MUTUALLY-INVERSISTIC LOGIC.MATHEMATICS.AND THEIR APPLICATIONS-互逆主义逻辑.数学和它们的应用-英文版

出版社:周训伟 中央编译出版社 (2013-03出版)
ISBN:9787511716118
作者:周訓偉

章节摘录

版权页:   插图:   Two third-order single empirical or mathematical connection propositions connectedby a connection operator form a third-order single logical connection proposition, if theproposition formed is a variable proposition; e.g., Ψ≤-1Ω is a third-order single logical con-nection proposition. Two third-order single empirical or mathematical connection propositions or distin-guished single empirical or mathematical connection propositions O1 and U1 connected by=-1 form a quasi-transcendent logical connection proposition, if the proposition formed isan invariable proposition. For example, Ψ=-1Ψ,Ψ∨Ψ=-1 U1, are quasi-transcendentlogical connection propositions. Two third-order single empirical or mathematical connectionpropositions connected by ≤-1 form a quasi-transcendent logical connection proposition,if the proposition formed is an invariable proposition; e.g., Ψ≤-1Ψ,Ψ∧Ω≤-1Ψ are quasi-transcendent logical connection propositions. A true quasi-transcendent logical connectionproposition is a quasi-transcendent logical theorem. The connection operator connecting single empirical or mathematical connection prop-ositions is called a logical connection operator or a fourth-order main constant. The lowercase Greek letters λ,δ,ζ denote logical connection operator variables or fourth-order mainvariables ranging over logical connection operators ∨/-1, ≤-1, = -1, <-1,∨-1, and ⊕-1. A logical connection operator variable connecting two distinct third-order singleempirical or mathematical connection propositions forms a fourth-order single logicalconnection proposition, which is a variable proposition; e.g., ΨλΩ is a fourth-order singlelogical connection proposition. The upper case Greek letters are single logical connection proposition variables,and are abbreviations for fourth-order single logical connection propositions ranging overthird-order single logical connection propositions; e.g., A is an abbreviation of ΨλΩ. O2 is a permanently false single logical connection proposition, U2 is a permanentlytrue single logical connection proposition. O2 and U2 are distinguished single logicalconnection propositions.

书籍目录

Preface Part 1 Mutually-inversistic logical calculus Chapter 1 Fundaments of predicate calculus 1.1 Material implication vs. mutually inverse implication 1.2 Formation ofterms and propositions 1.3 Simple-complexcomposition 1.4 Zeroth-level predicate calculus Chapter 2 Human cognitive processes and basic principles of mutually-inversistic logic 2.1 Mutually inverse special propositions vs. mutually inverse general propositions 2.2 Unary cognitive processes 2.3 Binary cognitive processes 2.4 Man's cognitive route 2.5 Classification ofcognitive processes 2.6 Inductive composition vs. decomposition 2.7 The principle ofinductive composition, the principle ofdecomposition, and the principle of mutual inverseness between inductive composition and decomposition 2.8 Truth tables ofinductive composition and decomposition for the connection operators 2.9 Mutually inverse diagrams for the connection operators 2.10 The principle ofmeaningfulness and meaninglessness duality for the distinguished propositions Chapter 3 First-level single quasi-predicate calculus 3.1 Meaningless and meaningful first-order single empirical or mathematical connection propositions 3.2 Free and bound first-order single empirical or mathematical connection propostions 3.3 First-levelexplicitinductivecomposition 3.4 First-levelimplicitinductivecomposition 3.5 Contradictorypropositions 3.6 First-leveldecomposition 3.7 Quasi-logicalconnectionpropositions 3.8 The decomposition system offirst-level single quasi-predicate calculus Chapter 4 Second-level single quasi-predicate calculus 4.1 Meaningless and meaningful second-order single logical connection propositions 4.2 Free and bound second-order single logical connection propositions 4.3 Second-levelexplicitinductivecomposition 4.4 Second-levelimplicitinductivecomposition 4.5 Second-leveldecomposition 4.6 Quasi-transcendentlogicalconnectionpropositions 4.7 Knowledge-cognitionscience 4.8 The decomposition system of second-level single quasi-predicate calculus Chapter 5 First-level multiple predicate calculus 5.1 Property fact proposition segments vs. non-property fact propositions 5.2 Mutually inverse multiple diagrams 5.3 Success diagrams vs. failure diagrams 5.4 Least success diagrams 5.5 Proposition chains and property proposition segment chains 5.6 Multiple empirical or mathematical connection propositions 5.7 Meaningful and bound multiple empirical or mathematical connection propositions 5.8 Mutually inverse multiple diagrams for multiple empmcal or mathematical connection propositions 5.9 Proposition chains, property proposition segment chains, and least success diagrams of multiple empirical or mathematical connection propositions 2.10 Decomposition system offirst-levelmultiple predicate calculus Chapter 6 Second-level multiple predicate calculus Chapter 7 Mutually-inversistic propositional calculus Part 2 Mutually-inversistic set theory Chapter 8 Fundamentals of mutually-inversistic set theory Chapter 9 The Main Chapter 10 The auxiliary Part 3 Mutually-inversistic proof theory vs mutually-inversistic model theory Chapter 11 Proof theory vs model theory Chapter 12 Mutually-inversistic proof theory Chapter 13 Mutually-inversistic model theory Part 4 Mutually-inversistic recursion theory Chapter 14 Mutually-inversistic recursion theory Part 5 Mutually-inversistic granular computing Chapter 15 Mutually-inversistic fuzzy logic based granular computing Chapter 16 Mutually-inversistic rough set based granular computing Chapter 17 Unified logics Part 7 Mutually-inversistic analytic geometry Chapter 18 Mutually-inversistic analytic geometry Part 8 Mutually-inversistic mathematical analysis Chapter 19 Double-sided discrete calculus Chapter 20 Single-sided discrete calculus Chapter 21 Unified calculus Part 9 Mutually-inversistic abstract algebra Chapter 22 Auxiliary algebras Chapter 23 Main-auxiliary algebras Part 10 Universal matrices Chapter 24 Universal matrices Part 11 Applications of decomposition Chapter 25 Inference rule systems vs mutually-inversistic automated decomposition systems Chapter 26 Mutually-inversistic relational databases Chapter 27 Mutually-inversistic planning and scheduling Chapter 28 Mutually-Inversistic Semantic Network Chapter 29 Mutually-inversistic expert systems Chapter 30 Transformation of second-level inference rule systems into second-level automated decomposition systems Chapter 31 Applications of First-Level Hypothetical Inference Chapter 32 Axiomatic systems brought into mutually-inversistic automated decomposition systems Part 12 Applications of implicit inductive compositions Chapter 33 Applications of implicit inductive compositions Part 13 Applications of explicit inductive composition Chapter 34 Mutually-inversistic machine learning Chapter 35 Multiple connection operators association rule mining Chapter 36 Mutually-inversistic program refinement Part 14 Applications ofmutually-inversistic mathematics Chapter 37 Applications of universal matrix Chapter 38 Mutually-inversistic many-valued computer Chapter 39 Applications of mutually-inversistic mathematical analysis References

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