Abstract
This paper is devoted to the proof of the completeness of deductive systems for dynamic extensions of arrow logic. These extensions are based on the relational constructs of composition and intersection. The proof of the completeness of our deductive systems uses the canonical model construction and the subordination model construction.
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References
Arsov, A. (1993). Completeness Theorems for Some Extensions of Arrow Logic (Master’s Dissertation, Sofia University).
Arsov, A. & Marx, M. (1993). Basic arrow logic with relation algebraic operators. In P. de Dekker & M. Stokhof (Eds.), Proceedings of the 9th Amsterdam Colloquium (pp. 93–112). Amsterdam University, Institute for Logic, Language and Computation.
Balbiani, P. (2003). Eliminating unorthodox derivation rules in an axiom system for iteration-free PDL with intersection. Fundamenta Informaticae, 56(3), 211–242.
Balbiani, P. & Orłowska, E. (1999). A hierarchy of modal logics with relative accessibility relations. Journal of Applied Non-classical Logics, 9(2–3), 303–328.
Balbiani, P. & Vakarelov, D. (2001). Iteration-free PDL with intersection: A complete axiomatization. Fundamenta Informaticae45(3), 173–194.
Balbiani, P. & Vakarelov, D. (2004). Dynamic extensions of arrow logic. Annals of Pure and Applied Logic, 127(1–3), 1–15.
Fariñas del Cerro, L. & Orłowska, E. (1985). DAL–A logic for data analysis. Theoretical Computer Science, 36, 251–264.
Demri, S. (2000). The nondeterministic information logic NIL is PSpace-complete. Fundamenta Informaticae, 42(3–4), 211–234.
Demri, S. & Gabbay, D. M. (2000a). On modal logics characterized by models with relative accessibility relations: Part I. Studia Logica, 65(3), 323–353.
Demri, S. & Gabbay, D. M. (2000b). On modal logics characterized by models with relative accessibility relations: Part II. Studia Logica, 66(3), 349–384.
Demri, S. & Orłowska, E. (2002). Incomplete Information: Structure, Inference, Complexity. Monographs in Theoretical Computer Science. An EATCS series Berlin: Springer.
Hughes, G. & Cresswell, M. (1984). A Companion to Modal Logic. Methuen and Co.
Marx, M. (1995). Algebraic Relativization and Arrow Logic (Doctoral Dissertation, Amsterdam University).
Orłowska, E. (1984). Modal logics in the theory of information systems. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 42(1/2), 213–222.
Orłowska, E. (1985a). Logic of indiscernibility relations. In A. Skowron (Ed.), Proceedings of Computation Theory with 5th Symposium, 1984 (Vol. 208, pp. 177–186). Lecture Notes in Computer Science. Zaborów, Poland: Springer.
Orłowska, E. (1985b). Logic of nondeterministic information. Studia Logica, 44(1), 91–100.
Orłowska, E. (1988). Kripke models with relative accessibility and their application to inferences from incomplete information. In G. Mirkowska & H. Rasiowa (Eds.), Mathematical Problems in Computation Theory (Vol. 21, pp. 329–339). Banach Centre Publications.
Orłowska, E. (1990). Kripke semantics for knowledge representation logics. Studia Logica, 49(2), 255–272.
Orłowska, E. & Pawlak, Z. (1984). Representation of nondeterministic information. Theoretical Computer Science, 29, 27–39.
Pawlak, Z. (1981). Information systems theoretical foundations. Information Systems, 6(3), 205–218.
Vakarelov, D. (1992). A modal theory of arrows: Arrow logics I. In D. Pearce & G. Wagner (Eds.), Proceedings of Logics in AI, European Workshop, JELIA ’92 (Vol. 633, pp. 1–24). Lecture Notes in Computer Science. Berlin, Germany: Springer.
Vakarelov, D. (1995). A duality between Pawlak’s knowledge representation systems and bi-consequence systems. Studia Logica, 55(1), 205–228.
Vakarelov, D. (1996). Many-dimensional arrow structures Arrow logics II. In M. Marx, L. Pólos, & M. Masuch (Eds.), Arrow Logic and Multi-modal Logic (pp. 141–187). Studies in Logic, Language and Information. Amsterdam: Center for the Study of Language and Information.
Vakarelov, D. (1998). Information systems, similarity relations and modal logics. In E. Orłowska (Ed.), Incomplete Information: Rough Set Analysis (Vol. 13, pp. 492–550). Studies in Fuzziness and Soft Computing. Heidelberg: Springer-Physica Verlag.
Acknowledgements
Special acknowledgement is heartly granted to Ewa Orłowska. Her research on rough set analysis, her use of modal logic as a general tool for the formalization of reasoning about incomplete information, the multifarious papers that she has written on that subject, her papers introducing modal logics such as DAL and NIL have exerted a profound influence on my research and a great deal of it was directly motivated and influenced by her ideas.
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Balbiani, P. (2018). About the Complete Axiomatization of Dynamic Extensions of Arrow Logic. In: Golińska-Pilarek, J., Zawidzki, M. (eds) Ewa Orłowska on Relational Methods in Logic and Computer Science. Outstanding Contributions to Logic, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-97879-6_12
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