diff --git a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json index 6337950..d54b9e6 100644 --- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json +++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json @@ -692,7 +692,7 @@ "_journal/2024-07/2024-07-12.md": "8073584fae2fe7bffcd4b69a7cd29058", "hashing/static.md": "3ec6eaee73fb9b599700f5a56b300b83", "hashing/addressing.md": "3c8151d2c98d1163641fd16efe1c2b64", - "ontology/index.md": "7e28be73b551865a71c171327702cbd8", + "ontology/index.md": "0994403dcd84415f1459752129b55f65", "ontology/permissivism.md": "07ef1e14269646957cfb9cb0a833968d", "ontology/properties.md": "52b2a8d1f0ac90aa771f7f154e1094a4", "_journal/2024-07-14.md": "9a74d2dd0f44db58e14f57c8908c3342", @@ -746,7 +746,7 @@ "ontology/rdf/index.md": "328f7b84d4893c45eef4f0d6e921ba69", "ontology/philosophy/permissivism.md": "07ef1e14269646957cfb9cb0a833968d", "ontology/philosophy/nominalism.md": "46245c644238157e15c7cb6def27d90a", - "ontology/philosophy/index.md": "d132b8f4a69bdb664c822366fb27fa64", + "ontology/philosophy/index.md": "4528422f2675bf6c4c8981f31e4e9583", "ontology/philosophy/dialetheism.md": "56dd05b38519f90c5cab93637978b3b3", "_journal/2024-07-29.md": "a480e577b06a94755b6ebf4ac9ee5732", "_journal/2024-07/2024-07-28.md": "b077c0bef8739930bc777d6fab485acd", @@ -791,7 +791,7 @@ "_journal/2024-08/2024-08-16.md": "da1127a1985074a3930b4c3512344025", "set/order.md": "0bfff1dbd51bc49a9c1df5766ff01044", "_journal/2024-08-18.md": "6f8aec69e00401b611db2a377a3aace5", - "ontology/philosophy/properties.md": "41b32249d3e4c23d73ddb3a417d65a4c", + "ontology/philosophy/properties.md": "52b2a8d1f0ac90aa771f7f154e1094a4", "_journal/2024-08-19.md": "94836e52ec04a72d3e1dbf3854208f65", "_journal/2024-08/2024-08-18.md": "6f8aec69e00401b611db2a377a3aace5", "_journal/2024-08/2024-08-17.md": "b06a551560c377f61a1b39286cd43cee", @@ -966,7 +966,7 @@ "_journal/2024-11/2024-11-21.md": "951b6034d60a40dbd8201c50abf0dbb9", "_journal/2024-11/2024-11-20.md": "951b6034d60a40dbd8201c50abf0dbb9", "_journal/2024-11/2024-11-19.md": "d879f57154cb27cb168eb1f1f430e312", - "set/cardinality.md": "b396048272652dcf49c875e723377ff4", + "set/cardinality.md": "29566dcf1454b9eed649b7d8c4d2335b", "geometry/area.md": "7f947bb5ac782495a1fb4a63bb2463e7", "_journal/2024-11-23.md": "911f82ab8aede5ecdb96493aef64b0b9", "_journal/2024-11/2024-11-22.md": "51117030e2364dbce3a8d507dead86ae", @@ -1017,7 +1017,7 @@ "_journal/2024-12/2024-12-11.md": "e7393c01b44c5b804f86f45b8b899b59", "encoding/uri.md": "394abe477b882e1414dd2fb151fea823", "encoding/xml.md": "01a66b1a102cccc682f8f1cab0f50bc6", - "encoding/rdf.md": "f5c2c0156046a9474bae3577e739c5ce", + "encoding/rdf.md": "87a47be25bc5754a11166a4b7663cada", "_journal/2024-12-15.md": "be66c8808d8bb66d4e7b91db7c93c94a", "_journal/2024-12/2024-12-14.md": "d2223f90fd1ce3d82a4fbb6828a1ec56", "_journal/2024-12/2024-12-13.md": "d2223f90fd1ce3d82a4fbb6828a1ec56", @@ -1037,8 +1037,12 @@ "threads/index.md": "28783464146ed09603b477bad4b761bc", "_journal/2024-12-20.md": "2e6b1826035eaa60aeb328f61d9bc976", "_journal/2024-12/2024-12-19.md": "cd09c9e522a3b206b8a3524d615fadd5", - "_journal/2024-12-21.md": "51bc26a6ec147bd57e0efffd75c266c6", - "_journal/2024-12/2024-12-20.md": "3c896dac68ce1bfb1f28cb7da4325c6c" + "_journal/2024-12-21.md": "b98f043f0f36684eb01e7b7588e30baf", + "_journal/2024-12/2024-12-20.md": "3c896dac68ce1bfb1f28cb7da4325c6c", + "encoding/xml/rdf.md": "f4491dd28b937da3182d701a863e40fe", + "encoding/xml/index.md": "01a66b1a102cccc682f8f1cab0f50bc6", + "ontology/reification.md": "ef8275957dcc1a7e5501722d4652e41c", + "ontology/rdf.md": "fd273c30bec6f46b68547f0d392620b1" }, "fields_dict": { "Basic": [ diff --git a/notes/ontology/index.md b/notes/ontology/index.md index 381d2bb..2d13cf3 100644 --- a/notes/ontology/index.md +++ b/notes/ontology/index.md @@ -1,124 +1,3 @@ --- title: Ontology -TARGET DECK: Obsidian::H&SS -FILE TAGS: ontology -tags: - - ontology --- - -## Overview - -Ontology is the philosophical study of being. Generally *things* are split into two broad categories: **abstract** and **concrete** things. These words are "terms of art" and their definition is not standardized in any way. - -%%ANKI -Basic -What did Quine declare as *the* ontological question? -Back: "What is there?" -Reference: Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009). - -END%% - -%%ANKI -Basic -Who is attributed *the* ontological question? -Back: Willard Van Orman Quine. -Reference: Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009). - -END%% - -%%ANKI -Cloze -{Ontology} is the {philosophical study of being}. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Cloze -{Epistemology} is the {philosophical study of knowledge}. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Cloze -{Taxonomy} is the {branch of science concerned with categorization}. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Cloze -{Mereology} is the {philosophical study of part-whole relationships}. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -What does Effingham mean when saying "concreta" and "abstracta" are terms of art? -Back: They are terms defined freely by a person to mean whatever one wants. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Cloze -In general, ontologists often categorize things as either {concreta} or {abstracta}. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Generally speaking, what does someone *probably* mean by "concrete" things? -Back: Things that exists in space and/or time. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Generally speaking, what does someone *probably* mean by "abstract" things? -Back: Things that exist in neither space nor time. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Is a material object considered concreta? -Back: Usually. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Is an immaterial object considered concreta? -Back: Possibly. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Is a material object considered abstracta? -Back: Not usually. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -%%ANKI -Basic -Is an immaterial object considered abstracta? -Back: Possibly. -Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). - -END%% - -## Bibliography - -* Francesco Orilia and Michele Paolini Paoletti, “Properties,” in _The Stanford Encyclopedia of Philosophy_, ed. Edward N. Zalta, Spring 2022 (Metaphysics Research Lab, Stanford University, 2022), [https://plato.stanford.edu/archives/spr2022/entries/properties/](https://plato.stanford.edu/archives/spr2022/entries/properties/). -* Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). -* Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009). \ No newline at end of file diff --git a/notes/ontology/dialetheism.md b/notes/ontology/philosophy/dialetheism.md similarity index 100% rename from notes/ontology/dialetheism.md rename to notes/ontology/philosophy/dialetheism.md diff --git a/notes/ontology/philosophy/index.md b/notes/ontology/philosophy/index.md new file mode 100644 index 0000000..535768d --- /dev/null +++ b/notes/ontology/philosophy/index.md @@ -0,0 +1,124 @@ +--- +title: Ontology (Philosophy) +TARGET DECK: Obsidian::H&SS +FILE TAGS: ontology +tags: + - ontology +--- + +## Overview + +Ontology is the philosophical study of being. Generally *things* are split into two broad categories: **abstract** and **concrete** things. These words are "terms of art" and their definition is not standardized in any way. + +%%ANKI +Basic +What did Quine declare as *the* ontological question? +Back: "What is there?" +Reference: Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009). + +END%% + +%%ANKI +Basic +Who is attributed *the* ontological question? +Back: Willard Van Orman Quine. +Reference: Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009). + +END%% + +%%ANKI +Cloze +{Ontology} is the {philosophical study of being}. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Cloze +{Epistemology} is the {philosophical study of knowledge}. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Cloze +{Taxonomy} is the {branch of science concerned with categorization}. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Cloze +{Mereology} is the {philosophical study of part-whole relationships}. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +What does Effingham mean when saying "concreta" and "abstracta" are terms of art? +Back: They are terms defined freely by a person to mean whatever one wants. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Cloze +In general, ontologists often categorize things as either {concreta} or {abstracta}. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Generally speaking, what does someone *probably* mean by "concrete" things? +Back: Things that exists in space and/or time. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Generally speaking, what does someone *probably* mean by "abstract" things? +Back: Things that exist in neither space nor time. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Is a material object considered concreta? +Back: Usually. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Is an immaterial object considered concreta? +Back: Possibly. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Is a material object considered abstracta? +Back: Not usually. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +%%ANKI +Basic +Is an immaterial object considered abstracta? +Back: Possibly. +Reference: Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). + +END%% + +## Bibliography + +* Francesco Orilia and Michele Paolini Paoletti, “Properties,” in _The Stanford Encyclopedia of Philosophy_, ed. Edward N. Zalta, Spring 2022 (Metaphysics Research Lab, Stanford University, 2022), [https://plato.stanford.edu/archives/spr2022/entries/properties/](https://plato.stanford.edu/archives/spr2022/entries/properties/). +* Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013). +* Simon Hewitt, “A Cardinal Worry for Permissive Metaontology,” _Metaphysica_ 16, no. 2 (September 18, 2015): 159–65, [https://doi.org/10.1515/mp-2015-0009](https://doi.org/10.1515/mp-2015-0009). \ No newline at end of file diff --git a/notes/ontology/nominalism.md b/notes/ontology/philosophy/nominalism.md similarity index 100% rename from notes/ontology/nominalism.md rename to notes/ontology/philosophy/nominalism.md diff --git a/notes/ontology/permissivism.md b/notes/ontology/philosophy/permissivism.md similarity index 100% rename from notes/ontology/permissivism.md rename to notes/ontology/philosophy/permissivism.md diff --git a/notes/ontology/properties.md b/notes/ontology/philosophy/properties.md similarity index 100% rename from notes/ontology/properties.md rename to notes/ontology/philosophy/properties.md diff --git a/notes/encoding/rdf.md b/notes/ontology/rdf.md similarity index 63% rename from notes/encoding/rdf.md rename to notes/ontology/rdf.md index db528b3..368bacc 100644 --- a/notes/encoding/rdf.md +++ b/notes/ontology/rdf.md @@ -1,7 +1,7 @@ --- title: RDF TARGET DECK: Obsidian::STEM -FILE TAGS: rdf +FILE TAGS: ontology::rdf tags: - rdf --- @@ -10,6 +10,8 @@ tags: The **Resource Description Framework** (RDF) is the foundational representation language of the Semantic Web. The basic building block of RDF is the **triple** containing a **subject**, **predicate**, and **object**. Global identifiers of resources are represented as [[uri|URIs]] (or, more generally, IRIs). These URIs can be expressed more compactly as [[uri#CURIEs|CURIEs]]. +A **graph** is a set of triples. A **named graph** is a particular set of triples with an associated name. When using named graphs, the term **quads** is often used in favor of triples. This refers to the original triple along with the name of the graph the triple is associated with. + %%ANKI Basic Which organization standardized RDF? @@ -128,114 +130,62 @@ Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web END%% -## Reification - -**Reification** refers to the process by which an abstract idea is made concrete. In the context of RDF, it refers to writing RDF statements about RDF statements. - %%ANKI Basic -What is reification? -Back: The process by which an abstract idea is made concrete. -Reference: “Reification (Knowledge Representation),” in _Wikipedia_, October 3, 2023, [https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)](https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)&oldid=1178437461). - -END%% - -%%ANKI -Basic -In the context of RDF, what does reification typically refer to? -Back: Creating RDF statements about RDF statements. -Reference: “Reification (Knowledge Representation),” in _Wikipedia_, October 3, 2023, [https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)](https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)&oldid=1178437461). - -END%% - -%%ANKI -Basic -In the context of RDF, what abstract notion is typically reified? -Back: RDF statements. +How does RDF define a graph? +Back: As a set of triples. Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. - + END%% %%ANKI Basic -What term describes making an abstract concept concrete? -Back: Reification. +How does RDF define a named graph? +Back: A graph with a name. Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. - + END%% -This kind of metadata about statements often take the forms of: - -* **Provenance**. Information about the source of a statement. -* **Likelihood**. Information quantifying some probability regarding the statement. -* **Context**. Information about a setting in which a statement holds. -* **Time frame**. Information that holds within a particular period of time. - %%ANKI -Basic -What might reifying a statement with respect to its provenance refer to? -Back: Information about the source of the statement. +Cloze +{1:Triples} are to {2:graphs} whereas {2:quads} are to {1:named graphs}. Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. - + END%% %%ANKI Basic -What "form" of reification does the following sentence take on? $$\text{Wikipedia says Shakespeare wrote Hamlet.}$$ -Back: Provenance. +What name is given to the members of a triple? +Back: "Subject", "predicate", and "object". Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. - + END%% %%ANKI Basic -What might reifying a statement with respect to its likelihood refer to? -Back: Information quantifying some probability of the statement holding. +What name is given to the members of a quad? +Back: "Subject", "predicate", "object", and "graph". Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. - + +END%% + +%%ANKI +Cloze +RDF is a {data model} whereas XML is a {serialization}. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. +Tags: xml + END%% %%ANKI Basic -What "form" of reification does the following sentence take on? $$\text{It is 90\% probable that Shakespeare wrote Hamlet.}$$ -Back: Likelihood. +How might RDF and XML relate to one another? +Back: XML can be used to serialize RDF. Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. - -END%% - -%%ANKI -Basic -What might reifying a statement with respect to its context refer to? -Back: Information about a setting in which the statement holds. -Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. - -END%% - -%%ANKI -Basic -What "form" of reification does the following sentence take on? $$\text{Kenneth Branagh played Hamlet in the movie.}$$ -Back: Context. -Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. - -END%% - -%%ANKI -Basic -What might reifying a statement with respect to its time frame refer to? -Back: Information about a period of time in which the statement holds. -Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. - -END%% - -%%ANKI -Basic -What "form" of reification does the following sentence take on? $$\text{Hamlet plays on Broadway Jan. 11th through Mar. 12th.}$$ -Back: Time frame. -Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. - +Tags: xml + END%% ## Bibliography -* Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. -* “Reification (Knowledge Representation),” in _Wikipedia_, October 3, 2023, [https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)](https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)&oldid=1178437461). \ No newline at end of file +* Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. \ No newline at end of file diff --git a/notes/ontology/reification.md b/notes/ontology/reification.md new file mode 100644 index 0000000..312b174 --- /dev/null +++ b/notes/ontology/reification.md @@ -0,0 +1,119 @@ +--- +title: Reification +TARGET DECK: Obsidian::H&SS +FILE TAGS: ontology +tags: + - ontology +--- + +## Overview + +**Reification** refers to the process by which an abstract idea is made concrete. For example, in the context of [[rdf|RDF]], it refers to writing RDF statements about RDF statements. + +%%ANKI +Basic +What is reification? +Back: The process by which an abstract idea is made concrete. +Reference: “Reification (Knowledge Representation),” in _Wikipedia_, October 3, 2023, [https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)](https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)&oldid=1178437461). + +END%% + +%%ANKI +Basic +In the context of RDF, what does reification typically refer to? +Back: Creating RDF statements about RDF statements. +Reference: “Reification (Knowledge Representation),” in _Wikipedia_, October 3, 2023, [https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)](https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)&oldid=1178437461). + +END%% + +%%ANKI +Basic +In the context of RDF, what abstract notion is typically reified? +Back: RDF statements. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. + +END%% + +%%ANKI +Basic +What term describes making an abstract concept concrete? +Back: Reification. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. + +END%% + +This kind of metadata about statements often take the forms of: + +* **Provenance**. Information about the source of a statement. +* **Likelihood**. Information quantifying some probability regarding the statement. +* **Context**. Information about a setting in which a statement holds. +* **Time frame**. Information that holds within a particular period of time. + +%%ANKI +Basic +What might reifying a statement with respect to its provenance refer to? +Back: Information about the source of the statement. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. + +END%% + +%%ANKI +Basic +What "form" of reification does the following sentence take on? $$\text{Wikipedia says Shakespeare wrote Hamlet.}$$ +Back: Provenance. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. + +END%% + +%%ANKI +Basic +What might reifying a statement with respect to its likelihood refer to? +Back: Information quantifying some probability of the statement holding. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. + +END%% + +%%ANKI +Basic +What "form" of reification does the following sentence take on? $$\text{It is 90\% probable that Shakespeare wrote Hamlet.}$$ +Back: Likelihood. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. + +END%% + +%%ANKI +Basic +What might reifying a statement with respect to its context refer to? +Back: Information about a setting in which the statement holds. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. + +END%% + +%%ANKI +Basic +What "form" of reification does the following sentence take on? $$\text{Kenneth Branagh played Hamlet in the movie.}$$ +Back: Context. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. + +END%% + +%%ANKI +Basic +What might reifying a statement with respect to its time frame refer to? +Back: Information about a period of time in which the statement holds. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. + +END%% + +%%ANKI +Basic +What "form" of reification does the following sentence take on? $$\text{Hamlet plays on Broadway Jan. 11th through Mar. 12th.}$$ +Back: Time frame. +Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. + +END%% + +## Bibliography + +* Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020. +* “Reification (Knowledge Representation),” in _Wikipedia_, October 3, 2023, [https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)](https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)&oldid=1178437461). \ No newline at end of file diff --git a/notes/set/cardinality.md b/notes/set/cardinality.md index 58526f2..73c9557 100644 --- a/notes/set/cardinality.md +++ b/notes/set/cardinality.md @@ -62,17 +62,11 @@ END%% No set is equinumerous to its [[set/index#Power Set Axiom|power set]]. This is typically shown using a diagonalization argument. -%%ANKI -Basic -What basic set operation produces a new set the original isn't equinumerous to? -Back: The power set operation. -Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). - -END%% +For any set $A$, $^A2 \approx \mathscr{P}(A)$. %%ANKI Basic -What kind of argument is typically made to prove no set is equinumerous to its power set? +What kind of argument is typically used to show $A \not\approx {\mathscr{P}(A)}$? Back: A diagonalization argument. Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). @@ -102,6 +96,94 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre END%% +%%ANKI +Basic +For any set $A$, $\mathscr{P}(A)$ is equinumerous to what set of functions? +Back: $^A2$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +Let $A$ be any set. How is bijection $H \colon \,^A2 \rightarrow \mathscr{P}(A)$ typically defined? +Back: $H(f) = \{a \in A \mid f(a) = 1\}$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +For any set $A$, $^A2$ is equinumerous to what of $A$? +Back: Its powerset. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +What kind of argument is typically used to show $A \not\approx {^A2}$? +Back: A diagonalization argument. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +For any set $A$, what is the cardinality of its powerset? +Back: $2^{\mathop{\text{card}}A}$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +What does $\mathop{\text{card}} \mathscr{P}(A)$ evaluate to? +Back: $2^{\mathop{\text{card}}A}$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +The cardinality of what set equals $2^{\mathop{\text{card}}A}$? +Back: $\mathscr{P}(A)$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +What does $\mathop{\text{card}} \mathscr{P}(\omega)$ evaluate to? +Back: $2^{\aleph_0}$ +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +Why is the "power set" named the way it is? +Back: Because $\mathop{\text{card}} \mathscr{P}(A)$ equals $2$ to the power of $\mathop{\text{card}} A$. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +*How* do we know $\aleph_0 \not\approx 2^{\aleph_0}$ holds? +Back: No set is equinumerous to its power set. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + +%%ANKI +Basic +For any cardinal number $\kappa$, *how* do we know $\kappa \not\approx 2^\kappa$? +Back: No set is equinumerous to its power set. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + ### Equivalence Concept For any sets $A$, $B$, and $C$: @@ -867,6 +949,13 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre END%% +%%ANKI +Cloze +For any cardinal number $\kappa$, addition's {$\kappa + \kappa$} equals multiplication's {$2 \cdot \kappa$}. +Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). + +END%% + ### Exponentiation Let $\kappa$ and $\lambda$ be any cardinal numbers. Then $\kappa^\lambda = \mathop{\text{card}}(^LK)$, where $K$ and $L$ are any sets of cardinality $\kappa$ and $\lambda$, respectively.