edits for prior to collaboration #6
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| ### Explanations | ||
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| _EXAMPLE GIVEN: To explain why `R` cannot be both asymmetric and symmetric, your explanation may take the form: Suppose `R` is both symmetric and asymmetric. Then by symmetry for any x and y, if x`R`y it follows that y`R`x. However, by asymmetry it also follows that it is not the case that y`R`x. Hence, `R` cannot be both symmetric and asymmetric. Similarly, to explain why `R` cannot be both transitive and inverse functional._ | ||
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If I understand correctly, for any functional property there can only be one bearer in relation to an instance. If xRy, then zRy is invalid because only (x) can bear this relation with (y). However, xRz is valid because an instance can be the bearer of a a functional property for multiple other instances. So, when you say that by functionality if "xRy and xRz then y = z" I am not sure if that is necessarily true. I do understand the line of think about cardinality for functional object properties which implies that y must equal z (perhaps I am misinterpreting-- I could also be totally wrong!) I'm happy to expand more on this with concrete examples.
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Did some further research. I may be conflating functional with inverse functional.
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Incomplete |
| #### (A) Transitive + Irreflexive (NS) | ||
| - Suppose `R` is both irreflexive and transitive. By irreflexivity, it is not the case that xRx. By transitivity, for any x and y, if x`R`y and y`R`z, it follows that x`R`z. | ||
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| When `R` is irreflexive it can never relate back to itself but when `R` is transitive, it can relate to multiple variables via the same relationship including but not necessarily limited to itself. |
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The combination is non-simple, which leads to greater computational complexity, and so is forbidden in OWL 2. In this context, a ‘simple’ object property is one that has no direct or indirect sub-properties that are either transitive or defined using a chain of distinct object properties.
| #### (B) Transitive + Functional (NS) | ||
| - Suppose `R` is both transitive and functional. By transitivity for any x and y, if x`R`y and y`R`z, it follows that x`R`z. By functionality, if x`R`y and x`R`z, then it follows that y=z. | ||
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| When `R` is functional, it relates to single variable where as when it is transitive it communicates a single type of relationship that can apply to multiple variables. These are in conflict. |
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Not really following the reasoning here. What exactly is the conflict?
| #### (C) Transitive + Inverse Functional (NS) | ||
| - Suppose `R` is both transitive and inverse functional. By transitivity for any x and y, if x`R`y and y`R`z, it follows that x`R`z. By inverse functional, if xRy and zRy, it follows that x=z. | ||
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| The argumentative limitations for the transitive and functional combination of properties applies here aswell. |
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Not quite, since inverse functional is not the same as functional. We need to be precise :)
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| The `R` relationship cannot be defined such that it relates something to itself and also cannot relate something to itself. | ||
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| ## Assignment Part 2 **PLEASE NOTE THIS IS INCOMPLETE |
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Where can I find the reviews of this work by your peers?
…l. Translated information into list & diagram form in order to pick and choose which ones to develop sparql queries for.
Minor formatting change made in order to test the difference between leaving comments on the commit via GitHub Desktop vs VSCode vs Web based GitHub.
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Created a file containing notes for tackling the assignment for project 2. |
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| ### NOTES FOR ASSIGNMENT | |||
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You've mixed in project 2 with this pull request; please disentangle (when you can, obviously no rush)
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