User Tools

Site Tools


public:t-713-mers:mers-25:reasoning-intro

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision
Previous revision
public:t-713-mers:mers-25:reasoning-intro [2025/09/23 09:26] leonardpublic:t-713-mers:mers-25:reasoning-intro [2025/09/25 11:06] (current) – [Non-Axiomatic Reasoning] leonard
Line 63: Line 63:
 \\ \\
  
-=====Fuzzy Logic=====+=====Fuzzy Reasoning=====
 |  Fuzzy Logic (FL)  | Extends classical logic by allowing truth values between 0 and 1 instead of just {T, F}. Designed for handling vagueness and graded membership in categories (e.g., “tall,” “warm,” “near”). | |  Fuzzy Logic (FL)  | Extends classical logic by allowing truth values between 0 and 1 instead of just {T, F}. Designed for handling vagueness and graded membership in categories (e.g., “tall,” “warm,” “near”). |
 |  FL Features  | Statements are not just true or false but can have a degree of truth (μ ∈ [0,1]). Uses membership functions and fuzzy sets. Combines with fuzzy operators (min, max, t-norms, etc.) for reasoning. | |  FL Features  | Statements are not just true or false but can have a degree of truth (μ ∈ [0,1]). Uses membership functions and fuzzy sets. Combines with fuzzy operators (min, max, t-norms, etc.) for reasoning. |
Line 80: Line 80:
 |  Evidence  | w<sup>+</sup> is positive evidence; w<sup>-</sup> is negative evidence.   |   |  Evidence  | w<sup>+</sup> is positive evidence; w<sup>-</sup> is negative evidence.   |  
 |  \\ Uncertainty  | Frequency: f = w<sup>+</sup> / w, where w = w<sup>+</sup> + w<sup>-</sup> (total evidence). \\ Confidence: c = w/(w + k), where k ≥ 1. \\ Ignorance: i = k/(w + k).  |  |  \\ Uncertainty  | Frequency: f = w<sup>+</sup> / w, where w = w<sup>+</sup> + w<sup>-</sup> (total evidence). \\ Confidence: c = w/(w + k), where k ≥ 1. \\ Ignorance: i = k/(w + k).  | 
-|  \\ Deduction  | The **premises** are given. \\ Figuring out the implication of facts (or predicting what may come). Producing implications from premises. \\  E.g. "The last domino will fall when all the other dominos between the first and the last have fallen"  +|  \\ Deduction  | The **premises** are given. \\ Figuring out the implication of facts (or predicting what may come). Producing implications from premises. \\  E.g."The last domino will fall when all the other dominos between the first and the last have fallen".\\ Represented as B → C < f1, c1 >, A → B < f2, c2 > ⊢ A → C < f3, c3 > 
-|  \\ Abduction  | A particular **outcome X** is given.  \\ Figuring out how things came to be the way they are (or how particular outcomes could be made to come about, or how particular outcomes could be prevented). \\  E.g. Sherlock Holmes, who is a genius abducer.   | +|  \\ Abduction  | A particular **outcome X** is given.  \\ Figuring out how things came to be the way they are (or how particular outcomes could be made to come about, or how particular outcomes could be prevented). \\  E.g. Sherlock Holmes, who is a genius abducer.\\ Represented as B → C < f1, c1 >, B → A < f2, c2 > ⊢ A → C < f3, c3 >   | 
-|  \\ Induction  | A **small set of examples** is given. \\ Figuring out the general case. Making general rules from a (small) set of examples. \\  E.g. "The sun has risen in the East every morning up until now, hence, the sun will also rise in the East tomorrow"  |+|  \\ Induction  | A **small set of examples** is given. \\ Figuring out the general case. Making general rules from a (small) set of examples. \\  E.g. "The sun has risen in the East every morning up until now, hence, the sun will also rise in the East tomorrow".\\ Represented as B → C < f1, c1 >, A → C < f2, c2 > ⊢ A → B < f3, c3 >   |
 |  \\ Analogy  | A set of **two (or more) things** is given. \\ Figuring out how things are similar or different. Making inferences about how something X may be (or is) through a comparison to something else Y, where X and Y share some observed properties. \\  E.g. "What does a pen have in common with an arrow?" "What is the difference between a rock and a ball?"  | |  \\ Analogy  | A set of **two (or more) things** is given. \\ Figuring out how things are similar or different. Making inferences about how something X may be (or is) through a comparison to something else Y, where X and Y share some observed properties. \\  E.g. "What does a pen have in common with an arrow?" "What is the difference between a rock and a ball?"  |
 |   | <sup>Author of the Non-Axiomatic Reasoning covered here: Pei Wang </sup>   | |   | <sup>Author of the Non-Axiomatic Reasoning covered here: Pei Wang </sup>   |
/var/www/cadia.ru.is/wiki/data/attic/public/t-713-mers/mers-25/reasoning-intro.1758619597.txt.gz · Last modified: 2025/09/23 09:26 by leonard

Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki