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1 | (18) |
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1.1 Three Levels Inherent in a Logic Discourse |
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1 | (4) |
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1.2 From Many-Valued Logics, Fuzzy Logics to Graded Consequence: A Brief Overview |
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5 | (2) |
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1.3 Different Shades of Imprecision |
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7 | (4) |
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1.4 Classical Consequence and Motivations for Lifting it to Many-Valuedness |
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11 | (4) |
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15 | (4) |
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2 Basics Of The Theory Of Graded Consequence |
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19 | (26) |
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2.1 Characterization of Graded Consequence Relation |
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19 | (3) |
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2.2 Semantic Consequence Relation Generalized |
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22 | (5) |
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2.3 A Generalization of Hilbert-Type Axiom System |
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27 | (9) |
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2.3.1 Graded Consequence by Fuzzy Axioms and Fuzzy Rules |
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28 | (3) |
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2.3.2 Soundness and Examples of Hilbert-Type Axiomatic Consequence in GCT |
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31 | (5) |
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2.4 Consistency, Inconsistency and Equivalence |
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36 | (2) |
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2.4.1 Consistency and Inconsistency |
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36 | (1) |
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37 | (1) |
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2.5 Level Cuts of a Graded Consequence Relation |
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38 | (3) |
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41 | (2) |
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43 | (2) |
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3 Introducing Negation In The Object Language Of The Theory Of Graded Consequence |
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45 | (38) |
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3.1 Extending the Notion Graded Consequence Relation in the Presence of Negation |
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45 | (10) |
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3.2 Semantic Import of (GC4) and (GC5) on the Meta-structure |
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55 | (12) |
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3.3 GC Algebra and its Properties |
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67 | (10) |
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3.4 Possible Three-Valued and Four-Valued GC-Algebras |
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77 | (4) |
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81 | (2) |
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4 Proof Theoretic Rules In Graded Consequence: From Semantic Perspective |
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83 | (42) |
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4.1 General Scheme for Proof Theory in GCT |
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83 | (12) |
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4.2 Proof Theory of GCT: Links Between Object and Meta-level Algebras |
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95 | (17) |
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4.2.1 Implication in the Object Language |
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98 | (3) |
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4.2.2 Conjunction in the Object Language |
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101 | (2) |
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4.2.3 Disjunction in the Object Language |
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103 | (4) |
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4.2.4 Negation in the Object Language |
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107 | (5) |
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4.3 Examples of Logics with Graded Notion of Consequence |
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112 | (7) |
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4.3.1 Many-Valued Logics as a Special Case of GCT |
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114 | (5) |
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4.4 A Comparative Analysis |
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119 | (4) |
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123 | (2) |
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5 Meta-Logical Notions Generalized: Graded Consequence With Fuzzy Set Of Premises |
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125 | (28) |
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5.1 Consequence Operator and Consequence Relation in the Context of Fuzzy Logics |
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125 | (3) |
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5.1.1 Pavelka's Fuzzy Consequence Operator and Chakraborty's Graded Consequence Relation |
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126 | (2) |
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5.1.2 Fuzzy Consequence Relation: Castro et al. |
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128 | (1) |
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5.2 Meta-Logic of Graded Consequence with Fuzzy Premises |
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128 | (14) |
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5.2.1 Graded Inconsistency and Graded Consequence |
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133 | (4) |
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137 | (3) |
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140 | (2) |
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5.3 Implicative Consequence Operator and Consequence Relation |
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142 | (2) |
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5.4 Implicative Consequence Relation in the Light of Consistency-Generating Relation |
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144 | (6) |
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5.4.1 From the Notion of Consistency-Generating Relation to the Notion of Consistency |
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148 | (2) |
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150 | (3) |
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6 Graded Consequence And Consequence In Different Approaches To Fuzzy Logics |
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153 | (22) |
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6.1 Fuzzy Logic vis-a-vis Graded Consequence |
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153 | (10) |
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6.1.1 Notion of Proof in Pavelka's Fuzzy Logic |
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155 | (2) |
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6.1.2 The Expressed Meaning for Consequence: Goguen to Hajek |
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157 | (1) |
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6.1.3 Pavelka's Notion of Proof Refrained Maintaining Distinction of Levels of Logic |
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158 | (5) |
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6.2 Rewriting the Theory of Graded Consequence Maintaining Level Distinction |
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163 | (6) |
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6.3 A Brief Revisit to Hajek's Logic RPL From the Perspective of Distinction of Levels |
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169 | (3) |
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6.4 Lukasiewicz Fuzzy Propositional Logic |
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172 | (1) |
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173 | (2) |
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7 Graded Consequence In Decision-Making: A Few Applications |
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175 | (44) |
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7.1 GCT with Interval Semantics: Different Approaches Towards Aggregating Information |
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175 | (13) |
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7.1.1 Interval Mathematics: Some Basic Notions |
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177 | (1) |
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7.1.2 Graded Consequence: Form (27) |
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178 | (2) |
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7.1.3 Extension of C as a Lattice Order Relation on Intervals |
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180 | (1) |
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7.1.4 Graded Consequence: Form (Σ') |
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181 | (3) |
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7.1.5 Graded Consequence: Form (Σ") |
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184 | (4) |
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7.2 GCT in the Context of Logic Infomorphism: A Case for Decision-Making in a Distributed Network |
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188 | (23) |
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7.2.1 Barwise and Seligman's Logic for Distributed System |
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190 | (5) |
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195 | (1) |
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7.2.3 Graded Consequence: Logic for Distributed System |
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196 | (15) |
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7.3 Sorites Paradox in the Light of GCT |
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211 | (5) |
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7.3.1 Different Approaches Towards Sorites Paradox |
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212 | (2) |
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7.3.2 Approach to Sorites Paradox in the Context of GCT |
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214 | (2) |
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216 | (3) |
| Index |
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219 | |
