum. Our approach to this task consists of deriving control rules from the actions of a human operator stabilizing the pendulum and subsequently using them for automatic control. Rule derivation is based on the learning from examples principle and does not require knowledge of a quantitative model of the system.

Abstract: This paper gives a blueprint for the development of a fully domain-independent single-agent and multi-agent heuristic search system. It gives a graph-theoretic representation of search problems based on conceptual graphs, and outlines two different learning systems. One, an ``informed learner," makes use of the the graph-theoretic definition of a search problem or game in playing and adapting to a game in the given environment. The other, a ``blind learner," is not given access to the rules of a domain, but must discover and then exploit the underlying mathematical structure of a given domain. Relevant work of others is referenced within the context of the blueprint. To illustrate further how one might go about creating general game-playing agents, we show how we can generalize the understanding obtained with the Morph chess system to all games involving the interactions of abstract mathematical relations. An example of a monitor for such domains is presented, along with an implementation of a blind and informed learning system known as MorphII. Performance results with MorphII are preliminary but encouraging and provide a few more data points with which to understand and evaluate the blueprint.

Abstract: Although game-tree search works well in perfect-information games, it is less suitable for imperfect-information games such as contract bridge. The lack of knowledge about the opponents’ possible moves gives the game tree a very large branching factor, making it impossible to search a significant portion of this tree in a reasonable amount of time. This paper describes our approach for overcoming this problem. We represent information about bridge in a task network extended to represent multi-agency and uncertainty. Our game-playing procedure uses this task network to generate game trees in which the set of alternative choices is determined not by the set of possible actions, but by the set of available tactical and strategic schemes. We have tested this approach on declarer play in the game of bridge, in an implementation called Tignum 2. On 5000 randomly generated notrump deals, Tignum 2 beat the strongest commercially available program by 1394 to 1302, with 2304 ties. These results are statistically significant at the α= 0.05 level. Tignum 2 searched an average of only 8745.6 moves per deal in an average time of only 27.5 seconds per deal on a Sun SPARCstation 10. Further enhancements to Tignum 2 are currently underway.

Abstract: This paper presents results of experiments showing how machine learning methods are useful for rule induction in the process of knowledge acquisition for expert systems. Four machine learning methods were used: ID3, ID3 with dropping conditions, and two options of the system LERS: LEM1 and LEM2. Also, two knowledge acquisition options of LERS were used as well. All six methods were used for rule induction from six real-life data sets. The main objective was to test how an expert system, supplied with these rule sets, will perform without information on a few attributes. Thus an expert system attempts to classify examples with all missing values of some attributes. As a result of experiments it is clear that all machine learning methods performed much worse than knowledge acquisition options of LERS. Thus, machine learning methods used for knowledge acquisition should be replaced by other methods of rule induction that will generate complete sets of rules. Knowledge acquisition options of LERS are examples of such appropriate ways of inducing rules for building knowledge bases.

Abstract: “Simpson's paradox,” first described nearly a century ago, is an anomaly that sometimes arises from pooling data. Dramatic instances of the paradox have occurred in real life in the domains of epidemiology and admissions policies. Many writers have recently described hypothetical examples of the paradox arising in other areas of life and it seems possible that the paradox may occur frequently in mundane domains but with less serious implications. Thus, it is not surprising that the paradox should arise in commonsense reasoning, that subarea of artificial intelligence that seeks to axiomatize reasoning in such mundane domains. It arises as the problem “approximate proof by cases” and the question of whether to accept it may well depend on whether we wish to construct performance or competence models of reasoning. This article gives a brief history of the paradox and discusses its occurrence in our own discipline. It argues that if the paradox occurs frequently but undramatically in real life, every uncertain reasoning system will have to deal with the problem in some way.

Abstract: The general use of subjective probabilities to model beliefs has been justified using many axiomatic schemes. This paper presents a rationale for probability models based on intuitive properties of belief orderings and the effect of evidence on beliefs. Qualitative probability, which imposes stringent constraints on belief representation schemes, is derived from four simple assumptions about beliefs and evidence. Properties shown to be sufficient for the adoption of probability proper by Cox (1978) are derived here from qualitative probability and a principle of plausible reasoning advanced by Polya (1954). Models based on complete orderings of beliefs extend easily to motivate set-valued representations of partial orderings as well.

Abstract: In order to provide a background for rough set modeling of uncertainty, two types of incompleteness of information are discussed. Representation of uncertain knowledge acquired from incomplete information is outlined within the framework of information logics. Relational proof theory for the information logics is presented. It is shown how these logics and their proof systems can be handled in the GLEF ATINF (Graphical & Logical Editing Framework) system. This computer program is a key component of the inference laboratory Atelier d'Inference (ATINF) developed at LIFIA-IMAG, our lab. It provides a general framework, independent of logic and proof systems, for combining inference tools, editing, and checking proofs. The basic principles of its design and implementation are given and its capabilities are discussed. Its application to define the information logics and their proof systems and to present proofs in these proof systems is discussed and illustrated.

Abstract: In this paper we present various logical characterizations of justification-based (nonmonotonic) truth maintenance systems (JTMS). These characterizations, which are proved to be equivalent, aim at describing dependency-directed backtracking (DDB) (i.e., the process of resolving conflicts which can arise when nogoods are allowed in the set of justifications), mainly relying on the intuitive idea that a contrapositrve use of justifications is needed to resolve inconsistencies. The idea is first formalized by means of the notion of three-valued labeling and then through a transformation which explicitly adds all contrapositives of the justifications. An abductive characterization of the JTMS is provided through a further transformation which converts a set of nonmonotonic justifications to a corresponding abduction framework. This approach provides a unifying framework, based on the notion of abduction, for describing both JTMSs and assumption-based TMSs (ATMSs).

Abstract: Finding the referent of a definite noun phrase is a classic problem in natural language processing. Most work assumes that when a program begins to analyze an utterance, it already has the knowledge it needs for identifying referents. If a robot accepts commands in natural language, this assumption may not hold. Suppose a user says, “Go get the book on the table in room 3,” but the robot has never been in room 3, so it lacks the knowledge it needs to identify the referent of “the book on the table in room 3.” To gain this knowledge, the robot must travel to room 3 and search. This article describes a simulated robot that accepts commands in English and actively searches for the referents of definite descriptions.

Abstract: In this paper, we present VSTA, our Prolog-based verifier, for formal specification and verification of systolic architectures. VSTA allows users to design systolic array architectures in the STA specification language (STA was developed earlier by Ling for formal description and reasoning of systolic designs) and semi-automatically verifies these designs The implementation of VSTA is based on a standard Prolog system. Its interface uses Motif system calls based on the X11 and UNIX environments. VSTA provides facilities to assist the user in the design of systolic array specifications. The system allows a formal proof to be derived interactively with suggestions from the user. The proof techniques used are mathematical induction and rewriting. The induction technique is adopted to exploit the regularity and locality nature of systolic array architectures. A number of verification tactics are developed and their operational rules are used in the verifier. Using the powerful symbolic computation ability of Prolog, particularly pattern matching, automatic backtracking, and depth-first searching, the verifier performs efficiently in the construction of proofs. We also describe the strategies we used in proving a matrix multiplication systolic array and an LU decomposition systolic array.

Abstract: The Allen and Koomen planner is intractable in two ways : the Allen interval algebra is an intractable temporal reasoner, and the collapsing problem introduces a large branching factor in the search space for a solution plan. We define independence and dependence for networks to address both problems. Independence is used to find a decomposition of an interval network, and dependence is used to focus search when faced with the collapsing problem.

Abstract: We analyze the problem of computing the minimal labels for a network of temporal relations in point algebra. Van Beek proposes an algorithm for accomplishing this task, which takes O(max(n 3 , n 2 . m)) time (for n points and m #-relations). We show that the proof of the correctness of this algorithm given by van Beek and Cohen is faulty, and we provide a new proof showing that the algorithm is indeed correct.

Abstract: Knowledge discovery in databases, or data mining, is an important direction in the development of data and knowledge-based systems. Because of the huge amount of data stored in large numbers of existing databases, and because the amount of data generated in electronic forms is growing rapidly, it is necessary to develop efficient methods to extract knowledge from databases. An attribute-oriented rough set approach has been developed for knowledge discovery in databases. The method integrates machine-learning paradigm, especially learning-from-examples techniques, with rough set techniques. An attribute-oriented concept tree ascension technique is first applied in generalization, which substantially reduces the computational complexity of database learning processes. Then the cause-effect relationship among the attributes in the database is analyzed using rough set techniques, and the unimportant or irrelevant attributes are eliminated. Thus concise and strong rules with little or no redundant information can be learned efficiently. Our study shows that attribute-oriented induction combined with rough set theory provide an efficient and effective mechanism for knowledge discovery in database systems.

Abstract: Sentential theories of belief hold that propositions (the things that agents believe and know) are sentences of a representation language. To analyze quantification into the scope of attitudes, these theories require a naming map-a function that maps objects to their names in the representation language. Epistemic logics based on sentential theories usually assume a single naming map, which is built into the logic. I argue that to describe everyday knowledge, the user of the logic must be able to define new naming maps for particular problems. Since the range of a naming map is usually an infinite set of names, defining a map requires quantification over names. This paper describes an epistemic logic with quantification over names, presents a theorem-proving algorithm based on translation to first-order logic, and proves soundness and completeness. The first version of the logic suffers from the problem of logical omniscience ; a second version avoids this problem, and soundness and completeness are proved for this version also.

Abstract: The epistemic notions of knowledge and belief have most commonly been modeled by means of possible worlds semantics. In such approaches an agent knows (or believes) all logical consequences of its beliefs. Consequently, several approaches have been proposed to model systems of explicit belief, more suited to modeling finite agents or computers. In this paper a general framework is developed for the specification of logics of explicit belief. A generalization of possible worlds, called situations, is adopted. However the notion of an accessibility relation is not employed; instead a sentence is believed if the explicit proposition expressed by the sentence appears among a set of propositions associated with an agent at a situation. Since explicit propositions may be taken as corresponding to «belief contexts» or «frames of mind», the framework also provides a setting for invgestigating such approaches to belief. The approach provides a uniform and flexible basis from which various issues of explicit belief may be addressed and from which systems may be contrasted and compared. A fampily of logics is developed using this framework, which extends previous approaches and addresses issues raised by these earlier approaches. The more interesting of these logics are tractable, in that determining if a belief follows from a set of beliefs, given certain assumptions, can be accomplished in polynomial time

Abstract: In this paper, we introduce the notion of interval structures in an attempt to establish a unified framework for representing uncertain information. Two views are suggested for the interpretation of an interval structure. A typical example using the compatibility view is the rough set model in which the lower and upper approximations form an interval structure. Incidence calculus adopts the allocation view in which an interval structure is defined by the tightest lower and upper incidence bounds. The relationship between interval structures and interval-based numeric belief and plausibility functions is also examined. As an application of the proposed model, an algorithm is developed for computing the tightest incidence bounds.

Abstract: Negotiations are very important in a multiagenl environment, particularly, in an environment where there are conflicts between the agents, and cooperation would be beneficial. We have developed a general structure for a Negotiating Automated Agent that consists of five modules: a Prime Minister, a Ministry of Defense, a Foreign Office, a Headquarters and Intelligence. These modules are implemented using a dynamic set of local agents belonging to the different modules. We used this structure to develop a Diplomacy player. Diplomat. Playing Diplomacy involves a certain amount of technical skills as in other board games, but the capacity to negotiate, explain, convince, promise, keep promises or break them, is an essential ingredient in good play. Diplomat was evaluated and consistently played better than human players.

Abstract: This paper describes a database model based on the original rough sets theory. Its rough relations permit the representation of a rough set of tuples not definable in terms of the elementary classes, except through use of lower and upper approximations. The rough relational database model also incorporates indiscernibility in the representation and in all the operators of the rough relational algebra. This indiscernibility is based strictly on equivalence classes which must be defined for every attribute domain. There are several obvious applications for which the rough relational database model can more accurately model an enterprise than does the standard relational model. These include systems involving ambiguous, imprecise, or uncertain data. Retrieval over mismatched domains caused by the merging of one or more applications can be facilitated by the use of indiscernibility, and naive system users can achieve greater recall with the rough relational database. In addition, applications inherently rough could be more easily implemented and maintained in the rough relational database.

Abstract: We have previously reported a number of tractable planning problems defined in the SAS + formalism. This article complements these results by providing a complete map over the complexity of SAS + planning under all combinations of the previously considered restrictions. We analyze the complexity of both finding a minimal plan and finding any plan. In contrast to other complexity surveys of planning, we study not only the complexity of the decision problems but also the complexity of the generation problems. We prove that the SAS + -PUS problem is the maximal tractable problem under the restrictions we have considered if we want to generate minimal plans. If we are satisfied with any plan, then we can generalize further to the SAS + -US problem, which we prove to be the maximal tractable problem in this case.

Abstract: The Galois (or concept) lattice produced from a binary relation has proved useful for many applications. Building the Galois lattice can be considered a conceptual clustering method because it results in a concept hierarchy. This article presents incremental algorithms for updating the Galois lattice and corresponding graph, resulting in an incremental concept formation method. Different strategies are considered based on a characterization of the modifications implied by such an update. Results of empirical tests are given in order to compare the performance of the incremental algorithms to three other batch algorithms. Surprisingly, when the total time for incremental generation is used, the simplest and less efficient variant of the incremental algorithms outperforms the batch algorithms in most cases. When only the incremental update time is used, the incremental algorithm outperforms all the batch algorithms. Empirical evidence shows that, on the average, the incremental update is done in time proportional to the number of instances previously treated. Although the worst case is exponential, when there is a fixed upper bound on the number of features related to an instance, which is usually the case in practical applications, the worst-case analysis of the algorithm also shows linear growth with respect to the number of instances.

Abstract: One of the most important problems in the application of knowledge discovery systems is the identification and subsequent updating of rules. Many applications require that the classification rules be derived from data representing exemplar occurrences of data patterns belonging to different classes. The problem of identifying such rules in data has been researched within the field of machine learning, and more recently in the context of rough set theory and knowledge discovery in databases. In this paper we present an incremental methodology for finding all maximally generalized rules and for adaptive modification of them when new data become available. The methodology is developed in the context of rough set theory and is based on the earlier idea of discernibility matrix introduced by Skowron.

Abstract: We present the syntax and proof theory of a logic of argumentation, LA. We also outline the development of a category theoretic semantics for LA. LA is the core of a proof theoretic model for reasoning under uncertainty. In this logic, propositions are labelled with a representation of the arguments which support their validity. Arguments may then be aggregated to collect more information about the potential validity of the propositions of interest. We make the notion of aggregation primitive to the logic, and then define strength mappings from sets of arguments to one of a number of possible dictionaries. This provides a uniform framework which incorporates a number of numerical and symbolic techniques for assigning subjective confidences to propositions on the basis of their supporting arguments. These aggregation techniques are also described, with examples

Abstract: We apply rough set constructs to inductive learning from a database. A design guideline is suggested, which provides users the option to choose appropriate attributes, for the construction of data classification rules. Error probabilities for the resultant rule are derived. A classification rule can be further generalized using concept hierarchies. The condition for preventing over generalization is derived. Moreover, given a constraint, an algorithm for generating a rule with minimal error probability is proposed.