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1
Content available remote Definability and Canonicity for Boolean Logic with a Binary Relation
Balbiani P., Tinchev T.
Fundamenta Informaticae
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2014
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Vol. 129, nr 4
301--327
EN
This paper studies the concepts of definability and canonicity in Boolean logic with a binary relation. Firstly, it provides formulas defining first-order or second-order conditions on frames. Secondly, it proves that all formulas corresponding to compatible first-order conditions on frames are canonical.
2
Content available remote A Modal Logic for Pawlak's Approximation Spaces with Rough Cardinality n
Balbiani P., Iliev P., Vakarelov D.
Fundamenta Informaticae
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2008
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Vol. 83, nr 4
451-464
EN
The natural modal logic corresponding to Pawlak's approximation spaces is S5, based on the box modality [R]A (and the diamond modality áRn~A=?[R]?A), where R is the corresponding indiscernibility relation of the approximation space S=(W,R). However the expressive power of S5 is too weak and, for instance, we cannot express that the space S has exactly n equivalence classes ( we say that S is roughly-finite and n is the rough cardinality of S). For this reason we extend the modal logic S5 with a new box modality [S]A, where S is the complement of R i.e. the discernibility relation of W. We propose a complete axiomatization, in this new language, of the logic ROUGHn corresponding to the class of approximation spaces with rough cardinality n. We prove that the satisfiability problem for ROUGHn is NP-complete.
3
Content available remote Modal Logics for Region-based Theories of Space
Balbiani P., Tinchev T., Vakarelov D.
Fundamenta Informaticae
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2007
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Vol. 81, nr 1-3
29-82
EN
We dedicate thispaper to Professor Andrzej Grzegorczyk. His paper "Axiomatization of geometry without points" is one the first contributions to the region-based theory of space.
4
Content available remote Arrow Logic with Arbitrary Intersections: Applications to Pawlak's Information Systems
Balbiani P., Vakarelov D.
Fundamenta Informaticae
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2007
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Vol. 75, nr 1-4
1-25
EN
We dedicate this paper to the memory of Zdislaw Pawlak, the founder of rough sets methodology in computer science. A great deal of our scientific work was motivated and influenced by Pawlak's ideas.
5
Content available remote Eliminating Unorthodox Derivation Rules in an Axiom System for Iteration-free PDL with Intersection
Balbiani P.
Fundamenta Informaticae
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2003
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Vol. 56, nr 3
211-242
EN
We devote this paper to the completeness of an axiom system for PDL - a variant of PDL which includes the program operations of composition and intersection. Most of the difficulty in the proof of the completeness theorem for PDL lies in the fact that intersection of accessibility relations is not modally definable. We overcome this difficulty by considering the concepts of theory and large program. Theories are sets of formulas that contain PDL and are closed under the inference rule of modus ponens. Large programs are built up from program variables and theories by means of the operations of composition and intersection, just as programs are built up from program variables and tests. Adapting these concepts to the subordination method, we can prove the completeness of our deductive system for PDL.
6
Content available remote A Modal Logic for Indiscernibility and Complementarity in Information Systems
Balbiani P., Vakarelov D.
Fundamenta Informaticae
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2002
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Vol. 50, nr 3,4
243-263
EN
In this paper, we study indiscernibility relations and complementarity relations in information systems. The first-order characterization of indiscernibility and complementarity is obtained through a duality result between information systems and certain structures of relational type characterized by first-order conditions. The modal analysis of indiscernibility and complementarity is performed through a modal logic which modalities correspond to indiscernibility relations and complementarity relations in information systems.
7
Content available remote Iteration-free PDL with intersection : a complete axiomatization
Balbiani P., Vakarelov D.
Fundamenta Informaticae
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2001
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Vol. 45, nr 3
173-194
EN
This paper is devoted to the completeness issue of PDL0Ç - an iteration-free fragment of Propositional Dynamic Logic with intersection of programs. The trouble with PDL0Ç is that the operation of intersection is not modally definable. Using new techniques connected with rules for intersection and the notions of large and maximal programs, the paper demonstrates that the presented proof theory for PDL0Ç is complete for the standard Kripke semantics of PDL0Ç.
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