Advances in DFS Theory
نویسندگان
چکیده
1 1 DFS Theory: A Review of Concepts 3 2 Some properties of DFSes 13 2.1 Correct generalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Properties of the induced truth functions . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Preservation of argument structure . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Monotonicity properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.5 Miscellaneous Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.6 Properties of the induced extension principle . . . . . . . . . . . . . . . . . . . . . 19 2.7 Properties with respect to the standard quantifiers . . . . . . . . . . . . . . . . . . 21 2.8 Special subclasses of DFSes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3 An Alternative Characterisation of DFSes 31 3.1 An Alternative Construction of Induced Connectives . . . . . . . . . . . . . . . . 31 3.2 Equivalence of both Constructions with respect to DFSes . . . . . . . . . . . . . . 33 3.3 The Revised Set of DFS Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4 Equivalence of Old and New Characterisation of DFSes . . . . . . . . . . . . . . . 38 4 Characterisation of the class ofMB-DFSes 39 5 Independence Proof for the Revised Axiom Set 51 6 Further Properties of DFSes and Principled Adequacy Bounds 53 6.1 Existence of Upper Specificity Bounds . . . . . . . . . . . . . . . . . . . . . . . . 53 6.2 Continuity Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.3 Propagation of Fuzziness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.4 Contextuality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.5 Convexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6.6 Fuzzy Argument Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 7 Properties ofMB-DFSes 61 8 Upper and Lower Bounds on Quantification Results 69
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