@base . @prefix : . @prefix owl: . @prefix rdf: . @prefix xml: . @prefix xsd: . @prefix rdfs: . @prefix skos: . @prefix dcterms: . # # # ################################################################# # # # # Annotation properties # # # ################################################################# # # # http://www.w3.org/2002/07/owl#qualifiedCardinality # # # # ################################################################# # # # # Object Properties # # # ################################################################# # # # https://w3id.org/emmo#EMMO_3446e167_c576_49d6_846c_215bb8878a55 # # # # ################################################################# # # # # Data properties # # # ################################################################# # # # https://w3id.org/emmo#EMMO_23b579e1_8088_45b5_9975_064014026c42 # # https://w3id.org/emmo#EMMO_faf79f53_749d_40b2_807c_d34244c192f4 # # # # ################################################################# # # # # Classes # # # ################################################################# # # # https://w3id.org/emmo#EMMO_048a14e3_65fb_457d_8695_948965c89492 # # https://w3id.org/emmo#EMMO_06658d8d_dcde_4fc9_aae1_17f71c0bcdec # # https://w3id.org/emmo#EMMO_0b6ebe5a_0026_4bef_a1c1_5be00df9f98e # # https://w3id.org/emmo#EMMO_18d180e4_5e3e_42f7_820c_e08951223486 # # https://w3id.org/emmo#EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a # # https://w3id.org/emmo#EMMO_1cba0b27_15d0_4326_933f_379d0b3565b6 # # https://w3id.org/emmo#EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895 # # https://w3id.org/emmo#EMMO_20ff3b34_c864_4936_8955_9345fc0a3b3c # # https://w3id.org/emmo#EMMO_21f56795_ee72_4858_b571_11cfaa59c1a8 # # https://w3id.org/emmo#EMMO_223d9523_4169_4ecd_b8af_acad1215e1ff # # https://w3id.org/emmo#EMMO_24b30ba4_90f4_423d_93d2_fd0fde349087 # # https://w3id.org/emmo#EMMO_28fbea28_2204_4613_87ff_6d877b855fcd # # https://w3id.org/emmo#EMMO_29afdf54_90ae_4c98_8845_fa9ea3f143a8 # # https://w3id.org/emmo#EMMO_2b1303e8_d4c3_453b_9918_76f1d009543f # # https://w3id.org/emmo#EMMO_2ff07b07_c447_490f_903a_f6a72a12d7bf # # https://w3id.org/emmo#EMMO_3c424d37_cf62_41b1_ac9d_a316f8d113d6 # # https://w3id.org/emmo#EMMO_46d5643b_9706_4b67_8bea_ed77d6026539 # # https://w3id.org/emmo#EMMO_4bc29b0f_8fcc_4026_a291_f9774a66d9b8 # # https://w3id.org/emmo#EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa # # https://w3id.org/emmo#EMMO_535d75a4_1972_40bc_88c6_ca566386934f # # https://w3id.org/emmo#EMMO_54dc83cb_06e1_4739_9e45_bc09cead7f48 # # https://w3id.org/emmo#EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 # # https://w3id.org/emmo#EMMO_5be83f9c_a4ba_4b9a_be1a_5bfc6e891231 # # https://w3id.org/emmo#EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3 # # https://w3id.org/emmo#EMMO_88470739_03d3_4c47_a03e_b30a1288d50c # # https://w3id.org/emmo#EMMO_89083bab_f69c_4d06_bf6d_62973b56cdc7 # # https://w3id.org/emmo#EMMO_89a0c87c_0804_4013_937a_6fe234d9499c # # https://w3id.org/emmo#EMMO_8c64fcfa_23aa_45f8_9e58_bdfd065fab8f # # https://w3id.org/emmo#EMMO_8de14a59_660b_454f_aff8_76a07ce185f4 # # https://w3id.org/emmo#EMMO_91447ec0_fb55_49f2_85a5_3172dff6482c # # https://w3id.org/emmo#EMMO_98d65021_4574_4890_b2fb_46430841077f # # https://w3id.org/emmo#EMMO_9e029526_79a2_47a8_a151_dd0545db471b # # https://w3id.org/emmo#EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527 # # https://w3id.org/emmo#EMMO_a365b3c1_7bde_41d7_a15b_2820762e85f4 # # https://w3id.org/emmo#EMMO_a6138ba7_e365_4f2d_b6b4_fe5a5918d403 # # https://w3id.org/emmo#EMMO_ae15fb4f_8e4d_41de_a0f9_3997f89ba6a2 # # https://w3id.org/emmo#EMMO_b5c58790_fb2d_42eb_b184_2a3f6ca60acb # # https://w3id.org/emmo#EMMO_d1d436e7_72fc_49cd_863b_7bfb4ba5276a # # https://w3id.org/emmo#EMMO_d8d2144e_5c8d_455d_a643_5caf4d8d9df8 # # https://w3id.org/emmo#EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6 # # https://w3id.org/emmo#EMMO_f6d0c26a_98b6_4cf8_8632_aa259131faaa # # https://w3id.org/emmo#EMMO_f8a2fe9f_458b_4771_9aba_a50e76afc52d # # https://w3id.org/emmo#EMMO_f8bd64d5_5d3e_4ad4_a46e_c30714fecb7f # # https://w3id.org/emmo#EMMO_f9bc8b52_85e9_4b53_b969_dd7724d5b8e4 # # https://w3id.org/emmo#EMMO_fe7e56ce_118b_4243_9aad_20eb9f4f31f6 # # https://w3id.org/emmo#EMMO_ffe760a2_9d1f_4aef_8bee_1f450f9cb00d # # Generated by the OWL API (version 4.5.25.2023-02-15T19:15:49Z) https://github.com/owlcs/owlapi a owl:Ontology; owl:versionIRI ; owl:imports , , ; dcterms:abstract "The math module defines the formal language of mathematics. Mathematical objects represents graphical objects based on graphical symbols arranged according the rules of math."@en; dcterms:contributor "Access, DE", "Fraunhofer IWM, DE", "Goldbeck Consulting Ltd (UK)", "SINTEF, NO", "University of Bologna, IT"; dcterms:creator "Adham Hashibon", "Emanuele Ghedini", "Georg Schmitz", "Gerhard Goldbeck", "Jesper Friis"; dcterms:license "https://creativecommons.org/licenses/by/4.0/legalcode"; dcterms:publisher "EMMC ASBL"; dcterms:title "Math"@en; rdfs:comment """Contacts: Gerhard Goldbeck Goldbeck Consulting Ltd (UK) email: gerhard@goldbeck-consulting.com Emanuele Ghedini University of Bologna (IT) email: emanuele.ghedini@unibo.it"""@en, "The EMMO requires HermiT reasoner plugin in order to visualize all inferences and class hierarchy (ctrl+R hotkey in Protege)."@en; owl:versionInfo "1.0.0-beta7" . owl:qualifiedCardinality a owl:AnnotationProperty . :EMMO_3446e167_c576_49d6_846c_215bb8878a55 a owl:ObjectProperty; rdfs:subPropertyOf :EMMO_eb3518bf_f799_4f9e_8c3e_ce59af11453b; rdfs:domain :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0; rdfs:range :EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895; skos:prefLabel "hasVariable"@en . :EMMO_23b579e1_8088_45b5_9975_064014026c42 a owl:DatatypeProperty . :EMMO_faf79f53_749d_40b2_807c_d34244c192f4 a owl:DatatypeProperty, owl:FunctionalProperty; rdfs:subPropertyOf :EMMO_b6292331_94af_4f00_976b_ea55960c2f1c; rdfs:domain :EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa; :EMMO_c7b62dd7_063a_4c2a_8504_42f7264ba83f "The owl:dataProperty that provides a serialisation of an EMMO numerical data entity."; skos:prefLabel "hasNumericalValue"@en . :EMMO_048a14e3_65fb_457d_8695_948965c89492 a owl:Class; rdfs:subClassOf :EMMO_f8a2fe9f_458b_4771_9aba_a50e76afc52d, _:genid1; skos:prefLabel "Laplacian"@en . _:genid1 a owl:Restriction; owl:hasValue "Δ"; owl:onProperty :EMMO_23b579e1_8088_45b5_9975_064014026c42 . :EMMO_06658d8d_dcde_4fc9_aae1_17f71c0bcdec a owl:Class; rdfs:subClassOf :EMMO_28fbea28_2204_4613_87ff_6d877b855fcd, _:genid2; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "1-dimensional array who's spatial direct parts are numbers."@en; skos:altLabel "1DArray"@en, "LinearArray"; skos:prefLabel "Vector"@en . _:genid2 a owl:Restriction; owl:someValuesFrom :EMMO_21f56795_ee72_4858_b571_11cfaa59c1a8; owl:onProperty :EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe . :EMMO_0b6ebe5a_0026_4bef_a1c1_5be00df9f98e a owl:Class; rdfs:subClassOf :EMMO_88470739_03d3_4c47_a03e_b30a1288d50c; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A relation which makes a non-equal comparison between two numbers or other mathematical expressions."@en; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "f(x) > 0"@en; skos:prefLabel "Inequality"@en . :EMMO_18d180e4_5e3e_42f7_820c_e08951223486 a owl:Class; owl:equivalentClass _:genid3; rdfs:subClassOf :EMMO_21f56795_ee72_4858_b571_11cfaa59c1a8, _:genid4, _:genid5; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A real number."@en; skos:prefLabel "Real"@en . _:genid3 a owl:Restriction; owl:someValuesFrom xsd:double; owl:onProperty :EMMO_faf79f53_749d_40b2_807c_d34244c192f4 . _:genid4 a owl:Restriction; owl:allValuesFrom xsd:double; owl:onProperty :EMMO_faf79f53_749d_40b2_807c_d34244c192f4 . _:genid5 a owl:Restriction; owl:onDataRange xsd:double; owl:qualifiedCardinality "1"^^xsd:nonNegativeInteger; owl:onProperty :EMMO_faf79f53_749d_40b2_807c_d34244c192f4 . :EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a a owl:Class; rdfs:subClassOf :EMMO_f9bc8b52_85e9_4b53_b969_dd7724d5b8e4; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "2x+3"@en; rdfs:comment "An expression that has parts only integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)"@en; skos:prefLabel "AlgebricExpression"@en . :EMMO_1cba0b27_15d0_4326_933f_379d0b3565b6 a owl:Class; rdfs:subClassOf :EMMO_28fbea28_2204_4613_87ff_6d877b855fcd, _:genid6; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "2-dimensional array who's spatial direct parts are vectors."@en; skos:altLabel "2DArray"@en; skos:prefLabel "Matrix"@en . _:genid6 a owl:Restriction; owl:someValuesFrom :EMMO_06658d8d_dcde_4fc9_aae1_17f71c0bcdec; owl:onProperty :EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe . :EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895 a owl:Class; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A variable is a symbolic object that stands for any other mathematical object, such as number, a vector, a matrix, a function, the argument of a function, a set, an element of a set."@en; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a """x k"""@en; skos:prefLabel "Variable"@en . _:genid7 a owl:Axiom; owl:annotatedSource :EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895; owl:annotatedProperty :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9; owl:annotatedTarget "A variable is a symbolic object that stands for any other mathematical object, such as number, a vector, a matrix, a function, the argument of a function, a set, an element of a set."@en; :EMMO_c84c6752_6d64_48cc_9500_e54a3c34898d "https://en.wikipedia.org/wiki/Variable_(mathematics)"^^xsd:anyURI . _:genid8 a owl:Axiom; owl:annotatedSource :EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895; owl:annotatedProperty skos:prefLabel; owl:annotatedTarget "Variable"@en; :EMMO_705f27ae_954c_4f13_98aa_18473fc52b25 "Fom Latin variabilis (\"changeable\")."@en . :EMMO_20ff3b34_c864_4936_8955_9345fc0a3b3c a owl:Class; rdfs:subClassOf :EMMO_28fbea28_2204_4613_87ff_6d877b855fcd, _:genid9; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "3-dimensional array who's spatial direct parts are matrices."@en; skos:altLabel "3DArray"@en; skos:prefLabel "Array3D"@en . _:genid9 a owl:Restriction; owl:someValuesFrom :EMMO_1cba0b27_15d0_4326_933f_379d0b3565b6; owl:onProperty :EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe . :EMMO_21f56795_ee72_4858_b571_11cfaa59c1a8 a owl:Class; rdfs:subClassOf :EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa, :EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A numerical data value."@en; rdfs:comment "A number individual provides the link between the ontology and the actual data, through the data property hasNumericalValue."@en, "A number is actually a string (e.g. 1.4, 1e-8) of numerical digits and other symbols. However, in order not to increase complexity of the taxonomy and relations, here we take a number as an \"atomic\" object, without decomposit it in digits (i.e. we do not include digits in the EMMO as alphabet for numbers)."@en, """In math usually number and numeral are distinct concepts, the numeral being the symbol or a composition of symbols (e.g. 3.14, 010010, three) and the number is the idea behind it. More than one numeral stands for the same number. In the EMMO abstract entities do not exists, and numbers are simply defined by other numerals, so that a number is the class of all the numerals that are equivalent (e.g. 3 and 0011 are numerals that stands for the same number). Or alternatively, an integer numeral may also stands for a set of a specific cardinality (e.g. 3 stands for a set of three apples). Rational and real numbers are simply a syntactic arrangment of integers (digits, in decimal system). The fact that you can't give a name to a number without using a numeral or, in case of positive integers, without referring to a real world objects set with specific cardinality, suggests that the abstract concept of number is not a concept that can be practically used. For these reasons, the EMMO will consider numerals and numbers as the same concept."""@en; skos:altLabel "Numeral"@en; skos:prefLabel "Number"@en . :EMMO_223d9523_4169_4ecd_b8af_acad1215e1ff a owl:Class; rdfs:subClassOf :EMMO_3c424d37_cf62_41b1_ac9d_a316f8d113d6; skos:prefLabel "Exponent"@en . :EMMO_24b30ba4_90f4_423d_93d2_fd0fde349087 a owl:Class; rdfs:subClassOf :EMMO_1cba0b27_15d0_4326_933f_379d0b3565b6; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A real matrix with shape 4x3."@en; skos:prefLabel "Shape4x3Matrix"@en . :EMMO_28fbea28_2204_4613_87ff_6d877b855fcd a owl:Class; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "Arrays are ordered mathematical objects who's elementary spatial parts are numbers. Their dimensionality is constructed with spatial direct parthood, where 1-dimensional arrays have spatial direct parts Number and n-dimensional array have spatial direct parts (n-1)-dimensional arrays."@en; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a """A Vector is a 1-dimensional Array with Number as spatial direct parts, a Matrix is a 2-dimensional Array with Vector as spatial direct parts, an Array3D is a 3-dimensional Array with Matrix as spatial direct parts, and so forth..."""@en; rdfs:comment """Array subclasses with a specific shape can be constructed with cardinality restrictions. See Shape4x3Matrix as an example."""@en, "Arrays are ordered objects, since they are a subclasses of Arrangement."@en; skos:prefLabel "Array"@en . :EMMO_29afdf54_90ae_4c98_8845_fa9ea3f143a8 a owl:Class; rdfs:subClassOf :EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "An equation that define a new variable in terms of other mathematical entities."@en; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a """The definition of velocity as v = dx/dt. The definition of density as mass/volume. y = f(x)"""@en; skos:prefLabel "DefiningEquation"@en . :EMMO_2b1303e8_d4c3_453b_9918_76f1d009543f a owl:Class; rdfs:subClassOf :EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3, _:genid10; skos:prefLabel "Multiplication"@en . _:genid10 a owl:Restriction; owl:hasValue "*"; owl:onProperty :EMMO_23b579e1_8088_45b5_9975_064014026c42 . :EMMO_2ff07b07_c447_490f_903a_f6a72a12d7bf a owl:Class; rdfs:subClassOf :EMMO_06658d8d_dcde_4fc9_aae1_17f71c0bcdec; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A real vector with 3 elements."@en; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "The quantity value of physical quantities if real space is a Shape3Vector."@en; skos:prefLabel "Shape3Vector"@en . :EMMO_3c424d37_cf62_41b1_ac9d_a316f8d113d6 a owl:Class; rdfs:subClassOf :EMMO_f6d0c26a_98b6_4cf8_8632_aa259131faaa; skos:prefLabel "AlgebricOperator"@en . :EMMO_46d5643b_9706_4b67_8bea_ed77d6026539 a owl:Class; rdfs:subClassOf :EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3, _:genid11; skos:prefLabel "Minus"@en . _:genid11 a owl:Restriction; owl:hasValue "-"; owl:onProperty :EMMO_23b579e1_8088_45b5_9975_064014026c42 . :EMMO_4bc29b0f_8fcc_4026_a291_f9774a66d9b8 a owl:Class; rdfs:subClassOf :EMMO_29afdf54_90ae_4c98_8845_fa9ea3f143a8; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A function defined using functional notation."@en; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "y = f(x)"@en; rdfs:comment "A mathematical relation that relates each element in the domain (X) to exactly one element in the range (Y)."@en; skos:altLabel "FunctionDefinition"@en; skos:prefLabel "MathematicalFunction"@en . :EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa a owl:Class; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A 'Mathematical' that has no unknown value, i.e. all its 'Variable\"-s parts refers to a 'Number' (for scalars that have a built-in datatype) or to another 'Numerical' (for complex numerical data structures that should rely on external implementations)."@en; skos:prefLabel "Numerical"@en . :EMMO_535d75a4_1972_40bc_88c6_ca566386934f a owl:Class; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0, :EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527, _:genid12; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "The equals symbol."@en; skos:prefLabel "Equals"@en . _:genid12 a owl:Restriction; owl:hasValue "="; owl:onProperty :EMMO_23b579e1_8088_45b5_9975_064014026c42 . :EMMO_54dc83cb_06e1_4739_9e45_bc09cead7f48 a owl:Class; owl:equivalentClass _:genid13; rdfs:subClassOf :EMMO_21f56795_ee72_4858_b571_11cfaa59c1a8, _:genid14; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A boolean number."@en; skos:prefLabel "Boolean"@en . _:genid13 a owl:Restriction; owl:someValuesFrom xsd:boolean; owl:onProperty :EMMO_faf79f53_749d_40b2_807c_d34244c192f4 . _:genid14 a owl:Restriction; owl:allValuesFrom xsd:boolean; owl:onProperty :EMMO_faf79f53_749d_40b2_807c_d34244c192f4 . :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 a owl:Class; rdfs:subClassOf :EMMO_d8d2144e_5c8d_455d_a643_5caf4d8d9df8; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "The class of general mathematical symbolic objects respecting mathematical syntactic rules."@en; rdfs:comment "A mathematical object in this branch is not representing a concept but an actual graphical object built using mathematcal symbols arranged in some way, according to math conventions."; skos:prefLabel "Mathematical"@en . :EMMO_5be83f9c_a4ba_4b9a_be1a_5bfc6e891231 a owl:Class; owl:equivalentClass _:genid15; rdfs:subClassOf _:genid18; skos:prefLabel "MathematicalSymbol"@en . _:genid15 a owl:Class; owl:intersectionOf _:genid17 . _:genid17 a rdf:List; rdf:first :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0; rdf:rest _:genid16 . _:genid16 a rdf:List; rdf:first :EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527; rdf:rest rdf:nil . _:genid18 a owl:Class; owl:complementOf _:genid19 . _:genid19 a owl:Restriction; owl:someValuesFrom :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0; owl:onProperty :EMMO_9380ab64_0363_4804_b13f_3a8a94119a76 . :EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3 a owl:Class; rdfs:subClassOf :EMMO_3c424d37_cf62_41b1_ac9d_a316f8d113d6; skos:prefLabel "ArithmeticOperator"@en . :EMMO_88470739_03d3_4c47_a03e_b30a1288d50c a owl:Class; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0, :EMMO_89a0c87c_0804_4013_937a_6fe234d9499c; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A mathematical string that express a relation between the elements in one set X to elements in another set Y."@en; rdfs:comment "The set X is called domain and the set Y range or codomain."@en; skos:prefLabel "MathematicalFormula"@en . :EMMO_89083bab_f69c_4d06_bf6d_62973b56cdc7 a owl:Class; rdfs:subClassOf :EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a, _:genid20; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "2+2"@en; skos:prefLabel "ArithmeticExpression"@en . _:genid20 a owl:Class; owl:complementOf _:genid21 . _:genid21 a owl:Restriction; owl:someValuesFrom :EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895; owl:onProperty :EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe . :EMMO_89a0c87c_0804_4013_937a_6fe234d9499c a owl:Class . :EMMO_8c64fcfa_23aa_45f8_9e58_bdfd065fab8f a owl:Class; rdfs:subClassOf :EMMO_9e029526_79a2_47a8_a151_dd0545db471b; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A variable that stand for a numerical constant, even if it is unknown."@en; skos:prefLabel "Constant"@en . :EMMO_8de14a59_660b_454f_aff8_76a07ce185f4 a owl:Class; rdfs:subClassOf :EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3, _:genid22; skos:prefLabel "Plus"@en . _:genid22 a owl:Restriction; owl:hasValue "+"; owl:onProperty :EMMO_23b579e1_8088_45b5_9975_064014026c42 . :EMMO_91447ec0_fb55_49f2_85a5_3172dff6482c a owl:Class; rdfs:subClassOf :EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "2 * x^2 + x + 3"@en; skos:prefLabel "Polynomial"@en . :EMMO_98d65021_4574_4890_b2fb_46430841077f a owl:Class; rdfs:subClassOf :EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6, _:genid23; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "2 * a - b = c"@en; rdfs:comment "An 'equation' that has parts two 'polynomial'-s"@en; skos:prefLabel "AlgebricEquation"@en . _:genid23 a owl:Restriction; owl:someValuesFrom :EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a; owl:onProperty :EMMO_dc57d998_23db_4d8e_b2cd_f346b195b846 . :EMMO_9e029526_79a2_47a8_a151_dd0545db471b a owl:Class; rdfs:subClassOf :EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A variable standing for a numerical defined mathematical object like e.g. a number, a vector of numbers, a matrix of numbers."@en; skos:prefLabel "NumericalVariable"@en . :EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527 a owl:Class . :EMMO_a365b3c1_7bde_41d7_a15b_2820762e85f4 a owl:Class; rdfs:subClassOf :EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3, _:genid24; skos:prefLabel "Division"@en . _:genid24 a owl:Restriction; owl:hasValue "/"; owl:onProperty :EMMO_23b579e1_8088_45b5_9975_064014026c42 . :EMMO_a6138ba7_e365_4f2d_b6b4_fe5a5918d403 a owl:Class; rdfs:subClassOf :EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "1 + 1 = 2"@en; skos:prefLabel "ArithmeticEquation"@en . :EMMO_ae15fb4f_8e4d_41de_a0f9_3997f89ba6a2 a owl:Class; rdfs:subClassOf :EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa, :EMMO_8c64fcfa_23aa_45f8_9e58_bdfd065fab8f, _:genid25; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A variable that stand for a well known numerical constant (a known number)."@en; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "π refers to the constant number ~3.14"@en; skos:prefLabel "KnownConstant"@en . _:genid25 a owl:Restriction; owl:allValuesFrom :EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa; owl:onProperty _:genid26 . _:genid26 owl:inverseOf :EMMO_3446e167_c576_49d6_846c_215bb8878a55 . :EMMO_b5c58790_fb2d_42eb_b184_2a3f6ca60acb a owl:Class; rdfs:subClassOf :EMMO_f8a2fe9f_458b_4771_9aba_a50e76afc52d, _:genid27; skos:prefLabel "Gradient"@en . _:genid27 a owl:Restriction; owl:hasValue "∇"; owl:onProperty :EMMO_23b579e1_8088_45b5_9975_064014026c42 . :EMMO_d1d436e7_72fc_49cd_863b_7bfb4ba5276a a owl:Class; rdfs:subClassOf :EMMO_9e029526_79a2_47a8_a151_dd0545db471b; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "Viscosity in the Navier-Stokes equation"@en; rdfs:comment "A variable whose value is assumed to be known independently from the equation, but whose value is not explicitated in the equation."@en; skos:prefLabel "Parameter"@en . :EMMO_d8d2144e_5c8d_455d_a643_5caf4d8d9df8 a owl:Class . :EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6 a owl:Class; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0, :EMMO_88470739_03d3_4c47_a03e_b30a1288d50c, _:genid28; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "The class of 'mathematical'-s that stand for a statement of equality between two mathematical expressions."@en; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a """2+3 = 5 x^2 +3x = 5x dv/dt = a sin(x) = y"""@en; rdfs:comment """An equation with variables can always be represented as: f(v0, v1, ..., vn) = g(v0, v1, ..., vn) where f is the left hand and g the right hand side expressions and v0, v1, ..., vn are the variables."""@en; skos:prefLabel "Equation"@en . _:genid28 a owl:Restriction; owl:someValuesFrom :EMMO_f9bc8b52_85e9_4b53_b969_dd7724d5b8e4; owl:onProperty :EMMO_dc57d998_23db_4d8e_b2cd_f346b195b846 . :EMMO_f6d0c26a_98b6_4cf8_8632_aa259131faaa a owl:Class; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0, :EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A mapping that acts on elements of one space and produces elements of another space."@en; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "The algebraic operator '+' that acts on two real numbers and produces one real number."@en, "The differential operator that acts on a C1 real function and produces another real function."@en; skos:prefLabel "MathematicalOperator"@en . :EMMO_f8a2fe9f_458b_4771_9aba_a50e76afc52d a owl:Class; rdfs:subClassOf :EMMO_f6d0c26a_98b6_4cf8_8632_aa259131faaa; skos:prefLabel "DifferentialOperator"@en . :EMMO_f8bd64d5_5d3e_4ad4_a46e_c30714fecb7f a owl:Class; owl:equivalentClass _:genid29; rdfs:subClassOf :EMMO_21f56795_ee72_4858_b571_11cfaa59c1a8, _:genid30, _:genid31; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "An integer number."@en; skos:prefLabel "Integer"@en . _:genid29 a owl:Restriction; owl:someValuesFrom xsd:integer; owl:onProperty :EMMO_faf79f53_749d_40b2_807c_d34244c192f4 . _:genid30 a owl:Restriction; owl:allValuesFrom xsd:integer; owl:onProperty :EMMO_faf79f53_749d_40b2_807c_d34244c192f4 . _:genid31 a owl:Restriction; owl:onDataRange xsd:integer; owl:qualifiedCardinality "1"^^xsd:nonNegativeInteger; owl:onProperty :EMMO_faf79f53_749d_40b2_807c_d34244c192f4 . :EMMO_f9bc8b52_85e9_4b53_b969_dd7724d5b8e4 a owl:Class; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0, :EMMO_89a0c87c_0804_4013_937a_6fe234d9499c; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A well-formed finite combination of mathematical symbols according to some specific rules."@en; skos:prefLabel "Expression"@en . :EMMO_fe7e56ce_118b_4243_9aad_20eb9f4f31f6 a owl:Class; rdfs:subClassOf :EMMO_9e029526_79a2_47a8_a151_dd0545db471b; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "The dependent variable for which an equation has been written."@en; :EMMO_b432d2d5_25f4_4165_99c5_5935a7763c1a "Velocity, for the Navier-Stokes equation."@en; skos:prefLabel "Unknown"@en . :EMMO_ffe760a2_9d1f_4aef_8bee_1f450f9cb00d a owl:Class; owl:equivalentClass _:genid32; rdfs:subClassOf _:genid35; skos:prefLabel "MathematicalConstruct"@en . _:genid32 a owl:Class; owl:intersectionOf _:genid34 . _:genid34 a rdf:List; rdf:first :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0; rdf:rest _:genid33 . _:genid33 a rdf:List; rdf:first :EMMO_89a0c87c_0804_4013_937a_6fe234d9499c; rdf:rest rdf:nil . _:genid35 a owl:Restriction; owl:someValuesFrom :EMMO_5be83f9c_a4ba_4b9a_be1a_5bfc6e891231; owl:onProperty :EMMO_9380ab64_0363_4804_b13f_3a8a94119a76 . _:genid36 owl:qualifiedCardinality "4"^^xsd:nonNegativeInteger . _:genid37 owl:qualifiedCardinality "1"^^xsd:nonNegativeInteger . _:genid38 owl:qualifiedCardinality "3"^^xsd:nonNegativeInteger .