@prefix : . @prefix owl: . @prefix rdf: . @prefix xml: . @prefix xsd: . @prefix rdfs: . @prefix skos: . @prefix dcterms: . @base . rdf:type 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:creator , :AdhamHashibon , :EmanueleGhedini , :GerhardGoldbeck , :JesperFriis ; dcterms:license "https://creativecommons.org/licenses/by/4.0/legalcode" ; dcterms:publisher ; dcterms:title "Math"@en ; rdfs:comment "The EMMO requires HermiT reasoner plugin in order to visualize all inferences and class hierarchy (ctrl+R hotkey in Protege)."@en ; owl:versionInfo "1.0.1" ; :EMMO_1246b120_abbe_4840_b0f8_3e4348b24a17 "emmo@emmc.eu" . ################################################################# # Annotation properties ################################################################# ### http://www.w3.org/2002/07/owl#qualifiedCardinality owl:qualifiedCardinality rdf:type owl:AnnotationProperty . ################################################################# # Object Properties ################################################################# ### https://w3id.org/emmo#EMMO_3446e167_c576_49d6_846c_215bb8878a55 :EMMO_3446e167_c576_49d6_846c_215bb8878a55 rdf:type 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 . ### https://w3id.org/emmo#EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe :EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe rdf:type owl:ObjectProperty . ################################################################# # Data properties ################################################################# ### https://w3id.org/emmo#EMMO_23b579e1_8088_45b5_9975_064014026c42 :EMMO_23b579e1_8088_45b5_9975_064014026c42 rdf:type owl:DatatypeProperty . ### https://w3id.org/emmo#EMMO_436c8a78_f95d_42a0_9854_07ad3736f061 :EMMO_436c8a78_f95d_42a0_9854_07ad3736f061 rdf:type owl:DatatypeProperty ; rdfs:subPropertyOf :EMMO_23b579e1_8088_45b5_9975_064014026c42 ; rdfs:domain :EMMO_5be83f9c_a4ba_4b9a_be1a_5bfc6e891231 ; skos:prefLabel "mathematicalSymbolValue"@en . ### https://w3id.org/emmo#EMMO_faf79f53_749d_40b2_807c_d34244c192f4 :EMMO_faf79f53_749d_40b2_807c_d34244c192f4 rdf:type owl:DatatypeProperty ; rdfs:subPropertyOf :EMMO_b6292331_94af_4f00_976b_ea55960c2f1c ; rdf:type owl:FunctionalProperty ; rdfs:domain :EMMO_8b305b63_6fa3_44dd_9679_17eb8403a07a ; skos:prefLabel "hasNumberValue"@en ; :EMMO_c7b62dd7_063a_4c2a_8504_42f7264ba83f "The owl:dataProperty that provides a serialisation of an EMMO numerical data entity." . ################################################################# # Classes ################################################################# ### https://w3id.org/emmo#EMMO_048a14e3_65fb_457d_8695_948965c89492 :EMMO_048a14e3_65fb_457d_8695_948965c89492 rdf:type owl:Class ; rdfs:subClassOf :EMMO_f8a2fe9f_458b_4771_9aba_a50e76afc52d , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_436c8a78_f95d_42a0_9854_07ad3736f061 ; owl:hasValue "Δ" ] ; skos:prefLabel "Laplacian"@en . ### https://w3id.org/emmo#EMMO_06658d8d_dcde_4fc9_aae1_17f71c0bcdec :EMMO_06658d8d_dcde_4fc9_aae1_17f71c0bcdec rdf:type owl:Class ; rdfs:subClassOf :EMMO_28fbea28_2204_4613_87ff_6d877b855fcd , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe ; owl:someValuesFrom :EMMO_21f56795_ee72_4858_b571_11cfaa59c1a8 ] ; skos:altLabel "1DArray"@en , "LinearArray" ; skos:prefLabel "Vector"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "1-dimensional array who's spatial direct parts are numbers."@en . ### https://w3id.org/emmo#EMMO_0b6ebe5a_0026_4bef_a1c1_5be00df9f98e :EMMO_0b6ebe5a_0026_4bef_a1c1_5be00df9f98e rdf:type owl:Class ; rdfs:subClassOf :EMMO_88470739_03d3_4c47_a03e_b30a1288d50c ; skos:example "f(x) > 0"@en ; skos:prefLabel "Inequality"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A relation which makes a non-equal comparison between two numbers or other mathematical expressions."@en . ### https://w3id.org/emmo#EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a :EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a rdf:type owl:Class ; rdfs:subClassOf :EMMO_f9bc8b52_85e9_4b53_b969_dd7724d5b8e4 ; 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:example "2x+3"@en ; skos:prefLabel "AlgebraicExpression"@en . ### https://w3id.org/emmo#EMMO_1cba0b27_15d0_4326_933f_379d0b3565b6 :EMMO_1cba0b27_15d0_4326_933f_379d0b3565b6 rdf:type owl:Class ; rdfs:subClassOf :EMMO_28fbea28_2204_4613_87ff_6d877b855fcd , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe ; owl:someValuesFrom :EMMO_06658d8d_dcde_4fc9_aae1_17f71c0bcdec ] ; skos:altLabel "2DArray"@en ; skos:prefLabel "Matrix"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "2-dimensional array who's spatial direct parts are vectors."@en . ### https://w3id.org/emmo#EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895 :EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895 rdf:type owl:Class ; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 ; skos:example """x k"""@en ; skos:prefLabel "Variable"@en ; :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 . [ rdf:type 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 ] . [ rdf:type 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 ] . ### https://w3id.org/emmo#EMMO_20ff3b34_c864_4936_8955_9345fc0a3b3c :EMMO_20ff3b34_c864_4936_8955_9345fc0a3b3c rdf:type owl:Class ; rdfs:subClassOf :EMMO_28fbea28_2204_4613_87ff_6d877b855fcd , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe ; owl:someValuesFrom :EMMO_1cba0b27_15d0_4326_933f_379d0b3565b6 ] ; skos:altLabel "3DArray"@en ; skos:prefLabel "Array3D"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "3-dimensional array who's spatial direct parts are matrices."@en . ### https://w3id.org/emmo#EMMO_21f56795_ee72_4858_b571_11cfaa59c1a8 :EMMO_21f56795_ee72_4858_b571_11cfaa59c1a8 rdf:type owl:Class ; rdfs:subClassOf :EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa , :EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527 ; 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_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A numerical data value."@en . ### https://w3id.org/emmo#EMMO_223d9523_4169_4ecd_b8af_acad1215e1ff :EMMO_223d9523_4169_4ecd_b8af_acad1215e1ff rdf:type owl:Class ; rdfs:subClassOf :EMMO_3c424d37_cf62_41b1_ac9d_a316f8d113d6 ; skos:prefLabel "Exponent"@en . ### https://w3id.org/emmo#EMMO_24b30ba4_90f4_423d_93d2_fd0fde349087 :EMMO_24b30ba4_90f4_423d_93d2_fd0fde349087 rdf:type owl:Class ; rdfs:subClassOf :EMMO_1cba0b27_15d0_4326_933f_379d0b3565b6 ; skos:prefLabel "Shape4x3Matrix"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A real matrix with shape 4x3."@en . ### https://w3id.org/emmo#EMMO_28fbea28_2204_4613_87ff_6d877b855fcd :EMMO_28fbea28_2204_4613_87ff_6d877b855fcd rdf:type owl:Class ; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 ; 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:example """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 ; skos:prefLabel "Array"@en ; :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 . ### https://w3id.org/emmo#EMMO_29afdf54_90ae_4c98_8845_fa9ea3f143a8 :EMMO_29afdf54_90ae_4c98_8845_fa9ea3f143a8 rdf:type owl:Class ; rdfs:subClassOf :EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6 ; skos:example """The definition of velocity as v = dx/dt. The definition of density as mass/volume. y = f(x)"""@en ; skos:prefLabel "DefiningEquation"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "An equation that define a new variable in terms of other mathematical entities."@en . ### https://w3id.org/emmo#EMMO_2b1303e8_d4c3_453b_9918_76f1d009543f :EMMO_2b1303e8_d4c3_453b_9918_76f1d009543f rdf:type owl:Class ; rdfs:subClassOf :EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3 , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_436c8a78_f95d_42a0_9854_07ad3736f061 ; owl:hasValue "*" ] ; skos:prefLabel "Multiplication"@en . ### https://w3id.org/emmo#EMMO_2ff07b07_c447_490f_903a_f6a72a12d7bf :EMMO_2ff07b07_c447_490f_903a_f6a72a12d7bf rdf:type owl:Class ; rdfs:subClassOf :EMMO_06658d8d_dcde_4fc9_aae1_17f71c0bcdec ; skos:example "The quantity value of physical quantities if real space is a Shape3Vector."@en ; skos:prefLabel "Shape3Vector"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A real vector with 3 elements."@en . ### https://w3id.org/emmo#EMMO_3c424d37_cf62_41b1_ac9d_a316f8d113d6 :EMMO_3c424d37_cf62_41b1_ac9d_a316f8d113d6 rdf:type owl:Class ; rdfs:subClassOf :EMMO_f6d0c26a_98b6_4cf8_8632_aa259131faaa ; skos:prefLabel "AlgebraicOperator"@en . ### https://w3id.org/emmo#EMMO_46d5643b_9706_4b67_8bea_ed77d6026539 :EMMO_46d5643b_9706_4b67_8bea_ed77d6026539 rdf:type owl:Class ; rdfs:subClassOf :EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3 , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_436c8a78_f95d_42a0_9854_07ad3736f061 ; owl:hasValue "-" ] ; skos:prefLabel "Minus"@en . ### https://w3id.org/emmo#EMMO_4bc29b0f_8fcc_4026_a291_f9774a66d9b8 :EMMO_4bc29b0f_8fcc_4026_a291_f9774a66d9b8 rdf:type owl:Class ; rdfs:subClassOf :EMMO_29afdf54_90ae_4c98_8845_fa9ea3f143a8 ; 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:example "y = f(x)"@en ; skos:prefLabel "MathematicalFunction"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A function defined using functional notation."@en . ### https://w3id.org/emmo#EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa :EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa rdf:type owl:Class ; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 ; skos:prefLabel "Numerical"@en ; :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 . ### https://w3id.org/emmo#EMMO_535d75a4_1972_40bc_88c6_ca566386934f :EMMO_535d75a4_1972_40bc_88c6_ca566386934f rdf:type owl:Class ; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 , :EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527 , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_436c8a78_f95d_42a0_9854_07ad3736f061 ; owl:hasValue "=" ] ; skos:prefLabel "Equals"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "The equals symbol."@en . ### https://w3id.org/emmo#EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 rdf:type owl:Class ; rdfs:subClassOf :EMMO_d8d2144e_5c8d_455d_a643_5caf4d8d9df8 ; skos:prefLabel "Mathematical"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "The class of general mathematical symbolic objects respecting mathematical syntactic rules."@en ; :EMMO_c7b62dd7_063a_4c2a_8504_42f7264ba83f "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."@en . ### https://w3id.org/emmo#EMMO_5be83f9c_a4ba_4b9a_be1a_5bfc6e891231 :EMMO_5be83f9c_a4ba_4b9a_be1a_5bfc6e891231 rdf:type owl:Class ; owl:equivalentClass [ owl:intersectionOf ( :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 :EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527 ) ; rdf:type owl:Class ] ; rdfs:subClassOf [ rdf:type owl:Class ; owl:complementOf [ rdf:type owl:Restriction ; owl:onProperty :EMMO_9380ab64_0363_4804_b13f_3a8a94119a76 ; owl:someValuesFrom :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 ] ] ; skos:prefLabel "MathematicalSymbol"@en . ### https://w3id.org/emmo#EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3 :EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3 rdf:type owl:Class ; rdfs:subClassOf :EMMO_3c424d37_cf62_41b1_ac9d_a316f8d113d6 ; skos:prefLabel "ArithmeticOperator"@en . ### https://w3id.org/emmo#EMMO_88470739_03d3_4c47_a03e_b30a1288d50c :EMMO_88470739_03d3_4c47_a03e_b30a1288d50c rdf:type owl:Class ; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 , :EMMO_89a0c87c_0804_4013_937a_6fe234d9499c ; rdfs:comment "The set X is called domain and the set Y range or codomain."@en ; skos:prefLabel "MathematicalFormula"@en ; :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 . ### https://w3id.org/emmo#EMMO_89083bab_f69c_4d06_bf6d_62973b56cdc7 :EMMO_89083bab_f69c_4d06_bf6d_62973b56cdc7 rdf:type owl:Class ; rdfs:subClassOf :EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a , [ rdf:type owl:Class ; owl:complementOf [ rdf:type owl:Restriction ; owl:onProperty :EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe ; owl:someValuesFrom :EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895 ] ] ; skos:example "2+2"@en ; skos:prefLabel "ArithmeticExpression"@en . ### https://w3id.org/emmo#EMMO_89a0c87c_0804_4013_937a_6fe234d9499c :EMMO_89a0c87c_0804_4013_937a_6fe234d9499c rdf:type owl:Class . ### https://w3id.org/emmo#EMMO_8c64fcfa_23aa_45f8_9e58_bdfd065fab8f :EMMO_8c64fcfa_23aa_45f8_9e58_bdfd065fab8f rdf:type owl:Class ; rdfs:subClassOf :EMMO_9e029526_79a2_47a8_a151_dd0545db471b ; skos:prefLabel "Constant"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A variable that stand for a numerical constant, even if it is unknown."@en . ### https://w3id.org/emmo#EMMO_8de14a59_660b_454f_aff8_76a07ce185f4 :EMMO_8de14a59_660b_454f_aff8_76a07ce185f4 rdf:type owl:Class ; rdfs:subClassOf :EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3 , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_436c8a78_f95d_42a0_9854_07ad3736f061 ; owl:hasValue "+" ] ; skos:prefLabel "Plus"@en . ### https://w3id.org/emmo#EMMO_91447ec0_fb55_49f2_85a5_3172dff6482c :EMMO_91447ec0_fb55_49f2_85a5_3172dff6482c rdf:type owl:Class ; rdfs:subClassOf :EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a ; skos:example "2 * x^2 + x + 3"@en ; skos:prefLabel "Polynomial"@en . ### https://w3id.org/emmo#EMMO_98d65021_4574_4890_b2fb_46430841077f :EMMO_98d65021_4574_4890_b2fb_46430841077f rdf:type owl:Class ; rdfs:subClassOf :EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6 , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_dc57d998_23db_4d8e_b2cd_f346b195b846 ; owl:someValuesFrom :EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a ] ; rdfs:comment "An 'equation' that has parts two 'polynomial'-s"@en ; skos:example "2 * a - b = c"@en ; skos:prefLabel "AlgebraicEquation"@en . ### https://w3id.org/emmo#EMMO_9e029526_79a2_47a8_a151_dd0545db471b :EMMO_9e029526_79a2_47a8_a151_dd0545db471b rdf:type owl:Class ; rdfs:subClassOf :EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895 ; skos:prefLabel "NumericalVariable"@en ; :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 . ### https://w3id.org/emmo#EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527 :EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527 rdf:type owl:Class . ### https://w3id.org/emmo#EMMO_a365b3c1_7bde_41d7_a15b_2820762e85f4 :EMMO_a365b3c1_7bde_41d7_a15b_2820762e85f4 rdf:type owl:Class ; rdfs:subClassOf :EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3 , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_436c8a78_f95d_42a0_9854_07ad3736f061 ; owl:hasValue "/" ] ; skos:prefLabel "Division"@en . ### https://w3id.org/emmo#EMMO_a6138ba7_e365_4f2d_b6b4_fe5a5918d403 :EMMO_a6138ba7_e365_4f2d_b6b4_fe5a5918d403 rdf:type owl:Class ; rdfs:subClassOf :EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6 ; skos:example "1 + 1 = 2"@en ; skos:prefLabel "ArithmeticEquation"@en . ### https://w3id.org/emmo#EMMO_ae15fb4f_8e4d_41de_a0f9_3997f89ba6a2 :EMMO_ae15fb4f_8e4d_41de_a0f9_3997f89ba6a2 rdf:type owl:Class ; rdfs:subClassOf :EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa , :EMMO_8c64fcfa_23aa_45f8_9e58_bdfd065fab8f , [ rdf:type owl:Restriction ; owl:onProperty [ owl:inverseOf :EMMO_3446e167_c576_49d6_846c_215bb8878a55 ] ; owl:allValuesFrom :EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa ] ; skos:example "π refers to the constant number ~3.14"@en ; skos:prefLabel "KnownConstant"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A variable that stand for a well known numerical constant (a known number)."@en . ### https://w3id.org/emmo#EMMO_b5c58790_fb2d_42eb_b184_2a3f6ca60acb :EMMO_b5c58790_fb2d_42eb_b184_2a3f6ca60acb rdf:type owl:Class ; rdfs:subClassOf :EMMO_f8a2fe9f_458b_4771_9aba_a50e76afc52d , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_436c8a78_f95d_42a0_9854_07ad3736f061 ; owl:hasValue "∇" ] ; skos:prefLabel "Gradient"@en . ### https://w3id.org/emmo#EMMO_d1d436e7_72fc_49cd_863b_7bfb4ba5276a :EMMO_d1d436e7_72fc_49cd_863b_7bfb4ba5276a rdf:type owl:Class ; rdfs:subClassOf :EMMO_9e029526_79a2_47a8_a151_dd0545db471b ; 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:example "Viscosity in the Navier-Stokes equation"@en ; skos:prefLabel "Parameter"@en . ### https://w3id.org/emmo#EMMO_d8d2144e_5c8d_455d_a643_5caf4d8d9df8 :EMMO_d8d2144e_5c8d_455d_a643_5caf4d8d9df8 rdf:type owl:Class . ### https://w3id.org/emmo#EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6 :EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6 rdf:type owl:Class ; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 , :EMMO_88470739_03d3_4c47_a03e_b30a1288d50c , [ rdf:type owl:Restriction ; owl:onProperty :EMMO_dc57d998_23db_4d8e_b2cd_f346b195b846 ; owl:someValuesFrom :EMMO_f9bc8b52_85e9_4b53_b969_dd7724d5b8e4 ] ; 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:example """2+3 = 5 x^2 +3x = 5x dv/dt = a sin(x) = y"""@en ; skos:prefLabel "Equation"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "The class of 'mathematical'-s that stand for a statement of equality between two mathematical expressions."@en . ### https://w3id.org/emmo#EMMO_f6d0c26a_98b6_4cf8_8632_aa259131faaa :EMMO_f6d0c26a_98b6_4cf8_8632_aa259131faaa rdf:type owl:Class ; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 , :EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527 ; skos:example "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_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A mapping that acts on elements of one space and produces elements of another space."@en . ### https://w3id.org/emmo#EMMO_f8a2fe9f_458b_4771_9aba_a50e76afc52d :EMMO_f8a2fe9f_458b_4771_9aba_a50e76afc52d rdf:type owl:Class ; rdfs:subClassOf :EMMO_f6d0c26a_98b6_4cf8_8632_aa259131faaa ; skos:prefLabel "DifferentialOperator"@en . ### https://w3id.org/emmo#EMMO_f9bc8b52_85e9_4b53_b969_dd7724d5b8e4 :EMMO_f9bc8b52_85e9_4b53_b969_dd7724d5b8e4 rdf:type owl:Class ; rdfs:subClassOf :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 , :EMMO_89a0c87c_0804_4013_937a_6fe234d9499c ; skos:prefLabel "Expression"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A well-formed finite combination of mathematical symbols according to some specific rules."@en . ### https://w3id.org/emmo#EMMO_fe7e56ce_118b_4243_9aad_20eb9f4f31f6 :EMMO_fe7e56ce_118b_4243_9aad_20eb9f4f31f6 rdf:type owl:Class ; rdfs:subClassOf :EMMO_9e029526_79a2_47a8_a151_dd0545db471b ; skos:example "Velocity, for the Navier-Stokes equation."@en ; skos:prefLabel "Unknown"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "The dependent variable for which an equation has been written."@en . ### https://w3id.org/emmo#EMMO_ffe760a2_9d1f_4aef_8bee_1f450f9cb00d :EMMO_ffe760a2_9d1f_4aef_8bee_1f450f9cb00d rdf:type owl:Class ; owl:equivalentClass [ owl:intersectionOf ( :EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0 :EMMO_89a0c87c_0804_4013_937a_6fe234d9499c ) ; rdf:type owl:Class ] ; rdfs:subClassOf [ rdf:type owl:Restriction ; owl:onProperty :EMMO_9380ab64_0363_4804_b13f_3a8a94119a76 ; owl:someValuesFrom :EMMO_5be83f9c_a4ba_4b9a_be1a_5bfc6e891231 ] ; skos:prefLabel "MathematicalConstruct"@en ; :EMMO_967080e5_2f42_4eb2_a3a9_c58143e835f9 "A construct of two or more mathematical symbols."@en . [ owl:qualifiedCardinality "3"^^xsd:nonNegativeInteger ] . [ owl:qualifiedCardinality "1"^^xsd:nonNegativeInteger ] . [ owl:qualifiedCardinality "4"^^xsd:nonNegativeInteger ] . ### Generated by the OWL API (version 4.5.29.2024-05-13T12:11:03Z) https://github.com/owlcs/owlapi