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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, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Kachniarz, Jaroslaw
    Szalas, Andrzej
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab.
    Meta-queries on deductive databases1999In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 40, no 1, p. 17-30Article in journal (Refereed)
    Abstract [en]

    We introduce the notion of a meta-query on relational databases and a technique which can be used to represent and solve a number of interesting problems from the area of knowledge representation using logic. The technique is based on the use of quantifier elimination and may also be used to query relational databases using a declarative query language called SHQL (Semi-Horn Query Language), introduced in [6]. SHQL is a fragment of classical first-order predicate logic and allows us to define a query without supplying its explicit definition. All SHQL queries to the database can be processed in polynomial time (both on the size of the input query and the size of the database). We demonstrate the use of the technique in problem solving by structuring logical puzzles from the Knights and Knaves domain as SHQL meta-queries on relational databases. We also provide additional examples demonstrating the flexibility of the technique. We conclude with a description of a newly developed software tool, The Logic Engineer, which aids in the description of algorithms using transformation and reduction techniques such as those applied in the meta-querying approach.

  • 3.
    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.

  • 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.
    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.

  • 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.
    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.

  • 6.
    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)
  • 7.
    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.
    A correspondence framework between three-valued logics and similarity-based approximate reasoning2007In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 75, no 1-4, p. 179-193Article in journal (Refereed)
    Abstract [en]

    This paper focuses on approximate reasoning based on the use of similarity spaces. Similarity spaces and the approximated relations induced by them are a generalization of the rough set-based approximations of Pawlak [17, 18]. Similarity spaces are used to define neighborhoods around individuals and these in turn are used to define approximate sets and relations. In any of the approaches, one would like to embed such relations in an appropriate logic which can be used as a reasoning engine for specific applications with specific constraints. We propose a framework which permits a formal study of the relationship between approximate relations, similarity spaces and three-valued logics. Using ideas from correspondence theory for modal logics and constraints on an accessibility relation, we develop an analogous framework for three-valued logics and constraints on similarity relations. In this manner, we can provide a tool which helps in determining the proper three-valued logical reasoning engine to use for different classes of approximate relations generated via specific types of similarity spaces. Additionally, by choosing a three-valued logic first, the framework determines what constraints would be required on a similarity relation and the approximate relations induced by it. Such information would guide the generation of approximate relations for specific applications.

  • 8.
    Doherty, Patrick
    et al.
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, The Institute of Technology.
    Szalas, Andrzej
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, The Institute of Technology. University of Warsaw, Poland .
    Automated Generation of Logical Constraints on Approximation Spaces Using Quantifier Elimination2013In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 127, no 1-4, p. 135-149Article in journal (Refereed)
    Abstract [en]

    This paper focuses on approximate reasoning based on the use of approximation spaces. Approximation spaces and the approximated relations induced by them are a generalization of the rough set-based approximations of Pawlak. Approximation spaces are used to define neighborhoods around individuals and rough inclusion functions. These in turn are used to define approximate sets and relations. In any of the approaches, one would like to embed such relations in an appropriate logical theory which can be used as a reasoning engine for specific applications with specific constraints. We propose a framework which permits a formal study of the relationship between properties of approximations and properties of approximation spaces. Using ideas from correspondence theory, we develop an analogous framework for approximation spaces. We also show that this framework can be strongly supported by automated techniques for quantifier elimination.

  • 9.
    Dunin-Keplicz, Barbara
    et al.
    Warsaw University.
    Anh Nguyen, Linh
    Warsaw University.
    Szalas, Andrzej
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    A Framework for Graded Beliefs, Goals and Intentions2010In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 100, no 1-4, p. 53-76Article in journal (Refereed)
    Abstract [en]

    In natural language we often use graded concepts, reflecting different intensity degrees of certain features. Whenever such concepts appear in a given real-life context, they need to be appropriately expressed in its models. In this paper, we provide a framework which allows for extending the BGI model of agency by grading beliefs, goals and intentions. We concentrate on TEAMLOG [6, 7, 8, 9, 12] and provide a complexity-optimal decision method for its graded version TEAMLOG(K) by translating it into CPDLreg (propositional dynamic logic with converse and "inclusion axioms" characterized by regular languages). We also develop a tableau calculus which leads to the first EXPTIME (optimal) tableau decision procedure for CPDLreg. As CPDLreg is suitable for expressing complex properties of graded operators, the procedure can also be used as a decision tool for other multiagent formalisms.

  • 10. 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.

  • 11.
    Nguyen, Linh Anh
    et al.
    Warsaw University.
    Szalas, Andrzej
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Checking Consistency of an ABox w.r.t. Global Assumptions in PDL2010In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 102, no 1, p. 97-113Article in journal (Refereed)
    Abstract [en]

    We reformulate Pratts tableau decision procedure of checking satisfiability of a set of formulas in PDL. Our formulation is simpler and its implementation is more direct. Extending the method we give the first Ex PT m E (optimal) tableau decision procedure not based on transformation for checking consistency of an ABox w.r.t. a TBox in PDL (here, PDL is treated as a description logic). We also prove a new result that the data complexity of the instance checking problem in PDL is coNP-complete.

  • 12.
    Petermann, Uwe
    et al.
    Karl-Marx-Universitaet, Leipzig.
    Szalas, Andrzej
    University of Warsaw.
    On Temporal Logic for Distributed Systems and its Application to Processes Communicating by Interrupts1989In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 12, no 2, p. 191-204Article in journal (Refereed)
  • 13.
    Szalas, Andrzej
    University of Warsaw.
    Algorithmic Logic with Recursive Functions1981In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 4, no 4, p. 975-995Article in journal (Refereed)
  • 14.
    Szalas, Andrzej
    University of Warsaw.
    On an Application of Algorithmic Theory of Stacks1984In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 7, no 3, p. 378-388Article in journal (Refereed)
  • 15.
    Szalas, Andrzej
    University of Warsaw.
    On Natural Deduction in First-Order Fixpoint Logics1996In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 26, no 1, p. 81-94Article in journal (Refereed)
    Abstract [en]

    In the current paper we present a powerful technique of obtaining natural deduction proof systems for first-order fixpoint logics. The term fixpoint logics  refers collectively to a class of logics consisting of modal logics with modalities definable at meta-level by fixpoint equations on formulas. The class was found very interesting as it contains most logics of programs with e.g. dynamic logic, temporal logic and the ¯-calculus among them. In this paper we present a technique that allows us to derive automatically natural deduction systems for modal logics from fixpoint equations defining the modalities

  • 16.
    Szalas, Andrzej
    University of Warsaw.
    Towards the Temporal Approach to Abstract Data Types1988In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 11, no 1, p. 49-64Article in journal (Refereed)
  • 17.
    Vitoria, Aida
    et al.
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Damasio, Carlos V
    Departamento de Informática da Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa.
    Maluszynski, Jan
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    From Rough Sets to Rough Knowledge Bases2003In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 57, no 2-4, p. 215-246Article in journal (Refereed)
    Abstract [en]

    This paper presents an expressive language for representing knowledge about vague concepts. It is based on the rough set formalism and it caters for implicit definition of rough relations by combining different regions (e.g. upper approximation, lower approximation, boundary) of other rough relations. The semantics of the proposed language is obtained by translating it to the language of extended logic programs whose meaning is captured by paraconsistent stable models. A query language is also discussed to retrieve information about the defined rough relations. Motivating examples illustrating the use of the language are described.

  • 18.
    Vitoria, Aida
    et al.
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Maluszynski, Jan
    Coll Econ and Comp Science, PL-10061 Olsztyn, Poland .
    Szalas, Andrzej
    Warsaw University, Institute Informat, PL-02097 Warsaw, Poland .
    Modelling and Reasoning with Paraconsistent Rough Sets2009In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 97, no 4, p. 405-438Article in journal (Refereed)
    Abstract [en]

    We present a language for defining paraconsistent rough sets and reasoning about them. Our framework relates and brings together two major fields: rough sets [23] and paraconsistent logic programming [9]. To model inconsistent and incomplete information we use a four-valued logic. The language discussed in this paper is based on ideas of our previous work [21, 32, 22] developing a four-valued framework for rough sets. In this approach membership function, set containment and set operations are four-valued, where logical values are t (true), f (false), i (inconsistent) and u (unknown). We investigate properties of paraconsistent rough sets as well as develop a paraconsistent rule language, providing basic computational machinery for our approach.

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