D. Vakarelov. "Modal logics for knowledge representation systems". Theoretical Computer Science, 90:433-- 456, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(2) Moreover, every relation RP satis es certain local conditions: for instance, the indiscernability relations are equivalence relations, and the similarity relations are re exive and symmetric. The rst information logic has been introduced in [OP81] and many others appeared later (see e.g. Vak91,Bal96,Kon97,Vak98,Ste98] Most information logics include further expressive means such a nominals whose combination with the intersection of modal parameters and the universal modality are known to make reasoning rather complex. In the following, we will concentrate ourselves on one such ....

D. Vakarelov. Modal logics for knowledge representation systems. Theoretical Computer Science, 90:433-456, 1991.

.... j] s( where the relations , and satisfy H d]d ] The specific operators in these logics are of the form , and x YZix . The completeness theorem for the standard frames such that the above condition and , I are satisfied, is obtained indirectly by the copying method of [40]. The class MIA of mixed algebras provides a framework for directly expressing and reasoning about the interplay between a modal operator . and a sufficiency operator ,x which are determined by the same frame relation. 8 Examples of mixed algebras 8.1 Complementarity algebras Recall ....

Vakarelov, D. (1991). Modal logics for knowledge representation systems. Theoretical Computer Science, 90, 433--456.

....the conditions on an equivalence relation. Leaving out axiom scheme (87) leads to strong similarity frames [42, 43] Ontology and logic of similarity relations have been studied in great detail in [68] Other normal information logics have been presented, for example, in [47] 49] 50] 65] [66]. Recent completeness results can be found in [2] 3] 12] and [13] 6.3 Relational proof systems A valuable tool in the formalisation and implementation of information logics are the relational proof systems introduced by Orl owska [52] which are sound and complete for standard modal logics. ....

Vakarelov, D. (1991). Modal logics for knowledge representation systems. Theoretical Computer Science, 90, 433--456.

....to the conditions on an equivalence relation. Leaving out axiom scheme (87) leads to strong similarity frames [42, 43] Ontology and logic of similarity relations have been studied in great detail in [68] Other normal information logics have been presented, for example, in [47] 49] 50] [65], 66] Recent completeness results can be found in [2] 3] 12] and [13] 6.3 Relational proof systems A valuable tool in the formalisation and implementation of information logics are the relational proof systems introduced by Orl owska [52] which are sound and complete for standard modal ....

Vakarelov, D. (1989). Modal logics for knowledge representation systems. In A. R. Meyer & M. Zalessky (Eds.), Symposium on Logic Foundations of Computer Science, Pereslavl--Zalessky, vol. 363 of LNCS, 257--277. SpringerVe r l a g

....that belong to different families. Hence, it is also natural to consider frames with families of relations of different types. A great variety of such frames is studied in the literature, see for example Demri [5] 6] Demri and Or lowska [7] Or lowska [18] 19] 21] 23] and Vakarelov [25] [26] [27] The motivation for using modal logics for reasoning about information relations comes from the methods of data analysis in information systems. In these methods, the modal like operators are used in the languages for representation of incomplete information. Let S = OB; AT ; fV AL a : a 2 ....

....modal logic [11] 12] only the parameters of the form : Gamma are missing. We examine the axiomatizability of the set of formulas valid in several classes of frames and we prove the completeness of these axiomatizations. Our proof is based on the techniques of the copying introduced by Vakarelov [26]. 2 Modal logics L2 In this section we present a class L2 of relative modal logics where the parameters are defined by the operation in such a way that, in the relational semantics of these logics, R( Gamma Delta) R( Gamma) R( Delta) 2.1 Language The linguistic basis of any modal logic ....

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D. Vakarelov. Modal logics for knowledge representation systems. Theoretical Computer Science, Volume 90, 433--456, 1991.

.... There are many existing logics based on Orlowska s approach (see e.g. FdCO85, Or lo89, Vak91, Bal97, Kon97a, Dem98a] For instance, some of these logics, based on rough set theory [Paw82] provide a fruitful framework to model reasoning in the presence of incomplete information (see e.g. [Vak91, Kon97a]) Our objectives. Formalising proof systems for such knowledge logics within the display logic framework (see e.g. Bel82] is the main objective of the paper. Existing proof systems for these logics are either Hilbert style systems [Bal97, BO98, Dem98b] which are not amenable to mechanisation, ....

....frames closed under intersection. However, in B4 and S54 the standard necessity operator [ff] can be defined by [ff]OE def = OE 4(ff)OE, and this might not always be the case for a B logic derived from an arbitrary (mono)modal logic L. Furthermore, Vakarelov s copying construction (see e.g. [Vak91]) used in the proof of the forthcoming Theorem 3.1 is known to behave badly with transitive relations. Hence, displaying S44 will still remain an open question at the end of the present paper. Decidability of S44 satisfiability is also open. In what follows, a B logic L = hFor; X i is said to be ....

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D. Vakarelov. Modal logics for knowledge representation systems. Theoretical Computer Science, 90:433--456, 1991.

.... being modally equivalent . Intuitively, a frame K from class C is informationally B representable if there is an information system and a frame K 0 derived from this system such that K 0 is in class C and, moreover, K is B related to K 0 . The first theorem of this kind has been proved in [Vak87, Vak89]. In [Or lo93] it has been observed that a property of informational representability might be meaningful in investigations of nonclassical logics, and a notion of informational representability has been proposed. In the present paper we introduce a general notion of informational ....

Dimiter Vakarelov. Modal logics for knowledge representation systems. In A. R. Meyer and Mikhail Taitslin, editors, Symposium on Logic Foundations of Computer Science, Pereslavl-Zalessky, pages 257--277. Springer-Verlag, LNCS 363, July 1989.

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D. Vakarelov. "Modal logics for knowledge representation systems". Theoretical Computer Science, 90:433-- 456, 1991.

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