
From Primes as the Pure Semantic Basis of Numerical Calculation
to Objective Semantic Computation and Reasoning
Yucong Duan
DIKW research group, Hainan University, China
Email: duanyucong@hotmail.com
Abstract:
Based on our previous report on that prime integers are the essential basis of natural numbers and our revelation on the composition models of superficial concepts of even integers, etc, we further propose in this work the promises of reconstructing computation and reasoning at objective semantic level comprising the pure or isolated semantics such as primes.
1. Introduction
Semantics locates not only in the center of artificial intelligence research as targeted content but also dominating the correctness, precision and probability of the expressed models of the content as expression mechanism. Although various approaches including ontology and metamodel have been proposed, subjective semantics, because of its individualized nature and usually hidden side of the incomplete expression form, is hard to be identified as objective and expressed with concepts. The prevailing incompleteness of the conversion from subjective semantics to objective semantics creates not only the difference of raw “Data” and meaning or purposeful “information” which binds individualized purpose with data, but also the general fact that natural language concepts usually involves multiple semantics of an expression due to the nondeterministic choices among several possible or uncertain purposes .
Taking the whole society as a whole, there are huge waste on communication efficiency and effectiveness to redundantly repeating the process of determine the targeted semantics among multiple possibilities if we temporarily omit the esthetic positive aspect occasionally brought by the cognitive uncertainty. From a constructive perspective, it will be wonderful to identify ideally some basic semantics and there related carriers or concepts. In this work, we choose to extend on the number domain, specifically over integers. Reasoning and computation is essentially reflecting or embodying the purpose of conveying semantics or meaning to oneself or others. Proof is actually relating semantics between known/hypothesis and unknown.
We propose to define objective semantic computation and reasoning as investigating and promoting the effective and efficient modeling and manipulation of semantics and their corresponding concepts.
2. The semantics of even integers
The semantics of even means that there are two identical or the same integers which added together to comprise the even number. This semantics of even is both necessary and complete in terms of independently describes the semantics of all even integers.
Even equals to the basic justification of the existence of the semantics of sameness. The semantics of basic of basic justification means that it matches to the pair of “A is the same as B”.
Even
::= sameness_{A=B}
We have proposed that primes are the carrier of essential semantics of integers[1] in terms of constructively composing other numbers. By essential, we mean that the primes are the most efficient identifiers to composing all other superficial level number types in terms of both average composition operations and description complicity.
3. The semantics of primes
The semantics of prime integers is pure based on the reference to the semantics of sameness.
prime
::=!composition
::=_{essentially}!even
4. The semantics of composition
The semantics of composition capability of an integer by multiplication or reversing of division for integers relies on the existence of semantics of sameness among all elementary integers.
composition_{multiply}
::=sameness_{number}
::=sameness_{essentically(prime)}
5. Consistent merging of individual vs. whole semantics
Philosophical indication:
All different elements as carriers of the semantics of difference as a whole is unified with the all different elements as carriers of the semantics of sameness in terms of the type level expression of
Even_{whole}
::=sameness_{whole({even(x)+even(y)})}
::=difference_{whole({prime(x)+prime(y)})}
=>
Sameness_{whole}
::=difference_{whole}
This is a semantic level evaluation which relates individual level difference or controversial semantics of sameness_{individual} vs. difference_{individual} as identical in terms of compositional elements as a whole for the semantics of capability of composing all or the whole of numbers of integers or even. From the cognitive aspect, the semantic existence of pair of a sameness and a difference originates in the strict coupling of the relativity or mutual reference of a same and a difference. Usually because of the existence of multiple semantics of words, sentences and other expressions, the rules among semantics are not observed while semantic sets are not taken as pure targets of investigation. We propose that objective semantic computation and reasoning can come up to serve related effective and efficient computation and reasoning purposes.
In a plain expression, the binary addition of all different integers, such as the whole set of primes, can comprise, or equal to, all binary addition results of all same numbers which include the whole set of even integers.
The consistency of the semantic level conclusion, such as the addition of all different numbers can equal to or map to the binary addition of all same pairs of integers , with the numerical validation at individual integer level, is not only intuitive, but also the semantic level intuition is stronger than, or dominates, the individual level calculation of validation.
References
1. Yucong Duan, A modeling of integers with prime pairs and its reversed extension and models. June 2021, DOI: 10.13140/RG.2.2.13232.28168. https://www.researchgate.net/publication/352056378_A_modeling_of_integers_with_prime_pairs_and_its_reversed_extension_and_models
2. Yucong Duan,Why we need Crossing "Data, Information, Knowledge and Wisdom (DIKW) modals " towards Strong Artificial Intelligence? March 2021.DOI: 10.13140/RG.2.2.27023.92326
3. Yucong Duan, Really necessarily clarify semantics of DIKW concepts or NO? February 2021. DOI: 10.13140/RG.2.2.15906.56004 https://www.researchgate.net/publication/349456378_Really_necessarily_clarify_semantics_of_DIKW_concepts_or_NO
4. Shijing Hu, Yucong Duan, Essence Computation Oriented Multisemantic Analysis Crossing Multimodal DIKW Graphs. January 2021. DOI: 10.1007/9783030675370_20 https://www.researchgate.net/publication/348667625_Essence_Computation_Oriented_Multisemantic_Analysis_Crossing_Multimodal_DIKW_Graphs
5. Yingbo Li, Yucong Duan, Zakaria Maamar, Haoyang Che, AnamariaBeatrice Spulber, Stelios Fuentes: Swarm Differential Privacy for Purpose Driven DataInformationKnowledgeWisdom Architecture. CoRR abs/2105.04045 (2021)
6. Yingbo Li, Yucong Duan, AnamariaBeatrice Spulber, Haoyang Che, Zakaria Maamar, Zhao Li, Chen Yang, Yu lei: Physical Artificial Intelligence: The Concept Expansion of NextGeneration Artificial Intelligence. CoRR abs/2105.06564 (2021)
7. Yucong Duan, Xiaobing Sun, Haoyang Che, Chunjie Cao, Zhao Li, Xiaoxian Yang: Modeling Data, Information and Knowledge for Security Protection of Hybrid IoT and Edge Resources. IEEE Access 7: 9916199176 (2019)
8. Yucong Duan: Existence Computation: Revelation on Entity vs. Relationship for Relationship Defined Everything of Semantics. SNPD 2019: 139144
9. Yucong Duan: Towards a Periodic Table of conceptualization and formalization on State, Style, Structure, Pattern, Framework, Architecture, Service and so on. SNPD 2019: 133138
10. Yucong Duan: Semantic Oriented Algorithm Design: A Case of Median Selection. SNPD 2018: 307311
11. Yucong Duan, Christophe Cruz, Christophe Nicolle: Identifying Objective True/False from Subjective Yes/No Semantic based on OWA and CWA. J. Comput. 8(7): 18471852 (2013)
12. Yucong Duan: A Dualism Based Semantics Formalization Mechanism for Model Driven Engineering. Int. J. Softw. Sci. Comput. Intell. 1(4): 90110 (2009)
13. Yucong, Duan, and Christophe Cruz. "Formalizing semantic of natural language through conceptualization from existence." IJIMT, (2011).
14. Yucong Duan, ShingChi Cheung, Xiaolan Fu, Yuqing Gu:A Metamodel Based Model Transformation Approach. SERA 2005: 184191
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