6 votes 6 votes In functional dependency Armstrong inference rules refers to Reflexive, Augmentation and Decomposition Transitive, Augmentation and Reflexive Augmentation, Transitive, Reflexive and Decomposition Reflexive, Transitive and Decomposition Databases isro2011 databases database-normalization + – Isha Gupta asked Jun 15, 2016 Isha Gupta 6.3k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 15 votes 15 votes Answer: Transitive, Augmentation and Reflexive Explanation: We can derive additional functional dependencies from the initial set using inference rules. Armstrongs's Axioms are most basic inference rules. These are 3 rules: Reflexivity: If Y is a subset of X, then X → Y Augmentation: If X → Y, then XZ → YZ Transitivity: If X → Y and Y → Z, then X → Z Additionally there are secondary rules derived from above 3 rules: Union: If X → Y and X → Z, then X → YZ Decomposition: If X → YZ, then X → Y and X → Z Pseudotransitivity: If X → Y and WY → Z, then WX → Z Composition: If X → Y and Z → W, then XZ → YW Reference: https://en.wikipedia.org/wiki/Functional_dependency Mangilal Saraswat answered Jun 16, 2016 selected Jun 23, 2016 by Arjun Mangilal Saraswat comment Share Follow See all 2 Comments See all 2 2 Comments reply thebiggercypher commented Sep 10, 2019 reply Follow Share If x -> z and y -> z can we write xy -> z ? 0 votes 0 votes `JEET commented Jan 7, 2020 reply Follow Share That's how a perfect answer should be written. 0 votes 0 votes Please log in or register to add a comment.
4 votes 4 votes Inference Rules An inference rule is an assertion that we can apply to a set of functional dependencies to derive other functional dependencies An initial set of functional dependencies is given (E.g., determined by some exploratory process) We can derive additional functional dependencies from the initial set using inference rules Armstrongs's Axioms: the most basic inference rules The Armstrong's axioms are the most basic inference rules Let X, Y and Z be three sets of attributes in the same relation R. The Armstrong's axioms are: Reflexivity rule: if Y ⊆ X then X → Y Augmentation rule: if X → Y then XZ → YZ Transitivity rule: if X → Y and Y → Z then X → Z Easier than it looks... The Armstrong's axioms are very intuitive I use a specific relation to illustrate them first (before proving their correctness) Consider the relation: Employee-Department SSN fname lname DNO DName +-------------+----------+----------+----------+----------+ | 111-11-1111 | John | Smith | 5 | Research | +-------------+----------+----------+----------+----------+ | 222-22-2222 | Jane | Doe | 4 | Payroll | +-------------+----------+----------+----------+----------+ | 333-33-3333 | Pete | Pan | 5 | Research | +-------------+----------+----------+----------+----------+ Examples of Armostrong axioms: Reflexivity rule: if Y ⊆ X then X → Y {fname, lname} → {fname} What it says is: if I see that same values for {fname, lname} I must also see that same value for {fname} - kinda obvious :-) Augmentation rule: if X → Y then XZ → YZ If {SSN} → {fname} then: {SSN, DName} → {fname, DName} Transitivity rule: if X → Y and Y → Z then X → Z If: {SSN} → {DNO} {DNO} → {DName} Then also: {SSN} → {DName} Visit this link below for more information on the same. :) http://www.mathcs.emory.edu/~cheung/Courses/377/Syllabus/9-NormalForms/InferenceRules.htm Devshree Dubey answered Jun 16, 2016 Devshree Dubey comment Share Follow See all 0 reply Please log in or register to add a comment.