Logical foundation of symmetric implicational methods for fuzzy reasoning

We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of “magic rules” for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state of the art with numerous generalizations and applications. The survey itself is complemented by a fairly complete bibliography (over 500 references) which we expect to update regularly.

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Morphology granule segmentation algorithm based on fuzzy reasoning of image features

Journal of Computer Applications ◽

10.3724/sp.j.1087.2010.03278 ◽

2011 ◽

Vol 30 (12) ◽

pp. 3278-3280

Author(s):

Ming HAN ◽

Lei-min LI ◽

Yu-qing HUANG

Keyword(s):

Fuzzy Reasoning ◽

Image Features ◽

Segmentation Algorithm

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Emotion-enhanced classification based on fuzzy reasoning

International Journal of Machine Learning and Cybernetics ◽

10.1007/s13042-021-01356-y ◽

2021 ◽

Author(s):

Ruiteng Yan ◽

Yan Yu ◽

Dong Qiu

Keyword(s):

Fuzzy Reasoning

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Petrophysical Facies Classification Based on Fuzzy Inference Networks

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.634-638.4017 ◽

2013 ◽

Vol 634-638 ◽

pp. 4017-4021

Author(s):

Jun Hui Pan ◽

Hui Wang ◽

Xiao Gang Yang

Keyword(s):

Fuzzy Inference ◽

Fuzzy Reasoning ◽

Real Data ◽

Analysis Data ◽

Classification Model ◽

Core Analysis ◽

Development Zone ◽

The Real ◽

Facies Classification ◽

Quantitative Indicators

Aiming at the petrophysical facies recognition, a novel identification method based on the weighted fuzzy reasoning networks is proposed in the paper. First, the types and indicators are obtained from core analysis data and the results given by experts, and then the standard patterning database of reservoir petrophysical facies is established. Secondly, by integrating expert experiences and quantitative indicators to reflect the change of petrophysical facies, the classification model of petrophysical facies based on the weighted fuzzy reasoning networks is designed. The preferable application results are presented by processing the real data from the Sabei development zone of Daqing oilfield.

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On Polymorphic Sessions and Functions

ACM Transactions on Programming Languages and Systems ◽

10.1145/3457884 ◽

2021 ◽

Vol 43 (2) ◽

pp. 1-55

Author(s):

Bernardo Toninho ◽

Nobuko Yoshida

Keyword(s):

Natural Deduction ◽

Sequent Calculus ◽

Linear Logic ◽

Linear Formulation ◽

Session Types ◽

Logical Foundation ◽

Π Calculus ◽

Soundness And Completeness ◽

System F ◽

Algebraic Representations

This work exploits the logical foundation of session types to determine what kind of type discipline for the Λ-calculus can exactly capture, and is captured by, Λ-calculus behaviours. Leveraging the proof theoretic content of the soundness and completeness of sequent calculus and natural deduction presentations of linear logic, we develop the first mutually inverse and fully abstract processes-as-functions and functions-as-processes encodings between a polymorphic session π-calculus and a linear formulation of System F. We are then able to derive results of the session calculus from the theory of the Λ-calculus: (1) we obtain a characterisation of inductive and coinductive session types via their algebraic representations in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation.

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