This document mixes HTML and
FL
(a KRL, i.e., a Knowledge Representation Language; it is here used in the
preformatted text parts).
It is an input+backup+presentation file for the
Multi-Source Ontology (MSO).
The MSO i) aligns and extends several ontologies, and
ii) can be extended by Web users via the shared KB server
WebKB-2 and its
shared KB (knowledge base) editing protocols.
In this document, for supertype links, "/^" is used instead of the more common "<" symbol.
Similarly, for subtype links, "\." is used instead of the more common ">" symbol.
The ontology in this document is original. Some content is added to it from time to time.
It is part of complementary "ontologies on formal languages":
The goals, underlying ideas, conventions and content of these ontologies are explained and illustrated in this article.
0. Relations between particular KRL notations (figure)
1. KRL notation that is mostly not graph based
1.1. Prefix operator based KRL notation
1.1.1. RIF-PS
1.1.2. CLIF
1.1.3. KIF
1.1.4. OWL Functional-Style Syntax (FSS)
1.2. Infix operator based KRL notation
1.2.1. N-Triples
1.2.2. N-Quads
2. KRL notation that is mostly graph based
2.1. KRL notation mostly graph based but not markup based
2.1.1. The notation of JSON-LD
2.2. KRL notation mostly graph based and markup based
2.2.1. RDF/XML
KRL_notation \. exclusion { (KRL-notation_mostly_non_graph_based = KRL-notation_mostly_relation_based KRL-notation_mostly_based_on_an_AND-set_of_statements_with_an_operator_and_its_arguments KRL-notation_mostly_based_on_positional_or_named_arguments, \. exclusion { KRL-notation_that_is_mainly_postfix-based (KRL-notation_that_is_mainly_infix-based \. N-triples N-Quads ) (KRL-notation_that_is_mainly_prefix-based //the operator appears first \. exclusion { (S-expression_based_KRL-notation = KRL-notation_based_on_list-like_operators-with-parameters, \. (Second-order_S-expression_based_KRL-notation r_model_type: Higher-order-logic_model, \. (KIF_notation = LISP_based_KIF KIF, r_model_type: KIF_model ) ) (First-order_S-expression_based_KRL-notation \. CLIF CGIF)) (M-expression_based_KRL-notation = KRL-notation_based_on_function-like_prefix_operators-with-parameters, \. (RIF_PS r_model_type: RIF, \. (RIF-FLD_PS r_model_type: RIF-FLD) (RIF-BLD_PS r_model_type: RIF-BLD) (RIF-Core_PS r_model_type: RIF-Core) ) (OWL_Functional-Style-Syntax r_model_type: OWL2) ) } ) } ) (KRL-notation_mostly_graph_based = KRL-notation_mostly_concept_node_based KRL-notation_mostly_object_based, \. exclusion { (KRL-notation_mostly_graph_based_and_markup_based \. (XML_based_notation \. (RDF/XML r_model_type: RDF) (XCL r_model_type: CL) (RIF/XML r_model_type: RIF, \. (RIF-FLD/XML r_model_type: RIF-FLD) (RIF-BLD/XML r_model_type: RIF-BLD) (RIF-Core/XML r_model_type: RIF-Core) ) ) ) (KRL-notation_mostly_graph_based_but_not_markup_based \. (Turtle r_model_type: RDF) (Turtle r_part-type: N-triples) (Notation3 r_part-type: Turtle) (JSON-LD_notation r_model_type: JSON-LD_model) (CGLF r_model_type: Higher-order-logic_model) (FL r_model_type: FL_model) ) } ) };
S-expression_based_KRL-notation /* cf. S-expression ('S' for "Symbolic") */
\. (Parenthesis_delimited_S-expression_based_KRL-notation
= ^(KRL_notation ?n r_KRL of: 1..* ^(CE rc of=: (an AE ?ae
rc_spec: fc_spec_(.[ "(" fc_OP_from_(?ae)
fc_ARGS_from_(?ae) ")" ],.{?n} ) ) )
);
M-expression-like_based_KRL-notation /* cf. M-expression ('M' for "Mathematics") */
\. (Parenthesis_delimited_M-expression_based_KRL-notation
= ^(KRL_notation ?n r_KRL of: 1..* ^(CE rc of=: (an AE ?ae
rc_spec: fc_spec_(.[ fc_OP_from_(?ae) "("
fc_ARGS_from_(?ae) ")" ],.{?n} ) ) )
) );
RIF-PS uses a function-style presentation for relationships except for rules.
However, RIF-PS is not particularly regular and hence its grammars (for
RIF-FLD,
RIF-BLD, ...) are not short.
In other words, RIF-PS is not defined via 1 (or a few) grammar rules and an ontology.
This is why its specifications below are not short either.
//--------- STRUCTURES:
Abstract_element@RIF ?a /* this figure illustrates the first relations */
rc_spec: fc_spec_(.[ fc_OP_from_(?a) "(" fc_ARGS_from_(?a) ")" ],.{RIF_PS}), //by default
\. (RIF_abstract_element_that_has_also_and_preferably_an_infix_presentation_in_RIF_PS ?i
rc_spec: fc_spec _(.[fc_ARG_(?i.r_link_source) fc_OP_from(?i)
fc_ARG_(?i.r_link_destination) ], .{RIF_PS} ),
\. Rule@RIF Equality@RIF Typing@RIF Supertyping@RIF )
(RIF_abstract_element_displayed_as_a_whitespace_separated_list_of_elements_in_RIF_PS ?sl
rc_spec: fc_spec _(.[fc_ARGS_(?sl)], .{RIF_PS}),
\. RIF_document_context Quantification_guard_list Quantification_variable_list )
(RIF_module_context_link ?l
rc: only ^(Concrete_element r_part of: RIF_PS, //reminder: rc = r_CE
rc of: Module_context@RIF), //no direct display
rc_spec: fc_spec _(.[fc_ARG_(?l.r_link_destination)],
.{RIF_PS} ), //only the destination is shown
(Annotation@RIF ?a rc_spec: fc_spec _(.[fc_OP_from_(?a) fc_ARG_from_(?a) ],.{RIF_PS}) )
(RIF_annotation_link ?l
rc_spec: fc_spec _(.["(*" fc_ARG_(?l.r_link_destination) "*)" fc_OP_(?l.r_link_source) ],
.{RIF_PS} ) );
//reminder: Document@RIF-FLD = f_link_type_("",r_context,Module_body@RIF,Module_context@RIF-FLD));
// Document ::= IRIMETA? 'Document' '(' Base? Prefix* Import* Group? ')'
Document@RIF ?d
rc_spec: fc_spec _(.[fc_op_("Document") "(" fc_ARG_(?d.r_link_destination)
fc_ARG_(?d.r_link_source) ")" ], .{RIF_PS} );
Module_context@RIF ?mc
rc_spec: fc_spec _(.[fc_ARGS(.[every ^(Phrase r_part of: ?mc, /^ Module_dialect_link@RIF-FLD)])
fc_ARGS(.[every ^(Phrase r_part of: ?mc, /^ Module_base_IRI_link@RIF-FLD)])
fc_ARGS(.[every ^(Phrase r_part of: ?mc, /^ rif#Prefix)])
fc_ARGS(.[every ^(Phrase r_part of: ?mc, /^ Module_import_link@RIF)])
fc_ARGS(.[every ^(Phrase r_part of: ?mc, /^ Remote_module_naming_link@RIF-FLD)])
], .{RIF_PS} );
r_not rc_type .: fc_spec _(.["Neg"], .{RIF_PS});
Frame@RIF ?f
rc_spec: fc_spec _(.[fc_OP_from(?f) '[' fc_ARGS_from(?f) ']' ], .{RIF_PS});
Half_link@RIF rc_spec: fc_spec _(.[fc_OP_from(?f) "->" fc_ARG(?f)], .{RIF_PS});
Named_argument@RIF ?na rc_spec: fc_spec_(.[fc_ARG_from(?na) "->" fc_OP_from(?na)], .{RIF_PS});
//--------- REFERENCES and VALUES:
Constant@RIF rc_spec: w3c_constant_ct;
String_value_token@RIF rc_spec: String_delimited_by_escapable_double_quote;
Variable@RIF rc_spec: w3c#Var, /^ Explicitly_bound_variable;
Name@RIF rc_spec: w3c#Name;
Importation_profile@RIF rc_spec: w3c_IRI_within_angle_brackets;
Aggregate_function@RIF ?a
rc_spec: fc_spec _(.[fc_OP_from_(?a) "{" fc_ARGS_from_(?a,"|") "}"],.{RIF_PS});
Aggregate_function_bound_list@RIF ?bl
rc_spec: fc_spec _(.[fc_OP_from_(?bl) "[" fc_ARGS_from_(?bl) "]"],.{RIF_PS});
Open_list@RIF ?f rc_spec: fc_spec_(.[fc_OP("List") "(" fc_ARG_from(?f)], .{RIF_PS});
Open_list_sequence_variable@RIF rc_spec: fc_spec_(.["|" fc_OP_from_(?f)], .{RIF_PS});
Structured_reference_to_a_element_in_a_remote_module@RIF ?r
rc_spec: fc_spec_(.[fc_OP_from(?r) "@" fc_ARG_from(?r)], .{RIF_PS});
Structured_reference_to_externally_defined_element@RIF ?r
rc_spec: fc_spec_(.[fc_OP("External") "(" fc_OP_from_(?r) fc_ARG_from(?r) ")" ], .{RIF_PS});
1.1.2. CLIF
See the ISO/IEC document of 2007 on CL.
//--------- STRUCTURES:
Abstract_element@CL ?a
rc_spec: fc_spec_(.[ "(" fc_OP_from_(?a) fc_ARGS_from_(?a) ")" ],.{CLIF}),
\. (CL_abstract_element_presented_in_CLIF_via_its_arguments_separated_by_spaces
rc_spec: fc_spec _(.[fc_ARGS_(?sl)], .{CLIF}),
\. Module_body@CL cl#Module_context Excluded_elements cl#Sub-phrase_list )
(CL_link_for_which_only_the_destination_is_presented_in_CLIF ?l
rc_spec: fc_spec _(.[fc_ARG_(?l.r_link_destination)], .{CLIF}),
\. cl#Module_name_link_in_module_context );
^(cl#Text r_link_destination: (a Module_context r_part: a Module_name_link ?l)) ?t
rc_spec: fc_spec_(.[ "(" fc_OP_("cl:text") fc_ARG_(?l.r_link_destination)
fc_ARGS_( (.[every ^(Phrase r_part of: ?t, != ?l)] /^ cl#Sub_phrases) )
")" ],.{CLIF} );
^(cl#Text r_link_destination: (a Module_context r_part: 0 Module_name_link)) ?t
rc_spec: fc_spec_(.[ fc_ARG_(?t.r_destination) ],.{CLIF} );
^(cl#Module r_link_destination: (a Module_context
r_part: 1 Module_name_link ?l
0 Module_excluded_element_link )) ?m
rc_spec: fc_spec_(.[ "(" fc_OP_("cl:module") fc_ARG_(?l.r_link_destination)
fc_ARGS_( (.[every ^(Phrase r_part of: ?m, != ?l)] /^ cl#Sub_phrases) )
")" ],.{CLIF} );
^(cl#Module r_link_destination: (a Module_context
r_part: 1 Module_name_link ?l
1 Module_excluded_element_link ?et)) ?m
rc_spec: fc_spec_(.[ "(" fc_OP_("cl:module") fc_ARG_(?l.r_link_destination)
fc_ARG_(?et /^ cl#Module_excluded_element_link_in_module_context)
fc_ARGS_( (.[every ^(Phrase r_part of: ?m, != ?l)] /^ cl#Sub-phrase_list) )
")" ],.{CLIF} );
cl#Module_excluded_element_link_in_module_context ?l
rc_spec: fc_spec_(.[ "(" fc_OP_("cl:excludes") fc_ARGS_(?l.r_link_destination) ")" ],.{CLIF});
^(Module_import_link r_member of: a cl#Sub-phrase_list) ?l
rc_spec: fc_spec_(.[ "(" fc_OP_("cl:imports") fc_ARGS_(?l.r_link_destination) ")" ],.{CLIF});
^(CLIF_annotation_link ?l = f_link_type _("",r_annotation,Phrase,String@CL),
rc_spec: fc_spec _(.["(" fc_OP_("cl:comment") fc_ARG_(?l.r_link_destination)
fc_ARG_(?l.r_link_source) ")" ],.{CLIF});
1.1.3. KIF
Abstract_element@KIF_model ?a
rc_spec: fc_spec_(.[ "(" fc_OP_from_(?a) fc_ARGS_from_(?a) ")" ],.{KIF});
1.1.4. OWL Functional-Style Syntax (FSS)
OWL_Functional-Style-Syntax r_short_name: FSS;
^(Abstract_element@OWL not r_operator: r_member) ?a
rc_spec: fc_spec_(.[ fc_OP_from_(?a) "(" fc_ARGS_from_(?a) ")" ],.{FSS});
^(Abstract_element@OWL r_operator: r_member) ?a
rc_spec: fc_spec_(.[ fc_OP_from_(?a) "(" fc_ARG_(?a.r_link_source)
fc_ARGS_(.[every ?a.r_link_destination.r_member]) ")" ], .{FSS} );
//Reminder: Document@OWL /^ Module;
// Module = f_link_type _("",r_context,Module_body,Module_context);
// Module_context /^ f_relation_type _("Context",r_and,.[0..* Link_in_module_context]);
// Module_body /^ f_relation_type _("Group",r_and,.[0..* Formula]);
//Grammar at https://www.w3.org/TR/owl2-syntax (sections 3.7 and 13)
// ontologyDocument := { prefixDeclaration } Ontology
// Ontology := 'Ontology' '(' [ ontologyIRI [ versionIRI ] ] directlyImportsDocuments
// ontologyAnnotations axioms ')'
Document@OWL ?d
rc_spec: fc_spec_(.[ fc_ARG_(.[every ^(Module_context_namespace-definition_link
r_part of: (a Module_context r_link_destination of: ?d) ) ])
fc_ARG_(?d.r_link_source) ], .{FSS} );
Module_context_namespace-definition_link@OWL ?l
rc_spec: fc_spec _(.[fc_op_("Prefix") "(" fc_ARG_(?l.r_link_source) "="
fc_ARG_(?d.r_link_destination) ")" ], .{FSS} );
Module_body@OWL ?mb
rc_spec: fc_spec _(.[fc_op_("Ontology") "(" fc_ARG_(?mb.r_identifier) fc_ARG(?mb.owl#versionInfo)
fc_ARGS_(.[every ^(Module_import_link_with_IRI@OWL
_ r_part of: (a Module_context r_context of: ?mb) ) ])
fc_ARGS(.[every ^(Module_import_link_with_IRI@OWL
r_part of: (a Module_context r_context of: ?mb) ) ])
fc_ARGS_(.[every ^(Module_annotation_link@OWL
r_part of: (a Module_context r_context of: ?mb) ) ])
fc_ARGS_from_(?mb) ")" ], .{FSS} );
^(owl#Axiom r_operator: r_member) ?a
rc_spec: fc_spec _(.[fc_op_(?a.r_name) "(" fc_ARGS_(.[every ?d.r_annotation])
fc_ARG_(?a.r_link_source)
fc_ARGS_(.[every ?a.r_link_destination.r_member]) ")" ], .{FSS} );
^(owl#Axiom not r_operator: r_member) ?a
rc_spec: fc_spec _(.[fc_op_(?a.r_name) "(" fc_ARGS_(.[every ?d.r_annotation])
fc_ARG_(?a.r_link_source) fc_ARG_(?a.r_link_destination) ")" ], .{FSS} );
owl#Restriction ?r
rc_spec: fc_spec _(.[fc_OP_(?r.r_name) "(" fc_ARGS_from_(?r) ")" ], .{FSS} );
owl#PropertyRestriction ?r
rc_spec: fc_spec _(.[fc_OP_(?r.r_name) "(" fc_ARG_(?r.owl#onProperty)
fc_ARGS_from_(?r) ")" ], .{FSS} );
owl#PropertyCardinalityRestriction ?r
rc_spec: fc_spec _(.[fc_OP_(?r.r_name) "("
fc_ARG_(?r.owl#r_relation_from_restriction_to_nonNegativeInteger)
fc_ARG_(?r.owl#onProperty) fc_ARGS_from_(?r) ")" ], .{FSS} );
\. (^(owl#ObjectPropertyCardinalityRestriction owl#onProperty_restriction: owl#Thing_IRI)
rc_spec: fc_spec _(.[fc_OP_(?r.r_name) "("
fc_ARG_(?r.owl#r_relation_from_restriction_to_nonNegativeInteger)
fc_ARG_(?r.owl#onProperty) ")" ], .{FSS} ) );
1.2. Infix operator based KRL notation
1.2.1. N-Triples
Conjunction_of_formulas@RDF
rc_spec: fc_spec_(.[ fc_ARGS_from_(?a) ],.{N-Triples});
NR_link@RDF ?l rc_spec: fc_spec_(.[fc_ARG_(?l.r_link_source) fc_OP_(?l)
fc_ARG_(?l.r_link_destination) ],.{N-Triples} );
1.2.2. N-Quads
Conjunction_of_formulas@RDF
rc_spec: fc_spec_(.[ fc_ARGS_from_(?a) ],.{N-Quads});
NR_link@RDF ?l rc_spec: fc_spec_(.[fc_ARG_(?l.r_link_source) fc_OP_(?l)
fc_ARG_(?l.r_link_destination) fc_ARG_(?l.r_context)
],.{N-Quads} );
2. KRL notation that is mostly graph based
2.1. KRL notation mostly graph based but not markup based
2.1.1. The notation of JSON-LD
JSON-LD_notation r_short_name: JN; JSON-LD_model r_short_name: JM;
//--------- STRUCTURES:
^(Conjunction_phrase@JM not /^ NR_frame) ?cp
rc_spec: fc_spec _(.[ "[" fc_ARGS_from_(?cp,",") "]" ], .{JN});
Minimal-frame_as_NR-phrase@JM ?mf
rc_spec: fc_spec _(.[ "{" fc_ARGS_from_(?mf,",") "}" ], .{JN});
Minimal_half-link@JM ?mh
rc_spec: fc_spec _(.[ fc_OP_from(?mh) ":" fc_ARG_(?mh.r_link_destination) ], .{JN})
\. (Minimal_half-link_in_rel-type-def_context@JM
\. (Minimal_half-link_in_rel-type-destination-def_context@JM ?mh
rc_spec: fc_spec _(.[fc_OP_(`"@type"') ":" fc_ARG_(?mh.r_link_destination) ], .{JN})
) );
Link_from_a_module_body@JM
rc: only ^(Concrete_element r_part of: JN, rc of: a Module_context@JM), //no direct display
\. Module_base_IRI_link@JM Module_context_namespace-definition_link@JM;
Module_context_namespace-definition_link@JM ?d
rc_spec: fc_spec _(.[fc_ARG_(?d.r_link_destination) ], .{JN});
Namespace_shortcut_definition_in_context@JM ?d
rc_spec: fc_spec _(.[fc_ARG_(?d.r_link_source) ":" fc_ARG_(?d.r_link_destination) ], .{JN});
Module_context_type-definition_link@JM ?d
rc_spec: fc_spec _(.[fc_ARG_(?d.r_link_destination) ], .{JN});
Relation-type_definition_in_context@JM ?d
rc_spec: fc_spec _(.[fc_OP_(?d.r_frame_head) ":"
fc_ARG_(.["{" fc_ARGS_from(?d) "}"]) ], .{JN});
r_binary_relation_type_predefined_in_JN //w3.org/TR/json-ld/#syntax-tokens-and-keywords (3.3)
\. (r_context@JM ~[Module_body@JM-:Module_context@JM}] rc.: `"@context"'@JN)
(r_id@J ~[?-:ID@J] rc.: `"@id"'@JN)
(r_value ~[?-:Built-in_value@J] rc.: `"@value"'@JN)
(r_language@J ~[String@JN-:Language@J] rc.: `"@language"'@JN)
(r_type@J ~[Typable_object-:ID@J] rc.: `"@type"'@JN)
(r_container_type@J ~[?-:Container_type@J] rc.: `"@container"'@JN)
(r_list_items@J ~[?-:Container@J] rc.: `"@list"'@JN)
(r_set_items@J ~[?-:Container@J] rc.: `"@set"'@JN)
(r_reverse@J ~[?-:Objectified_link@J] rc.: `"@reverse"'@JN)
(r_key_name_@J ~[?-:string@J] rc.: `"@index"'@JN)
(r_base_IRI@J ~[Context_frame@J-:Absolute_IRI@J] rc.: `"@base"'@JN)
(r_default_namespace@J ~[Context_frame@J-:IRI@J] rc.: `"@vocab"'@JN)
(r_graph_items@J ~[Phrase@J-:set{Frame}] rc.: `"@graph"'@JN);
//--------- REFERENCES and VALUES:
JM_AE_with_string_like_representation_in_JN ?a
rc_spec: fc_stringSpec _(.[ '"' ?a.r_value '"' ],'\\',.{JN}),
\. String@JM IRI@JM Language@JM;
Blank_node_identifier@JM ?b
rc_spec: fc_stringSpec _(.[ '"_:' ?b.r_value ],'',.{JN});
2.2. KRL notation mostly graph based and markup based
2.2.1. RDF/XML
^(Abstract_element@RDF not r_part: an AE) ?a
rc_spec: fc_spec _(.[""], .{RDF/XML} );
^(Frame_as_reference@RDF r_part: an AE) ?a
rc_spec: fc_spec _(.["<"fc_op_(?a.r_op.r_name)">" fc_ARGS_from_(?a)
"" ], .{RDF/XML} );
^(Frame_as_reference@RDF r_part: 0 ^(Half_link not r_link_destination: a Token@RDF) ?a
rc_spec: fc_spec _(.["<"fc_op_(?a.r_op.r_name)" fc_ARGS_from_(?a)"/>" ], .{RDF/XML} );
Half_link@RDF
rc_spec: fc_spec _(.["<"fc_op_(?a.r_op.r_name)" fc_ARG_(?a.r_link_destination)"/>"
], .{RDF/XML} );