From Primes as the Pure Semantic Basis of Numerical Calculation
to Objective Semantic Computation and Reasoning
DIKW research group, Hainan University, China
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
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
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”.
We have proposed that primes are the carrier of essential semantics of integers 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.
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.
5. Consistent merging of individual vs. whole semantics
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
This is a semantic level evaluation which relates individual level difference or controversial
semantics of samenessindividual vs. differenceindividual 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.
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.
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.
4. Shijing Hu, Yucong Duan, Essence Computation Oriented Multi-semantic Analysis Crossing
Multi-modal DIKW Graphs. January 2021. DOI: 10.1007/978-3-030-67537-0_20
5. Yingbo Li, Yucong Duan, Zakaria Maamar, Haoyang Che, Anamaria-Beatrice Spulber, Stelios
Fuentes: Swarm Differential Privacy for Purpose Driven Data-Information-Knowledge-Wisdom
Architecture. CoRR abs/2105.04045 (2021)
6. Yingbo Li, Yucong Duan, Anamaria-Beatrice Spulber, Haoyang Che, Zakaria Maamar, Zhao
Li, Chen Yang, Yu lei: Physical Artificial Intelligence: The Concept Expansion of
Next-Generation 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: 99161-99176 (2019)
8. Yucong Duan: Existence Computation: Revelation on Entity vs. Relationship for
Relationship Defined Everything of Semantics. SNPD 2019: 139-144
9. Yucong Duan: Towards a Periodic Table of conceptualization and formalization on State, Style,
Structure, Pattern, Framework, Architecture, Service and so on. SNPD 2019: 133-138
10. Yucong Duan: Semantic Oriented Algorithm Design: A Case of Median Selection. SNPD
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): 1847-1852 (2013)
12. Yucong Duan: A Dualism Based Semantics Formalization Mechanism for Model Driven
Engineering. Int. J. Softw. Sci. Comput. Intell. 1(4): 90-110 (2009)
13. Yucong, Duan, and Christophe Cruz. "Formalizing semantic of natural language through
conceptualization from existence." IJIMT, (2011).
14. Yucong Duan, Shing-Chi Cheung, Xiaolan Fu, Yuqing Gu:A Metamodel Based Model
Transformation Approach. SERA 2005: 184-191