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Orłowska, Ewa
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16 Citations
In the paper we define a class of languages for representation o knowledge in those application areas when a complete information about a domain is not available. In the languages we introduce modal operators determined by accessibility relations depending on parameters.
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Orłowska, Ewa
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4 Citations
Possible world semantics of logical languages introduced by Kanger and Kripke around 1960 is the most widely used technique for formal presentation of nonclassical logics. In spite of some shortcomings connected with the incompleteness phenomenon, it provides an intuitively clear interpretation of the fact that a formula is satisfied in some possible worlds and it might not be satisfied in some of the others. With this interpretation formulas can be treated as those subsets of a universe of possible worlds in which they are true. In most of the possible world models the truth conditions for the intensional propositional operations are articulated in terms of properties of a binary or ternary accessibility relation between possible worlds. It follows that from a formal point of view possible world semantical structures are not uniform. The part responsible for the extensional fragment of a logic under consideration determines a Boolean algebra of sets, and the part responsible for the intensional fragment refers to an algebra of relations. Our main objective in the present paper is to develop a unifying algebraic treatment of both extensional and intensional parts of logical systems.
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Orłowska, Ewa
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25 Citations
This article provides an overview of development of Kripke semantics for logics determined by information systems. The proposals are made to extend the standard Kripke structures to the structures based on information systems. The underlying logics are defined and problems of their axiomatization are discussed. Several open problems connected with the logics are formulated. Logical aspects of incompleteness of information provided by information systems are considered.
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GolińskaPilarek, Joanna; Orłowska, Ewa
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7 Citations
We present two proof systems for firstorder logic with identity and without function symbols. The first one is an extension of the RasiowaSikorski system with the rules for identity. This system is a validity checker. The rules of this system preserve and reflect validity of disjunctions of their premises and conclusions. The other is a Tableau system, which is an unsatisfiability checker. Its rules preserve and reflect unsatisfiability of conjunctions of their premises and conclusions. We show that the two systems are dual to each other. The duality is expressed in a formal way which enables us to define a transformation of proofs in one of the systems into the proofs of the other.
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Demri, Stéphane; Orłowska, Ewa
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In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRelogics (finitely reducible logics) and LaFiRelogics (FiRelogics with local agreement of accessibility relations) are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics from these classes have the finite model property with respect to the class of ♦formulae, i.e. each ♦formula has a ℒmodel iff it has a finite ℒmodel. Roughly speaking, a ♦formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators.
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Orłowska, Ewa
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In the paper ordering relations for comparison of verisimilitude of theories are introduced and discussed. The relations refer to semantic analysis of the results of theories, in particular to analysis of concepts the theories deal with.
By
Düntsch, Ivo; Orłowska, Ewa
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1 Citations
We present two discrete dualities for double Stone algebras. Each of these dualities involves a different class of frames and a different definition of a complex algebra. We discuss relationships between these classes of frames and show that one of them is a weakening of the other. We propose a logic based on double Stone algebras.
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