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  • 1.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Grabowski, M
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Towards a framework for approximate ontologies2003In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 57, no 2-4, p. 147-165Article in journal (Refereed)
    Abstract [en]

    Currently, there is a great deal of interest in developing tools for the generation and use of ontologies on the WWW. These knowledge structures are considered essential to the success of the semantic web, the next phase in the evolution of the WWW. Much recent work with ontologies assumes that the concepts used as building blocks are crisp as opposed to approximate. It is a premise of this paper that approximate concepts and ontologies will become increasingly more important as the semantic web becomes a reality. We propose a framework for specifying, generating and using approximate ontologies. More specifically, (1) a formal framework for defining approximate concepts, ontologies and operations on approximate concepts and ontologies is presented. The framework is based on intuitions from rough set theory, (2) algorithms for automatically generating approximate ontologies from traditional crisp ontologies or from large data sets together with additional knowledge are presented. The knowledge will generally be related to similarity measurements between individual objects in the data sets, or constraints of a logical nature which rule out particular constellations of concepts and dependencies in generated ontologies. The techniques for generating approximate ontologies are parameterizable. The paper provides specific instantiations and examples.

  • 2.
    Doherty, Patrick
    et al.
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Lukaszewicz, Witold
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    A study in modal embeddings of NML3.1996In: Partiality, Modality, and Nonmonotonicity, Studies in Logic, Language and Information. / [ed] Patrick Doherty, Stanford, California: CSLI Publications , 1996, p. 145-168Chapter in book (Other academic)
  • 3.
    Doherty, Patrick
    et al.
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Lukaszewicz, Witold
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Circumscribing features and fluents1994In: Temporal Logic: First International Conference, ICTL'94 Bonn, Germany, July 11–14, 1994 Proceedings / [ed] Dov M. Gabbay and Hans Jürgen Ohlbach, Berlin/New York: Springer Berlin/Heidelberg, 1994, p. 82-100Chapter in book (Refereed)
    Abstract [en]

    Sandewall has recently proposed a systematic approach to the representation of knowledge about dynamical systems that includes a general framework in which to assess the range of applicability of existing and new logics for action and change and to provide a means of studying whether and in what sense the logics of action and change are relevant for intelligent agents. As part of the framework, a number of logics of preferential entailment are introduced and assessed for particular classes of action scenario descriptions. This paper provides syntactic characterizations of several of these relations of preferential entailment in terms of standard FOPC and circumscription axioms. The intent is to simplify the process of comparison with existing formalisms which use more traditional techniques and to provide a basis for studying the feasibility of compiling particular classes of problems into logic programs.

  • 4.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Circumscribing features and fluents. A fluent logic for reasoning about action and change.1994In: 8th International Symposium on Methodologies for Intelligent Systems,1994, Springer Verlag , 1994Conference paper (Refereed)
  • 5.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Defaults as first-class citizens1992In: Proceedings of the 22nd International Symposium on Multiple-Valued Logic (SMVL), IEEE Computer Society , 1992, p. 146-154Conference paper (Refereed)
    Abstract [en]

    A nonmonotonic logic with explicit defaults, NML3, is presented. It is characterized by the following features: (1) the use of the strong Kleene three-valued logic as a basis; (2) the addition of an explicit default operator which enables distinguishing tentative conclusions from ordinary conclusions in the object language; and (3) the use of the idea of preferential entailment to generate nonmonotonic behavior. The central feature of the formalism, the use of an explicit default operator with a model-theoretic semantics based on the notion of a partial interpretation, distinguishes NML3 from most previous formalisms. By capitalizing on the distinction between tentative and ordinary conclusions, NML3 provides increased expressibility in comparison to many of the standard nonmonotonic formalisms and greater flexibility in the representation of subtle aspects of default reasoning. This is shown through examples.

  • 6.
    Doherty, Patrick
    et al.
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Lukaszewicz, Witold
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Distinguishing between facts and default assumptions.1992In: Non-Monotonic Reasoning and Partial Semantics. Ellis Horwood Workshops. / [ed] W. van der Hoek, New York: Ellis Horwood Ltd. , 1992Chapter in book (Other academic)
  • 7.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    FONML3 - A first-order non-monotonic logic with explicit defaults.1992In: European Conference on Artificial Intelligence, ECAI-92,1992, Chichester: John Wiley and Sons , 1992Conference paper (Refereed)
  • 8.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    FONML3 - A first-order non-monotonic logic with explicit defaults.1992Report (Other academic)
  • 9.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    NML-3 - A non-monotonic logic with explicit defaults1992In: Journal of applied non-classical logics, ISSN 1166-3081, Vol. 2, no 1, p. 9-48Article in journal (Refereed)
  • 10.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    NML3 - A non-monotonic logic with explicit defaults.1991Report (Other academic)
  • 11.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Madalin´ska-Bugaj, E.
    Computing MPMA updates using dijkstra's semantics.1999In: 12th International Symposium on Methodologies for Intelligent Systems,1999, Springer , 1999Conference paper (Refereed)
  • 12.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Madalin´ska-Bugaj, E.
    The PMA and relativizing minimal change for action update2000In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 44, no 1-2, p. 95-131Article in journal (Refereed)
    Abstract [en]

    Recently, a great deal of progress has been made using nonmonotonic temporal logics to formalize reasoning about action and change. In particular, much focus has been placed on the proper representation of non-deterministic actions and the indirect effects of actions. For the latter the use of causal or fluent dependency rule approaches has been dominant. Although much recent effort has also been spent applying the belief revision/update (BR/U) approach to the action and change domain, there has been less progress in dealing with nondeterministic update and indirect effects represented as integrity constraints. We demonstrate that much is to be gained by cross-fertilization between the two paradigms and we show this in the following manner. We first propose a generalization of the PMA, called the modified MPMA which uses intuitions from the TL paradigm to permit representation of nondeterministic update and the use of integrity constraints interpreted as causal or fluent dependency rules. We provide several syntactic characterizations of MPMA, one of which is in terms of a simple temporal logic and provide a representation theorem showing equivalence between the two. In constructing the MPMA, we discovered a syntactic anomaly which we call the redundant atom anomaly that many TL approaches suffer from. We provide a method for avoiding the problem which is equally applicable across paradigms. We also describe a syntactic characterization of MPMA in terms of Dijkstra semantics. We set up a framework for future generalization of the BR/U approach and conclude with a formal comparison of related approaches.

  • 13.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Madalinska-Bugaj, Ewa
    The PMA and relativizing change for action update1998In: Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning (KR), Morgan Kaufmann Publishers , 1998, p. 258-269Conference paper (Refereed)
    Abstract [en]

    Using intuitions from the temporal reasoning community, we provide a generalization of the PMA, called the modified PMA (MPMA), which permits the representation of disjunctive updates and the use of integrity constraints interpreted as causal constraints. In addition, we provide a number of syntactic characterizations of the MPMA, one of which is constructed by mapping an MPMA update of a knowledge base into a temporal narrative in a simple temporal logic (STL). The resulting representation theorem provides a basis for computing entailments of the MPMA and could serve as a basis for further generalization of the belief update approach for reasoning about action and change.

  • 14.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Skowron, Andrzej
    Institute of Mathematics Warsaw University.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Approximation Transducers and Trees: A Technique for Combining Rough and Crisp Knowledge2004In: Rough-Neural Computing: Techniques for Computing with Words / [ed] Andrzej Skowron,Lech Polkowski ,Sankar K Pal, Berlin, Heidelberg, New York: Springer , 2004, p. 189-218Chapter in book (Other academic)
    Abstract [en]

    Soft computing comprises various paradigms dedicated to approximately solving real-world problems, e.g., in decision making, classification or learning; among these paradigms are fuzzy sets, rough sets, neural networks, and genetic algorithms.

    It is well understood now in the soft computing community that hybrid approaches combining various paradigms provide very promising attempts to solving complex problems. Exploiting the potential and strength of both neural networks and rough sets, this book is devoted to rough-neurocomputing which is also related to the novel aspect of computing based on information granulation, in particular to computing with words. It provides foundational and methodological issues as well as applications in various fields.

  • 15.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Skowron, Andrzej
    Faculty of Mathematics, Informatics and Mechanics Warsaw University.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Knowledge Representation Techniques.: a rough set approach2006Book (Other academic)
    Abstract [en]

    The basis for the material in this book centers around a long term research project with autonomous unmanned aerial vehicle systems. One of the main research topics in the project is knowledge representation and reasoning. The focus of the research has been on the development of tractable combinations of approximate and nonmonotonic reasoning systems. The techniques developed are based on intuitions from rough set theory. Efforts have been made to take theory into practice by instantiating research results in the context of traditional relational database or deductive database systems. This book contains a cohesive, self-contained collection of many of the theoretical and applied research results that have been achieved in this project and for the most part pertain to nonmonotonic and approximate reasoning systems developed for an experimental unmanned aerial vehicle system used in the project. This book should be of interest to the theoretician and applied researcher alike and to autonomous system developers and software agent and intelligent system developers.

  • 16.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    A characterization result for circumscribed normal logic programs. Revised version accepted for publication: Special issue of honor of H. Rasiowa, Fundamenta Informaticae.1995Report (Other academic)
  • 17.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    A reduction result for circumscribed semi-horn formulas1996In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 28, no 3,4, p. 261-272Article in journal (Refereed)
    Abstract [en]

    Circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic and commonsense reasoning, but difficult to apply in practice due to the use of second-order formulas. One proposal for dealing with the computational problems is to identify classes of first-order formulas whose circumscription can be shown to be equivalent to a first-order formula. In previous work, we presented an algorithm which reduces certain classes of second-order circumscription axioms to logically equivalent first-order formulas. The basis for the algorithm is an elimination lemma due to Ackermann. In this paper, we capitalize on the use of a generalization of Ackermann's Lemma in order to deal with a subclass of universal formulas called semi-Horn formulas. Our results subsume previous results by Kolaitis and Papadimitriou regarding a characterization of circumscribed definite logic programs which are first-order expressible. The method for distinguishing which formulas are reducible is based on a boundedness criterion. The approach we use is to first reduce a circumscribed semi-Horn formula to a fixpoint formula which is reducible if the formula is bounded, otherwise not. In addition to a number of other extensions, we also present a fixpoint calculus which is shown to be sound and complete for bounded fixpoint formulas.

  • 18.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Approximate Databases and Query Techniques for Agents with Heterogenous Perceptual Capabilities2004In: Proceedings of the 7th International Conference on Information Fusion, Mountain View, CA: ISIF , 2004, p. 175-182Conference paper (Refereed)
    Abstract [en]

    In this paper, we propose a framework that provides software and robotic agents with the ability to ask approximate questions to each other in the context of heterogeneous and contextually limited perceptual capabilities. The framework focuses on situations where agents have varying ability to perceive their environments. These limitations on perceptual capability are formalized using the idea of tolerance spaces. It is assumed that each agent has one or more approximate databases where approximate relations are represented using intuitions from rough set theory. It is shown how sensory and other limitations can be taken into account when constructing approximate databases for each respective agent. Complex relations inherit the approximativeness inherent in the sensors and primitive relations used in their definitions. Agents then query these databases and receive answers through the filters of their perceptual limitations as represented by tolerance spaces and approximate queries. The techniques used are all tractable.

  • 19.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Approximative Query Techniques for Agents with Heterogeneous Ontologies and Perceptive Capabilities2004In: Proceedings of the 9th International Conference on the Principles of Knowledge Representation and Reasoning / [ed] Didier Dubois, Christopher A. Welty, Mary-Anne Williams, Menlo Park, California: AAAI Press , 2004, p. 459-468Conference paper (Refereed)
    Abstract [en]

    In this paper, we propose a framework that provides software and robotic agents with the ability to ask approximate questions to each other in the context of heterogeneous ontologies and heterogeneous perceptive capabilities.The framework combines the use of logic-based techniques with ideas from approximate reasoning. Initial queries by an agent are transformed into approximate queries using weakest sufficient and strongest necessary conditions on the query and are interpreted as lower and upper approximations on the query. Once the base communication ability is provided, the framework is extended to situations where there is not only a mismatch between agent ontologies, but the agents have varying ability to perceive their environments. This will affect each agent’s ability to ask and interpret results of queries. Limitations on perceptive capability are formalized using the idea of tolerance spaces.

  • 20.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    CAKE: A computer aided knowledge engineering technique.2002In: Proceedings of the 15th European Conference on Artificial Intelligence,2002 / [ed] Frank van Harmelen, IOS Press, 2002, p. 220-224Conference paper (Refereed)
    Abstract [en]

    Introduction: Logic engineering often involves the development of modeling tools and inference mechanisms (both standard and non-standard) which are targeted for use in practical applications where expressiveness in representation must be traded off for efficiency in use. Some representative examples of such applications would be the structuring and querying of knowledge on the semantic web, or the representation and querying of epistemic states used with softbots, robots or smart devices. In these application areas, declarative representations of knowledge enhance the functionality of such systems and also provide a basis for insuring the pragmatic properties of modularity and incremental composition. In addition, the mechanisms developed should be tractable, but at the same time, expressive enough to represent such aspects as default reasoning, or approximate or incomplete representations of the environments in which the entities in question are embedded or used, be they virtual or actual. [...]

  • 21.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Communication between agents with heterogeneous perceptual capabilities2007In: Information Fusion, ISSN 1566-2535, E-ISSN 1872-6305, Vol. 8, no 1, p. 56-69Article in journal (Refereed)
    Abstract [en]

    In real world applications robots and software agents often have to be equipped with higher level cognitive functions that enable them to reason, act and perceive in changing, incompletely known and unpredictable environments. One of the major tasks in such circumstances is to fuse information from various data sources. There are many levels of information fusion, ranging from the fusing of low level sensor signals to the fusing of high level, complex knowledge structures. In a dynamically changing environment even a single agent may have varying abilities to perceive its environment which are dependent on particular conditions. The situation becomes even more complex when different agents have different perceptual capabilities and need to communicate with each other. In this paper, we propose a framework that provides agents with the ability to fuse both low and high level approximate knowledge in the context of dynamically changing environments while taking account of heterogeneous and contextually limited perceptual capabilities. To model limitations on an agent's perceptual capabilities we introduce the idea of partial tolerance spaces. We assume that each agent has one or more approximate databases where approximate relations are represented using lower and upper approximations on sets. Approximate relations are generalizations of rough sets. It is shown how sensory and other limitations can be taken into account when constructing and querying approximate databases for each respective agent. Complex relations inherit the approximativeness of primitive relations used in their definitions. Agents then query these databases and receive answers through the filters of their perceptual limitations as represented by (partial) tolerance spaces and approximate queries. The techniques used are all tractable. © 2005 Elsevier B.V. All rights reserved.

  • 22.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Computing circumscription revisited.1995In: Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI), 1995, p. 1502-1508Conference paper (Refereed)
  • 23.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Computing circumscription revisited: A reduction algorithm.1994Report (Other academic)
    Abstract [en]

    In recent years, a great deal of attention has been devoted to logics of "commonsense" reasoning. Among the candidates proposed, circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic reasoning, but difficult to apply in practice. The major reason for this is the nd-order nature of circumscription axioms and the difficulty in finding proper substitutions of predicate expressions for predicate variables.  One solution to this problem is to compile, where possible, nd-order formulas into equivalent 1st-order formulas. Although some progress has been made using this approach, the results are not as strong as one might desire and they are isolated in nature. In this article, we provide a general method which can be used in an algorithmic manner to reduce circumscription axioms to 1st-order formulas. The algorithm takes as input an arbitrary 2nd-order formula and either returns as output an equivalent 1st-order formula, or terminates with failure. The class of 2nd-order formulas, and analogously the class of circumscriptive theories which can be reduced, provably subsumes those covered by existing results. We demonstrate the generality of the algorithm using circumscriptive theories with mixed quantifiers (some involving Skolemization), variable constants, non-separated formulas, and formulas with n-ary predicate variables. In addition, we analyze the strength of the algorithm and compare it with existing approaches providing formal subsumption results.

  • 24.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Computing circumscription revisited: A reduction algorithm1997In: Journal of automated reasoning, ISSN 0168-7433, E-ISSN 1573-0670, Vol. 18, no 3, p. 297-336Article in journal (Refereed)
    Abstract [en]

    In recent years, a great deal of attention has been devoted to logics of common-sense reasoning. Among the candidates proposed, circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic reasoning, but difficult to apply in practice. The major reason for this is the second-order nature of circumscription axioms and the difficulty in finding proper substitutions of predicate expressions for predicate variables. One solution to this problem is to compile, where possible, second-order formulas into equivalent first-order formulas. Although some progress has been made using this approach, the results are not as strong as one might desire and they are isolated in nature. In this article, we provide a general method that can be used in an algorithmic manner to reduce certain circumscription axioms to first-order formulas. The algorithm takes as input an arbitrary second-order formula and either returns as output an equivalent first-order formula, or terminates with failure. The class of second-order formulas, and analogously the class of circumscriptive theories that can be reduced, provably subsumes those covered by existing results. We demonstrate the generality of the algorithm using circumscriptive theories with mixed quantifiers (some involving Skolemization), variable constants, nonseparated formulas, and formulas with n-ary predicate variables. In addition, we analyze the strength of the algorithm, compare it with existing approaches, and provide formal subsumption results.

  • 25.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Computing strongest necessary and weakest sufficient conditions of first-order formulas2001In: 17th International Joint Conference on Artificial Intelligence,2001, San Francisco, CA, USA: Morgan Kaufmann Publishers Inc. , 2001, p. 145-151Conference paper (Refereed)
    Abstract [en]

    A technique is proposed for computing the weakest sufficient (wsc) and strongest necessary (snc) conditions for formulas in an expressive fragment of first-order logic using quantifier elimination techniques. The efficacy of the approach is demonstrated by using the techniques to compute snc's and wsc's for use in agent communication applications, theory approximation and generation of abductive hypotheses. Additionally, we generalize recent results involving the generation of successor state axioms in the propositional situation calculus via snc's to the first-order case. Subsumption results for existing approaches to this problem and a re-interpretation of the concept of forgetting as a process of quantifier elimination are also provided.

  • 26.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Declarative PTIME queries for relational databases using quantifier elimination1999In: Journal of logic and computation (Print), ISSN 0955-792X, E-ISSN 1465-363X, Vol. 9, no 5, p. 737-758Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider the problem of expressing and computing queries on relational deductive databases in a purely declarative query language, called SHQL (Semi-Horn Query Language). Assuming the relational databases in question are ordered, we show that all SHQL queries are computable in PTIME (polynomial time) and the whole class of PTIME queries is expressible in SHQL. Although similar results have been proven for fixpoint languages and extensions to datalog, the claim is that SHQL has the advantage of being purely declarative, where the negation operator is interpreted as classical negation, mixed quantifiers may be used and a query is simply a restricted first-order theory not limited by the rule-based syntactic restrictions associated with logic programs in general. We describe the PTIME algorithm used to compute queries in SHQL which is based in part on quantifier elimination techniques and also consider extending the method to incomplete relational databases using intuitions related to circumscription techniques.

  • 27.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Declarative ptime queries to relational databases.1996Report (Other academic)
    Abstract [en]

      

  • 28.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Efficient reasoning using the local closed-world assumption2000In: Proceedings of the 9th International Conference on Artificial Intelligence: Methodology, Systems and Applications (AIMSA), Springer Berlin/Heidelberg, 2000, p. 49-58Conference paper (Refereed)
    Abstract [en]

    We present a sound and complete, tractable inference method for reasoning with localized closed world assumptions (LCWA’s) which can be used in applications where a reasoning or planning agent can not assume complete information about planning or reasoning states. This Open World Assumption is generally necessary in most realistic robotics applications. The inference procedure subsumes that described in Etzioni et al [9], and others. In addition, it provides a great deal more expressivity, permitting limited use of negation and disjunction in the representation of LCWA’s, while still retaining tractability. The ap- proach is based on the use of circumscription and quantifier elimination techniques and inference is viewed as querying a deductive database. Both the preprocessing of the database using circumscription and quan- tifier elimination, and the inference method itself, have polynomial time and space complexity.

  • 29.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Explaining explanation closure1996In: Proceedings of the 9th International Symposium on Methodologies for Intelligent Systems,1996 / [ed] Zbigniew W. Ras, Maciek Michalewicz, Springer Berlin/Heidelberg, 1996, p. 521-530Conference paper (Refereed)
    Abstract [en]

    Recently, Haas, Schubert, and Reiter, have developed an alternative approach to the frame problem which is based on the idea of using explanation closure axioms. The claim is that there is a monotonic solution for characterizing nonchange in serial worlds with fully specified actions, where one can have both a succinct representation of frame axioms and an effective proof theory for the characterization. In the paper, we propose a circumscriptive version of explanation closure, PMON, that has an effective proof theory and works for both context dependent and nondeterministic actions. The approach retains representational succinctness and a large degree of elaboration tolerance, since the process of generating closure axioms is fully automated and is of no concern to the knowledge engineer. In addition, we argue that the monotonic/nonmonotonic dichotomy proposed by others is not as sharp as previously claimed and is not fully justified.

  • 30.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    General domain circumscription and its effective reductions.1998In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 36, no 1, p. 23-55Article in journal (Refereed)
    Abstract [en]

    We first define general domain circumscription (GDC) and provide it with a semantics. GDC subsumes existing domain circumscription proposals in that it allows varying of arbitrary predicates, functions, or constants, to maximize the minimization of the domain of a theory. We then show that for the class of semi-universal theories without function symbols, that the domain circumscription of such theories can be constructively reduced to logically equivalent first-order theories by using an extension of the DLS algorithm, previously proposed by the authors for reducing second-order formulas. We also show that for a certain class of domain circumscribed theories, that any arbitrary second-order circumscription policy applied to these theories is guaranteed to be reducible to a logically equivalent first-order theory. In the case of semi-universal theories with functions and arbitrary theories which are not separated, we provide additional results, which although not guaranteed to provide reductions in all cases, do provide reductions in some cases. These results are based on the use of fixpoint reductions.

  • 31.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    General domain circumscription and its first-order reduction.1996Report (Other academic)
  • 32.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    General domain circumscription and its first-order reduction.1996In: Proceedings of the 1st International Conference on Formal and Applied Practical Reasoning (FAPR) / [ed] Dov Gabbay, Hans Olbach, Springer Berlin/Heidelberg, 1996, p. 93-109Conference paper (Refereed)
    Abstract [en]

    We first define general domain circumscription (GDC) and provide it with a semantics. GDC subsumes existing domain circumscription proposals in that it allows varying of arbitrary predicates, functions, or constants, to maximize the minimization of the domain of a theory We then show that for the class of semi-universal theories without function symbols, that the domain circumscription of such theories can be constructively reduced to logically equivalent first-order theories by using an extension of the DLS algorithm, previously proposed by the authors for reducing second-order formulas. We also isolate a class of domain circumscribed theories, such that any arbitrary second-order circumscription policy applied to these theories is guaranteed to be reducible to a logically equivalent first-order theory. In the case of semi-universal theories with functions and arbitrary theories which are not separated, we provide additional results, which although not guaranteed to provide reductions in all cases, do provide reductions in some cases. These results are based on the use of fixpoint reductions.

  • 33.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Information Granules for Intelligent Knowledge Structures2003In: Proceedings of the 9th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC) / [ed] Guoyin Wang, Qing Liu, Yiyu Yao, Andrzej Skowron, Springer , 2003, p. 405-412Conference paper (Refereed)
    Abstract [en]

    The premise of this paper is that the acquisition, aggregation, merging and use of information requires some new ideas, tools and techniques which can simplify the construction, analysis and use of what we call ephemeral knowledge structures. Ephemeral knowledge structures are used and constructed by granular agents. Each agent contains its own granular information structure and granular information structures of agents can be combined together. The main concept considered in this paper is an information granule. An information granule is a concise conceptual unit that can be integrated into a larger information infrastructure consisting of other information granules and dependencies between them. The novelty of this paper is that it provides a concise and formal definition of a particular view of information granule and its associated operators, as required in advanced knowledge representation applications.

  • 34.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    On mutual understanding among communicating agents2003In: Proceedings of the International Workshop on Formal Approaches to Multi-Agent Systems (FAMAS) / [ed] B. Dunin-Keplicz and R. Verbrugge, 2003, p. 83-97Conference paper (Refereed)
  • 35.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Tolerance Spaces and Approximative Representational Structures2003In: Proceedings of the 26th German Conference on Artificial Intelligence (KI), Springer , 2003, p. 475-489Conference paper (Refereed)
    Abstract [en]

    In traditional approaches to knowledge representation, notions such as tolerance measures on data, distance between objects or individuals, and similarity measures between primitive and complex data structures are rarely considered. There is often a need to use tolerance and similarity measures in processes of data and knowledge abstraction because many complex systems which have knowledge representation components such as robots or software agents receive and process data which is incomplete, noisy, approximative and uncertain. This paper presents a framework for recursively constructing arbitrarily complex knowledge structures which may be compared for similarity, distance and approximativeness. It integrates nicely with more traditional knowledge representation techniques and attempts to bridge a gap between approximate and crisp knowledge representation. It can be viewed in part as a generalization of approximate reasoning techniques used in rough set theory. The strategy that will be used is to define tolerance and distance measures on the value sets associated with attributes or primitive data domains associated with particular applications. These tolerance and distance measures will be induced through the different levels of data and knowledge abstraction in complex representational structures. Once the tolerance and similarity measures are in place, an important structuring generalization can be made where the idea of a tolerance space is introduced. Use of these ideas is exemplified using two application domains related to sensor modeling and communication between agents.

  • 36.
    Doherty, Patrick
    et al.
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Skowron, Andrew
    University of Warsaw, Poland.
    Lukaszewicz, Witold
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Szalas, Andrzej
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Preface2003In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 57, no 2-4, p. i-iiiArticle in journal (Other academic)
  • 37.
    Doherty, Patrick
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Similarity, approximations and vagueness2005In: Proceedings of the 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC) / [ed] Dominik Slezak, Guoyin Wang, Marcin S. Szczuka, Ivo Düntsch, Yiyu Yao, Springer, 2005, p. 541-550Conference paper (Refereed)
    Abstract [en]

    The relation of similarity is essential in understanding and developing frameworks for reasoning with vague and approximate concepts. There is a wide spectrum of choice as to what properties we associate with similarity and such choices determine the nature of vague and approximate concepts defined in terms of these relations. Additionally, robotic systems naturally have to deal with vague and approximate concepts due to the limitations in reasoning and sensor capabilities. Halpern [1] introduces the use of subjective and objective states in a modal logic formalizing vagueness and distinctions in transitivity when an agent reasons in the context of sensory and other limitations. He also relates these ideas to a solution to the Sorities and other paradoxes. In this paper, we generalize and apply the idea of similarity and tolerance spaces [2,3,4,5], a means of constructing approximate and vague concepts from such spaces and an explicit way to distinguish between an agent’s objective and subjective states. We also show how some of the intuitions from Halpern can be used with similarity spaces to formalize the above-mentioned Sorities and other paradoxes.

  • 38. Madalinska-Bugaj, E
    et al.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Formalizing defeasible logic in CAKE2003In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 57, no 2-3, p. 193-213Article in journal (Refereed)
    Abstract [en]

    Due to its efficiency, defeasible logic is one of the most interesting non-monotonic formalisms. Unfortunately, the logic has one major limitation: it does not properly deal with cyclic defeasible rules. In this paper, we provide a new variant of defeasible logic, using CAKE method. The resulting formalism is tractable and properly deals with circular defeasible rules.

  • 39. Madalinska-Bugaj, Ewa
    et al.
    Lukaszewicz, Witold
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Belief revision revisited2005In: Advances in Artificial Intelligence: Proceedings of the 4th Mexican International Conference on Artificial Intelligence (MICAI), Springer , 2005, Vol. 3789, p. 31-40Conference paper (Refereed)
    Abstract [en]

    In this paper, we propose a new belief revision operator, together with a method of its calculation. Our formalization differs from most of the traditional approaches in two respects. Firstly, we formally distinguish between defeasible observations and indefeasible knowledge about the considered world. In particular, our operator is differently specified depending on whether an input formula is an observation or a piece of knowledge. Secondly, we assume that a new observation, but not a new piece of knowledge, describes exactly what a reasoning agent knows at the moment about the aspect of the world the observation concerns.

1 - 39 of 39
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