286 research outputs found
Integrity Constraints Revisited: From Exact to Approximate Implication
Integrity constraints such as functional dependencies (FD), and multi-valued
dependencies (MVD) are fundamental in database schema design. Likewise,
probabilistic conditional independences (CI) are crucial for reasoning about
multivariate probability distributions. The implication problem studies whether
a set of constraints (antecedents) implies another constraint (consequent), and
has been investigated in both the database and the AI literature, under the
assumption that all constraints hold exactly. However, many applications today
consider constraints that hold only approximately. In this paper we define an
approximate implication as a linear inequality between the degree of
satisfaction of the antecedents and consequent, and we study the relaxation
problem: when does an exact implication relax to an approximate implication? We
use information theory to define the degree of satisfaction, and prove several
results. First, we show that any implication from a set of data dependencies
(MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most
quadratic in the number of variables; when the consequent is an FD, the factor
can be reduced to 1. Second, we prove that there exists an implication between
CIs that does not admit any relaxation; however, we prove that every
implication between CIs relaxes "in the limit". Finally, we show that the
implication problem for differential constraints in market basket analysis also
admits a relaxation with a factor equal to 1. Our results recover, and
sometimes extend, several previously known results about the implication
problem: implication of MVDs can be checked by considering only 2-tuple
relations, and the implication of differential constraints for frequent item
sets can be checked by considering only databases containing a single
transaction
Incorporating record subtyping into a relational data model
Most of the current proposals for new data models support the construction of heterogeneous sets. One of the major challenges for such data models is to provide strong typing in the presence of heterogenity. Therefore the inclusion of as much as possible information concerning legal structural variants is needed. We argue that the shape of some part of a heterogeneous scheme is often determined by the contents of some other part of the scheme. This relationship can be formalized by a certain type of integrity constraint we have called attribute dependency. Attribute dependencies combine the expressive power of general sums with a notation that fits into relational models. We show that attribute dependencies can be used, besides their application in type and integrity checking, to incorporate record subtyping into a relational model. Moreover, the notion of attribute dependency yields a stronger assertion than the traditional record subtyping rule as it considers some refinements to be caused by others.
To examine the differences between attribute dependencies and traditional record subtyping and to be able to predict how attribute dependencies behave under transformations like query language operations we develop an axiom system for their derivation and prove it to be sound and complete. We further investigate the interaction between functional and attribute dependencies and examine an extended axiom system capturing both forms of dependencies
Record Subtyping in Flexible Relations by means of Attribute Dependencies
The model of flexible relations supports heterogeneous
sets of tuples in a strongly typed way. The elegance of the standard relational model is preserved by using a single, generic scheme constructor.In each model supporting structural variants the shape of some part of a heterogeneous scheme may be determined by the contents of some other part of the scheme. We formalize this relationship by a certain kind of integrity constraint we have called "attribute dependency" (AD). We motivate how ADs can be used, besides their application in type and integrity checking, to incorporate record subtyping into our extended relational model Moreover, we show that ADs yield a stronger assertion than the traditional record subtyping rule as they
consider interdependencies among refinements. We discuss how ADs are related to query processing and how they may help to identify redundant operations
Measure-Based Inconsistency-Tolerant Maintenance of Database Integrity
[EN] To maintain integrity, constraint violations should be prevented or repaired. However, it may not be feasible to avoid inconsistency, or to repair all violations at once. Based on an abstract concept of violation measures, updates and repairs can be checked for keeping inconsistency bounded, such that integrity violations are guaranteed to never get out of control. This measure-based approach goes beyond conventional methods that are not meant to be applied in the presence of inconsistency. It also generalizes recently introduced concepts of inconsistency-tolerant integrity maintenance.Partially supported by FEDER and the Spanish grants TIN2009-14460-C03 and TIN2010-17139Decker, H. (2013). Measure-Based Inconsistency-Tolerant Maintenance of Database Integrity. Lecture Notes in Computer Science. 7693:149-173. https://doi.org/10.1007/978-3-642-36008-4_7S1491737693Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. 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Plenum Press (1978)Curino, C., Moon, H., Deutsch, A., Zaniolo, C.: Update Rewriting and Integrity Constraint Maintenance in a Schema Evolution Support System: PRISM++. PVLDBΒ 4, 117β128 (2010)Dawson, J.: The compactness of first-order logic: From GΓΆdel to LindstrΓΆm. History and Philosophy of LogicΒ 14(1), 15β37 (1993)Decker, H.: The Range Form of Databases and Queries or: How to Avoid Floundering. In: Proc. 5th ΓGAI. Informatik-Fachberichte, vol.Β 208, pp. 114β123. Springer (1989)Decker, H.: Drawing Updates From Derivations. In: Kanellakis, P.C., Abiteboul, S. (eds.) ICDT 1990. LNCS, vol.Β 470, pp. 437β451. Springer, Heidelberg (1990)Decker, H.: Extending Inconsistency-Tolerant Integrity Checking by Semantic Query Optimization. In: Bhowmick, S.S., KΓΌng, J., Wagner, R. (eds.) DEXA 2008. LNCS, vol.Β 5181, pp. 89β96. Springer, Heidelberg (2008)Decker, H.: Answers That Have Integrity. In: Schewe, K.-D., Thalheim, B. (eds.) SDKB 2010. LNCS, vol.Β 6834, pp. 54β72. Springer, Heidelberg (2011)Decker, H.: Causes of the Violation of Integrity Constraints for Supporting the Quality of Databases. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2011, Part V. LNCS, vol.Β 6786, pp. 283β292. Springer, Heidelberg (2011)Decker, H.: Inconsistency-tolerant Integrity Checking based on Inconsistency Metrics. In: KΓΆnig, A., Dengel, A., Hinkelmann, K., Kise, K., Howlett, R.J., Jain, L.C. (eds.) KES 2011, Part II. LNCS, vol.Β 6882, pp. 548β558. Springer, Heidelberg (2011)Decker, H.: Partial Repairs that Tolerate Inconsistency. In: Eder, J., Bielikova, M., Tjoa, A.M. (eds.) ADBIS 2011. LNCS, vol.Β 6909, pp. 389β400. Springer, Heidelberg (2011)Decker, H.: Consistent Explanations of Answers to Queries in Inconsistent Knowledge Bases. In: Roth-Berghofer, T., Tintarev, N., Leake, D. (eds.) Explanation-aware Computing, Proc. IJCAI 2011 Workshop ExaCt 2011, pp. 71β80 (2011), http://exact2011.workshop.hm/index.phpDecker, H., Martinenghi, D.: Classifying integrity checking methods with regard to inconsistency tolerance. In: Proc. PPDP 2008, pp. 195β204. ACM Press (2008)Decker, H., Martinenghi, D.: Modeling, Measuring and Monitoring the Quality of Information. In: Heuser, C.A., Pernul, G. (eds.) ER 2009. LNCS, vol.Β 5833, pp. 212β221. Springer, Heidelberg (2009)Decker, H., Martinenghi, D.: Inconsistency-tolerant Integrity Checking. IEEE TKDEΒ 23(2), 218β234 (2011)Decker, H., MuΓ±oz-EscoΓ, F.D.: Revisiting and Improving a Result on Integrity Preservation by Concurrent Transactions. In: Meersman, R., Dillon, T., Herrero, P. (eds.) OTM 2010 Workshops. LNCS, vol.Β 6428, pp. 297β306. Springer, Heidelberg (2010)Dung, P., Kowalski, R., Toni, F.: Dialectic Proof Procedures for Assumption-based Admissible Argumentation. Artificial IntelligenceΒ 170(2), 114β159 (2006)Ebbinghaus, H.-D., Flum, J.: Finite Model Theory, 2nd edn. Springer (2006)Embury, S., Brandt, S., Robinson, J., Sutherland, I., Bisby, F., Gray, A., Jones, A., White, R.: Adapting integrity enforcement techniques for data reconciliation. Information SystemsΒ 26, 657β689 (2001)Enderton, H.: A Mathematical Introduction to Logic, 2nd edn. Academic Press (2001)Eiter, T., Fink, M., Greco, G., Lembo, D.: Repair localization for query answering from inconsistent databases. ACM TODS 33(2), article 10 (2008)Furfaro, F., Greco, S., Molinaro, C.: A three-valued semantics for querying and repairing inconsistent databases. Ann. Math. Artif. Intell.Β 51(2-4), 167β193 (2007)Grant, J., Hunter, A.: Measuring the Good and the Bad in Inconsistent Information. In: Proc. 22nd IJCAI, pp. 2632β2637 (2011)Greco, G., Greco, S., Zumpano, E.: A logical framework for querying and repairing inconsistent databases. IEEE TKDEΒ 15(6), 1389β1408 (2003)Guessoum, A., Lloyd, J.: Updating knowledge bases. New Generation ComputingΒ 8(1), 71β89 (1990)Guessoum, A., Lloyd, J.: Updating knowledge bases II. New Generation ComputingΒ 10(1), 73β100 (1991)Gupta, A., Sagiv, Y., Ullman, J., Widom, J.: Constraint checking with partial information. In: Proc. PODS 1994, pp. 45β55. ACM Press (1994)Hunter, A.: Measuring Inconsistency in Knowledge via Quasi-Classical Models. In: Proc. 18th AAAI &14th IAAI, pp. 68β73 (2002)Hunter, A., Konieczny, S.: Approaches to Measuring Inconsistent Information. In: Bertossi, L., Hunter, A., Schaub, T. (eds.) Inconsistency Tolerance. LNCS, vol.Β 3300, pp. 191β236. Springer, Heidelberg (2005)Hunter, A., Konieczny, S.: Measuring inconsistency through minimal inconsistent sets. In: Brewka, G., Lang, J. (eds.) Principles of Knowledge Representation and Reasoning (Proc. 11th KR), pp. 358β366. AAAI Press (2008)Hunter, A., Konieczny, S.: On the measure of conflicts: Shapley Inconsistency Values. Artificial IntelligenceΒ 174, 1007β1026 (2010)Kakas, A., Mancarella, P.: Database updates through abduction. In: Proc. 16th VLDB, pp. 650β661. Morgan Kaufmann (1990)Kakas, A., Kowalski, R., Toni, F.: The role of Abduction in Logic Programming. In: Gabbay, D., Hogger, C., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol.Β 5, pp. 235β324. Oxford University Press (1998)Lee, S.Y., Ling, T.W.: Further improvements on integrity constraint checking for stratifiable deductive databases. In: Proc. VLDB 1996, pp. 495β505. Morgan Kaufmann (1996)Lehrer, K.: Relevant Deduction and Minimally Inconsistent Sets. Journal of PhilosophyΒ 3(2,3), 153β165 (1973)Mu, K., Liu, W., Jin, Z., Bell, D.: A Syntax-based Approach to Measuring the Degree of Inconsistency for Belief Bases. J. Approx. ReasoningΒ 52(7), 978β999 (2011)Lloyd, J., Sonenberg, L., Topor, R.: Integrity constraint checking in stratified databases. J. Logic ProgrammingΒ 4(4), 331β343 (1987)Lozinskii, E.: Resolving contradictions: A plausible semantics for inconsistent systems. J. Automated ReasoningΒ 12(1), 1β31 (1994)Ma, Y., Qi, G., Hitzler, P.: Computing inconsistency measure based on paraconsistent semantics. J. Logic ComputationΒ 21(6), 1257β1281 (2011)Martinenghi, D., Christiansen, H.: Transaction Management with Integrity Checking. In: Andersen, K.V., Debenham, J., Wagner, R. (eds.) DEXA 2005. LNCS, vol.Β 3588, pp. 606β615. Springer, Heidelberg (2005)Martinenghi, D., Christiansen, H., Decker, H.: Integrity Checking and Maintenance in Relational and Deductive Databases and Beyond. In: Ma, Z. (ed.) Intelligent Databases: Technologies and Applications, pp. 238β285. IGI Global (2006)Martinez, M.V., Pugliese, A., Simari, G.I., Subrahmanian, V.S., Prade, H.: How Dirty Is Your Relational Database? An Axiomatic Approach. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol.Β 4724, pp. 103β114. Springer, Heidelberg (2007)Meyer, J., Wieringa, R. (eds.): Deontic Logic in Computer Science. Wiley (1994)Nicolas, J.M.: Logic for improving integrity checking in relational data bases. Acta InformaticaΒ 18, 227β253 (1982)Plexousakis, D., Mylopoulos, J.: Accommodating Integrity Constraints During Database Design. In: Apers, P.M.G., Bouzeghoub, M., Gardarin, G. (eds.) EDBT 1996. LNCS, vol.Β 1057, pp. 495β513. Springer, Heidelberg (1996)Rahm, E., Do, H.: Data Cleaning: Problems and Current Approaches. Data Engineering BulletinΒ 23(4), 3β13 (2000)Sadri, F., Kowalski, R.: A theorem-proving approach to database integrity. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 313β362. Morgan Kaufmann (1988)Thimm, M.: Measuring Inconsistency in Probabilistic Knowledge Bases. In: Proc. 25th UAI, pp. 530β537. 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Augmented Post Systems: Syntax, Semantics, and Applications
Augmented Post systems (APS) are string-operating Prolog-like knowledge representation, affiliated with the βSet of Stringsβ Framework (SSF). APS descriptive and logical inference capabilities provide natural integration of Big Data with online analytic processing. This chapter is dedicated to strict formal definition of APS syntax, mathematical and operational semantics, and to its most valuable implementational issues, as well as to APS application to Big Data, Internet of Things, cyberphysical industry, and cybersecurity areas
ΠΠ±ΠΎΠ±ΡΠ΅Π½Π½ΡΠ΅ ΡΠΈΠΏΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΠ΅ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ Ρ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠΌΠΈ Π·Π½Π°ΡΠ΅Π½ΠΈΡΠΌΠΈ Π² Π±Π°Π·Π°Ρ Π΄Π°Π½Π½ΡΡ
The paper discusses a new type of dependency in databases, which is a generalization of inclusion dependencies. Traditionally, such dependencies are used in practice to ensure referential integrity. In this case, the restriction is established only between a pair of relations, the first of which is called the main, the second is external. In practice, referential integrity often needs to be established for a larger number of relations, where several main and several external relations participate in the same constraint. Such a structure corresponds to an ultragraph. The paper provides a rationale for generalized inclusion dependencies that take into account the presence of null values in external relations. Based on the study of the properties of typed dependencies, a system of axioms is obtained, for which consistency (soundness) and completeness are proved.Π ΡΡΠ°ΡΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ Π½ΠΎΠ²ΡΠΉ Π²ΠΈΠ΄ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π² Π±Π°Π·Π°Ρ
Π΄Π°Π½Π½ΡΡ
, ΡΠ²Π»ΡΡΡΠΈΠΉΡΡ ΠΎΠ±ΠΎΠ±ΡΠ΅Π½ΠΈΠ΅ΠΌ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ. Π’ΡΠ°Π΄ΠΈΡΠΈΠΎΠ½Π½ΠΎ ΡΠ°ΠΊΠΈΠ΅ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ Π½Π° ΠΏΡΠ°ΠΊΡΠΈΠΊΠ΅ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ Π΄Π»Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ ΡΡΡΠ»ΠΎΡΠ½ΠΎΠΉ ΡΠ΅Π»ΠΎΡΡΠ½ΠΎΡΡΠΈ. ΠΡΠΈ ΡΡΠΎΠΌ, ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½ΠΈΠ΅ ΡΡΡΠ°Π½Π°Π²Π»ΠΈΠ²Π°Π΅ΡΡΡ ΡΠΎΠ»ΡΠΊΠΎ ΠΌΠ΅ΠΆΠ΄Ρ ΠΏΠ°ΡΠΎΠΉ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠΉ, ΠΏΠ΅ΡΠ²ΠΎΠ΅ ΠΈΠ· ΠΊΠΎΡΠΎΡΡΡ
Π½Π°Π·ΡΠ²Π°Π΅ΡΡΡ Π³Π»Π°Π²Π½ΡΠΌ, Π²ΡΠΎΡΠΎΠ΅ β Π²Π½Π΅ΡΠ½ΠΈΠΌ. ΠΠ° ΠΏΡΠ°ΠΊΡΠΈΠΊΠ΅ ΡΡΡΠ»ΠΎΡΠ½ΡΡ ΡΠ΅Π»ΠΎΡΡΠ½ΠΎΡΡΡ ΡΠ°ΡΡΠΎ ΡΡΠ΅Π±ΡΠ΅ΡΡΡ ΡΡΡΠ°Π½ΠΎΠ²ΠΈΡΡ Π΄Π»Ρ Π±ΠΎΠ»ΡΡΠ΅Π³ΠΎ ΡΠΈΡΠ»Π° ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠΉ, Π³Π΄Π΅ Π² ΠΎΠ΄Π½ΠΎΠΌ ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½ΠΈΠΈ ΡΡΠ°ΡΡΠ²ΡΡΡ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ Π³Π»Π°Π²Π½ΡΡ
ΠΈ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ ΠΏΠΎΠ΄ΡΠΈΠ½Π΅Π½Π½ΡΡ
ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠΉ. Π’Π°ΠΊΠ°Ρ ΡΡΡΡΠΊΡΡΡΠ° ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΠ΅Ρ ΡΠ»ΡΡΡΠ°Π³ΡΠ°ΡΡ. Π ΡΠ°Π±ΠΎΡΠ΅ ΠΏΡΠΈΠ²Π΅Π΄Π΅Π½ΠΎ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΎΠ±ΠΎΠ±ΡΠ΅Π½Π½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ, ΡΡΠΈΡΡΠ²Π°ΡΡΠΈΡ
Π½Π°Π»ΠΈΡΠΈΠ΅ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΡ
Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ Π²ΠΎ Π²Π½Π΅ΡΠ½ΠΈΡ
ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡΡ
. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΠ²ΠΎΠΉΡΡΠ² ΡΠΈΠΏΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ ΠΏΠΎΠ»ΡΡΠ΅Π½Π° ΡΠΈΡΡΠ΅ΠΌΠ° Π°ΠΊΡΠΈΠΎΠΌ, Π΄Π»Ρ ΠΊΠΎΡΠΎΡΠΎΠΉ Π΄ΠΎΠΊΠ°Π·Π°Π½Π° Π½Π΅ΠΏΡΠΎΡΠΈΠ²ΠΎΡΠ΅ΡΠΈΠ²ΠΎΡΡΡ (Π½Π°Π΄Π΅ΠΆΠ½ΠΎΡΡΡ) ΠΈ ΠΏΠΎΠ»Π½ΠΎΡΠ°
ΠΠ½Π°Π»ΠΈΠ· ΡΠΈΠΏΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ Ρ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠΌΠΈ Π·Π½Π°ΡΠ΅Π½ΠΈΡΠΌΠΈ
Null values have become an urgent problem since the creation of the relational dataΒ model. The impact of the uncertainty aο¬ects all types of dependencies used in the design and operationΒ of the database. This fully applies to the inclusion dependencies, which are the theoretical basis forΒ referential integrity on the data. Attempts to solve this problem contain inaccuracy in the statementΒ of the problem and its solution. The errors in formulation of the problem can be associated with theΒ use in the deο¬nition of untyped inclusion dependencies, which leads to permutations of the attributes,Β although, the attributes in database technology are identiο¬ed by name and not by their place. In addition, linking with the use of the inclusion dependencies of heterogeneous attributes, even of the same type, is a sign of lost functional dependencies and leads to interaction of inclusion dependencies and non-trivial functional dependencies. Inaccuracies in the solution of the problem are contained in the statements of axioms and the proof of their properties, including completeness. In this paper we propose an original solution of this problem only for typed inclusion dependencies in the presence of Null values: a new axiom system is proposed, its completeness and soundness are proved. On the basis of inference rules we developed an algorithm for the construction of a not surplus set of typed inclusion dependencies. The correctness of the algorithm is proved.ΠΠ΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΡΡΠ°Π»ΠΈ Π°ΠΊΡΡΠ°Π»ΡΠ½ΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠΎΠΉ Ρ ΠΌΠΎΠΌΠ΅Π½ΡΠ° ΡΠΎΠ·Π΄Π°Π½ΠΈΡ ΡΠ΅Π»ΡΡΠΈΠΎΠ½Π½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π΄Π°Π½Π½ΡΡ
. ΠΠ»ΠΈΡΠ½ΠΈΠ΅ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΠ΅ΠΉ ΡΠΊΠ°Π·ΡΠ²Π°Π΅ΡΡΡ Π½Π° Π²ΡΠ΅Ρ
Π²ΠΈΠ΄Π°Ρ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ,Β ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΡΡ
ΠΏΡΠΈ ΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΠΈ ΡΠΊΡΠΏΠ»ΡΠ°ΡΠ°ΡΠΈΠΈ Π±Π°Π·Ρ Π΄Π°Π½Π½ΡΡ
. Π ΠΏΠΎΠ»Π½ΠΎΠΉ ΠΌΠ΅ΡΠ΅ ΡΡΠΎ ΠΎΡΠ½ΠΎΡΠΈΡΡΡ ΠΈΒ ΠΊ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΡΠΌ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ, ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠ²Π»ΡΡΡΡΡ ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΎΡΠ½ΠΎΠ²ΠΎΠΉ ΡΡΡΠ»ΠΎΡΠ½ΠΎΠΉ ΡΠ΅Π»ΠΎΡΡΠ½ΠΎΡΡΠΈ Π½Π°Β Π΄Π°Π½Π½ΡΠ΅. ΠΠΎΠΏΡΡΠΊΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΡΠΊΠ°Π·Π°Π½Π½ΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΡΠΎΠ΄Π΅ΡΠΆΠ°Ρ Π½Π΅ΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΊΠ°ΠΊ Π² ΠΏΠΎΡΡΠ°Π½ΠΎΠ²ΠΊΠ΅ Π·Π°Π΄Π°ΡΠΈ,Β ΡΠ°ΠΊ ΠΈ Π² ΡΠ°ΠΌΠΎΠΌ Π΅Π΅ ΡΠ΅ΡΠ΅Π½ΠΈΠΈ. Π ΠΏΠΎΡΡΠ°Π½ΠΎΠ²ΠΎΡΠ½ΡΠΌ ΠΎΡΠΈΠ±ΠΊΠ°ΠΌ ΠΌΠΎΠΆΠ½ΠΎ ΠΎΡΠ½Π΅ΡΡΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ Π² ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠΈ Π½Π΅ΡΠΈΠΏΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ, ΡΡΠΎ ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ ΠΏΠ΅ΡΠ΅ΡΡΠ°Π½ΠΎΠ²ΠΊΠ°ΠΌ Π°ΡΡΠΈΠ±ΡΡΠΎΠ², Ρ
ΠΎΡΡ Π²Β ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΡΡ
Π±Π°Π· Π΄Π°Π½Π½ΡΡ
Π°ΡΡΠΈΠ±ΡΡΡ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΡΠΈΡΡΡΡΡΡ ΠΏΠΎ ΠΈΠΌΠ΅Π½ΠΈ, Π° Π½Π΅ ΠΏΠΎ ΠΈΡ
ΠΏΠΎΠ·ΠΈΡΠΈΠΈ. ΠΡΠΎΠΌΠ΅ ΡΠΎΠ³ΠΎ,Β ΡΠ²ΡΠ·ΡΠ²Π°Π½ΠΈΠ΅ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΡΡ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ ΡΠ°Π·Π½ΠΎΡΠΎΠ΄Π½ΡΡ
, ΠΏΡΡΡΡ Π΄Π°ΠΆΠ΅ ΠΎΠ΄Π½ΠΎΡΠΈΠΏΠ½ΡΡ
, Π°ΡΡΠΈΠ±ΡΡΠΎΠ² ΡΠ²Π»ΡΠ΅ΡΡΡΒ ΠΏΡΠΈΠ·Π½Π°ΠΊΠΎΠΌ ΠΏΠΎΡΠ΅ΡΡΠ½Π½ΠΎΠΉ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΈ ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡ Π½Π΅ΡΡΠΈΠ²ΠΈΠ°Π»ΡΠ½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ ΠΈ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ. ΠΠ°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ Π΄ΠΎΠ»ΠΆΠ½ΡΒ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΡΡ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠ΅ ΡΠΎΠΎΡΠ½Π΅ΡΠ΅Π½ΠΈΠ΅ ΠΎΠ±ΡΠ΅ΠΊΡΠΎΠ² Π΄ΡΡΠ³ Ρ Π΄ΡΡΠ³ΠΎΠΌ, Π° Π½Π΅ Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ Π°ΡΡΠΈΠ±ΡΡΠΎΠ². ΠΠ΅ΡΠΎΡΠ½ΠΎΡΡΠΈ Π² ΡΠ΅ΡΠ΅Π½ΠΈΠΈ ΡΠΊΠ°Π·Π°Π½Π½ΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΡΡ Π² ΡΠΎΡΠΌΡΠ»ΠΈΡΠΎΠ²ΠΊΠ°Ρ
Π°ΠΊΡΠΈΠΎΠΌ ΠΈ Π΄ΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΡΡΠ²Π΅ ΠΈΡ
Β ΡΠ²ΠΎΠΉΡΡΠ², Π² ΡΠΎΠΌ ΡΠΈΡΠ»Π΅ ΠΏΠΎΠ»Π½ΠΎΡΡ. Π ΡΡΠΎΠΉ ΡΡΠ°ΡΡΠ΅ ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΠΎΡΠΈΠ³ΠΈΠ½Π°Π»ΡΠ½ΠΎΠ΅ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ ΡΡΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΡΠΎΠ»ΡΠΊΠΎ Π΄Π»Ρ ΡΠΈΠΏΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ ΠΏΡΠΈ Π½Π°Π»ΠΈΡΠΈΠΈ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΡ
Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ:Β ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π° ΡΠΈΡΡΠ΅ΠΌΠ° Π°ΠΊΡΠΈΠΎΠΌ, Π΄ΠΎΠΊΠ°Π·Π°Π½Π° Π΅Π΅ ΠΏΠΎΠ»Π½ΠΎΡΠ° ΠΈ Π½Π΅ΠΏΡΠΎΡΠΈΠ²ΠΎΡΠ΅ΡΠΈΠ²ΠΎΡΡΡ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΏΡΠ°Π²ΠΈΠ» Π²ΡΠ²ΠΎΠ΄Π° ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ Π½Π΅ ΠΈΠ·Π±ΡΡΠΎΡΠ½ΠΎΠ³ΠΎ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²Π° ΡΠΈΠΏΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉΒ Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΡ. ΠΠΎΠΊΠ°Π·Π°Π½Π° ΠΊΠΎΡΡΠ΅ΠΊΡΠ½ΠΎΡΡΡ ΡΡΠΎΠ³ΠΎ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ°
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