Abstract
Chapter 3 contains a vast introduction to the mathematical theory of recursive multisets including description of syntax, semantics, and formal mathematical properties of various classes of multiset grammars and multiset metagrammars, which are represented inter alia as a new non-conventional model of computing—goal—and knowledge-driven computation by ubiquitous generation of sets of multisets.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Akerkar R, Sajja P (2010) Knowledge-based systems. Jones and Bartlett Publishers, Sudbury
Apt K (2003) Principles of constraint programming. Cambridge University Press, Cambridge, p 420. https://doi.org/10.1017/CBO9780511615320
Blizard WD (1989) Multiset theory. Notre Dame J Form Log 30:36–66
Bratko I (2012) Prolog programming for artificial intelligence. Addison-Wesley, New York
Chomsky N (2005) Syntactic structures. Mouton de Gruyter, The Hague
Cross TB (2017) The uses of artificial intelligence in business. Prentice Hall, New York. TECHtionary.com
Dannen C (2017) Introducing Ethereum and solidity—foundations of cryptocurrency and blockchain programming for beginners. Apress, New York
Darwen H (2012) An introduction to relational database theory. bookboon.com, London, UK
Date CI (2012) An introduction to database systems, 8th edn. Pearson, London
Frunkwirth T, Abdennadher S (2003) Essentials of constraint programming. Springer, Berlin, p 398. https://doi.org/10.1007/978-3-662-05138-2
Hickman JL (1980) A note on the concept of multiset. Bull Aust Math Soc 22:211–217. https://doi.org/10.1017/5000497270000650X
Hopcroft JE, Motwani R, Ullman J (2001) Introduction to automata theory, languages, and computation. Addison-Wesley, Reading
Kendal SL, Green M (2007) An introduction to knowledge engineering. Springer, London
Lake J (1976) Sets, fuzzy sets, multisets and functions. J Lond Math Soc 12:323–326
Marriott K, Stucky PG (2003) Programming with constraints: an introduction. MIT Press, Cambridge
Meduna A (2014) Formal languages and computation: models and their application. CRC Press, New York
Meyer RK, McRobbie MA (1982) Multisets and relevant implication. I, II. Aust J Philos 60:107–139. https://doi.org/10.1080/00048408212340551
Pannu A (2015) Artificial intelligence and its application in different areas. Int J Eng Innov Technol 4(4):79–84
Petrovskiy AB (2002) Main notions of the multisets theory. Editorial URSS, Moscow. (In Russian)
Petrovskiy AB (2003) Spaces of Sets and Multisets. Editorial URSS, Moscow. (In Russian)
Petrovskiy AB (2018) Theory of measured sets and multisets. Nauka, Moscow. (In Russian)
Red’ko VN, Bui DB, Grishko YA (2015) Modern state of multisets theory from the entity point of view. Cybern Syst Anal 51:171–178
Sainter P, Oldham K, Larkin A, Murton A, Brimble R (2000) Product knowledge management within knowledge-based engineering systems. In: Proceedings of ASME 2000 design engineering technical conference. ASME, Baltimore, pp 1–8
Schmidt G (2010) Relational mathematics. Encyclopedia of mathematics and its applications, vol 132. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511778810
Sheremet IA (1994) Intelligent software environments for computerized information processing systems. Nauka, Moscow. (In Russian)
Sheremet IA (2010) Recursive multisets and their applications. Nauka, Moscow. (In Russian)
Sheremet IA (2011a) Recursive multisets and their applications. NG Verlag, Berlin
Sheremet IA (2013) Augmented post systems: the mathematical framework for knowledge and data engineering in network-centric environment. EANS, Berlin
Sheremet I, Zhukov I (2016) Optimizing multiset metagrammars. Formal Definitions Int J Comput Eng Inform Technol 8(7):106–114
Sheremet I (2019a) Multiset-based knowledge representation for the assessment and optimization of large-scale sociotechnical systems. In: Vizureanu P (ed) Enhanced expert systems. IntechOpen, London. https://doi.org/10.5772/intechopen.81698. https://www.intechopen.com/books/enhanced-expert-systems/multiset-based-knowledge-representation-for-the-assessment-and-optimization-of-large-scale-sociotech
Sheremet I (2020b) Augmented post systems: syntax, semantics, and applications. In: Sud K, Erdogmus P, Kadry S (eds) Introduction to data science and machine learning. IntechOpen, London. https://doi.org/10.5772/intechopen.86207. https://www.intechopen.com/online-first/augmented-post-systems-syntax-semantics-and-applications
Siekmann JH (ed) (2014) Handbook of the history of logic, Computational logic, vol 9. Elsevier, Amstedam
Simovici DA, Djeraba C (2008) Mathematical tools for data mining: set theory, partial orders, combinatorics. Springer Science & Business Media, London
Singh D, Ibrahim AM, Yohanna T, Singh JN (2007) An overview of applications of multisets. Novi Sad J Math 37:37–92
Wallace M (2002) Constraint logic programming. In: Computational logic: logic programming and beyond, Lecture notes in computer science, vol 2407. Springer, New York, pp 512–556
Yeoh W, Yokoo M (2012) Distributed problem solving. AI Mag 33(3):53–65
Zheng Z, Xie S, Dai H-N, Chen X, Wang H (2018) Blockchain challenges and opportunities: a survey. Int J Web Grid Serv 14(4):352–376. https://doi.org/10.1504/IJWGS.2018.095647
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Sheremet, I.A. (2022). Syntax, Semantics, and Mathematical Properties of Multiset Grammars. In: Multigrammatical Framework for Knowledge-Based Digital Economy. Springer, Cham. https://doi.org/10.1007/978-3-031-13858-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-031-13858-4_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-13857-7
Online ISBN: 978-3-031-13858-4
eBook Packages: Computer ScienceComputer Science (R0)