ISO TC211 workshop to consider the impact of non-relational technologies on TC211 standards Contents Background Space-Time Component (plus Names) First workstream – Foundations: Quick View Second workstream - Overview Mapping General : Spatial Objects Part 42 – Mapping: Spatial Objects OS Open Names: Mapping Relations (Foundation Extension) Organisation Term-ology TLO Survey & Ontological Assessment Process FDM Components Shift from representation to models Remove geometry and topology redundancy Reorient geometry and topology – as classification Collapse redundant geometrical and topological objects Mapping - Names Mapping Mereology Mapping Coordinates Background: organisation NDT/IMF/FDM/TLO Deep Organizational Structure Digital Framework Task Group (DFTG) National Digital Twin programme (NDTp) www.cdbb.cam.ac.uk/what-we-do/national-digital-twin-programme www.cdbb.cam.ac.uk www.gov.uk/government/organisations/department-for-business-energy-and-industrial-strategy www.constructioninnovationhub.org.uk Construction Innovation Hub (CIH) Department for Business, Energy & Industrial Strategy (BEIS) Centre for Digital Britain (CDBB) 4 The Information Management Framework UK’s National Digital Twin programme ( NDTp ) Information Management Framework (IMF) www.cdbb.cam.ac.uk/news/pathway-towards-IMF a national system for connecting digital assets designed to enable competition on delivery and encourage innovation and development over time style.visibility style.visibility style.visibility style.visibility Foundation Data Model –Top-Level Ontology “Our Foundation Data Model will need to address the questions proper to an upper ontology, which can describe general concepts independent of a problem domain.” The pathway towards an Information Management Framework Background: term-ology The -ology (and – metry ) terms we need -ology: a subject of study; a branch of knowledge - metry : the process of measuring Two senses of ontology Foundational Ontology ontology is: “the set of things whose existence is acknowledged by a particular theory or system of thought.” [1] [1]. E. J. Lowe in the Oxford Companion to Philosophy. Semantic Web Ontology ontology is: an “explicit specification of a conceptualization” [1] a “formal specification of a shared conceptualization” [2] “a formal, explicit specification of a shared conceptualization.” [3] [1]. T. R. Gruber. A Translation Approach to Portable Ontologies. Knowledge Acquisition, 5(2):199–220, 1993. [2]. W. Borst. Construction of Engineering Ontologies. PhD thesis, Institute for Telematica and Information Technology, University of Twente, Enschede, The Netherlands, 1997 [3] R. Studer, R. Benjamins, and D. Fensel . Knowledge engineering: Principles and methods. Data & Knowledge Engineering, 25(1–2):161–198, 1998 More terms – epistemology and agentology {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} ontology what is god-like view – view from nowhere epistemology what is known view from somewhere agentology what is known and done (by the agent-system) view from an agent Approach: Ontology is the foundation. Epistemology/Agentology is expressed in terms of the ontology. Agentology is an expansion of epistemology. It arises from the recognition that one cannot ontologise away all the epistemology (essential indexical) for more see: https://www.academia.edu/35739957/ Ontology and Agentology/Epistemology: A separation of concerns perspective Ontology Agentology/Epistemology Technology ‘Locked’ Zone Application Agnostic Zone Greenfield Zone Application Dependent Zone Computation Dependent Zone Technology Dependent Zone Captures and describes content of the business domain Captures and describes the application’s knowledge of the business domain Specifies the computational design Specifies the physical design BORO Architectural Framework Technology Agnostic Computation Agnostic Business Architecture System Architecture Legacy System(s) No System(s) Business Domain Models Business Application Models Logical Models Physical Models Key Mapping Point Mapping Point Mapping Point Mapping Point based upon the OMG’s MDA separate real world and system concerns Even more terms – mereology and onomatology {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} mereology wholes and parts the study of parts and the wholes they form onomatology names the study of the etymology, history, and use of proper names Approach: Good examples of obvious ‘universal’ patterns Passes the Groucho Marx four-year-old child test: Rufus T. Firefly: Clear? Huh! Why a four-year-old child could understand this report! Run out and find me a four-year-old child, I can't make head or tail of it. Interesting because: clear, obvious, general patterns, also usually are obviously missing from computer information system And even more terms – mereotopology, morphology and geometry {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} mereotopology mereology plus topology adds connections between parts morphology shapes form and structure – includes homology (hole-ology) geometry measurement distance, size, and relative position of figures. Approach: Mereology is a good base, but it needs extending with topology, morphology and then geometry Use a component-based approach to build from the base Background: TLO Survey & Ontological Assessment A Survey of Top-Level Ontologies: A framework To inform the ontological choices for a Foundation Data Model Appendix E: Summary of Framework Assessment Matrix Results 31 ontological choices 37 top ontologies shortlisted and assessed The ontological choices shape the architecture of the ontology Making an ontological assessment Evidence-based Conceptual Prototyping Mining the ontological requirements for a domain For an example based upon UNICLASS see: https://www.academia.edu/44210409 https://www.academia.edu/44326217 or https://borosolutions.net/multi-level-types-uniclass-multi-2020 Ontological Framework Assessment Two useful tools – among many Both can be applied to any data schema (or data) Background: Process Evidence-based Conceptual Prototyping AKA bCLEARer Stages in the process {35758FB7-9AC5-4552-8A53-C91805E547FA} b(e) Collect Collect the datasets in scope in order to establish the broad scope of the process – establishing a bCLEARer master dataset Load Define the detailed scope by selecting from the Collect dataset the data in scope Translate the dataset into the cell-based format – the table paradigm Evolve Reveal the underlying semantics of the Load Dataset – ‘entification’ – in an ‘ entified ’ dataset Mine the ontology from the ‘ entified ’ dataset – the EVOLVE ontology dataset Assimilate Merge the EVOLVE ontology dataset into the full ontology model Reuse Publish dataset in a format suitable for the reuse context bCLEARer – mining ontologies collect load evolve assimilate reuse data collect collect collect increasing semantic maturity reuse reuse Foundational ontology A repeated sequence of processes: increasing semantic maturity Mapping onto Levels of Semantic Maturity increasing value of analytics increasing usage across the enterprise raw data semantic data structured data integrated semantic data reuse reuse collect load evolve assimilate collect load evolve assimilate C L E A R b er collect load evolve assimilate reuse increasing semantic maturity visualizing the mapping to semantic maturity style.visibility ppt_x ppt_y ppt_x ppt_y ppt_x ppt_y ppt_x ppt_y ppt_x ppt_y style.visibility style.visibility style.visibility style.visibility style.visibility Background: FDM Components Space-Time FDM Components - Two in focus Core Foundation Relations (Foundation Extension) Topic 1 Topic 2 For another day Names Topic 1.1 Used for some of the space-time data Space-Time Component (plus Names) Background: Overview – Space-Time Component The Task The task is to develop the framework for a core component of the FDM that focuses on the ontology for objects in space-time. The prime aim of this task will be to illustrate the architecture of this ontology component. This will give people a good understanding of how this component works and establish a firm structure upon which the component can be developed. Two (plus one) broad kinds of objects The focus for this task will be broadly two (plus one) kinds of objects: spatial objects and spatial locations for these objects names Workstreams There are two connected workstreams: the first aiming to build the formal ontological foundations for the two broad kinds of objects, and the second aiming to show how current industry standard schemas and data maps into the FDM component ontology These two workstreams are connected through worldlines and worldline reference frames. The first workstream aims to build up these and the second workstream to use these. There are plans for a third workstream, based upon the first two where deformation over time is looked at. This can be seen as where the ‘shape’ of the spatial object ‘deforms’ relative to its spatial location. We will look at, for example, ISO 10303’s use of change of geometrical shape while preserving topological shape. Overview – Two workstreams First workstream The first workstream will adopt a catholic, component based constructional approach to the foundations. Where practical, the catholic foundation will embrace all the possible normal options. So, for example, it will allow for spaces that are discrete and dense and those that are atomic and non-atomic. It will build up the foundations in components as this architecture both allows for flexibility in composition as well as evolution - this will require a clear understanding of the dependencies between the components. Second workstream The second workstream has identified two source areas and the associated industry standard schemas: CAD geometry as implemented by ISO 10303 Part 42 and buildingSMART’s IFCs and geographic information as implemented by TC 211 (including the INSPIRE data models) and geoSPARQL Two workstreams – breakdown - visualisation First Workstream Foundations CAD Geometry ISO 10303 Part 42 buildingSMART IFC geographic information INSPIRE – OS Open Names geoSPARQL Second Workstream Spatial Objects Coordinates Names First workstream – Foundations: Quick View Space-Time Component First workstream – base components A catholic, component based constructional approach to the foundations of space-time Build from the foundations / ground up. Coordinate Systems dependent upon Worldframes worldframes coordinate systems Fixing how points are labelled Fixing what it means to be at rest spatial structure Cartesian coordinate systems temporal structure temporal metric spatial metric Coordinate frame components and dependencies worldframes xyz -worldvolumes origin wordline temporal direction temporal scale spatial scale Galilean worldtimes xyz -worldvolume directions spatial structure Spherical Polar coordinate systems spatial metric Spherical Polar Coordinate System dependencies worldframes z-axis- worldsheet origin wordline z-centred-worldvolumes spatial scale Galilean worldtimes radial distance z-centred-worldvolume direction origin- apexed -z-cone-worldvolumes origin- apexed -z-cone-worldvolume direction angular metric angular scale temporal structure temporal metric temporal direction temporal scale Second workstream - Overview Space-Time Component Populating the FDM with Standard Sources Data owners populate Standard Sources Populating the FDM with Standard Sources ISO 10303 Part 42 Space-Time INSPIRE populate Top-Level Ontology Reference Data Library OS Open Names Process - Evidence-based Conceptual Prototyping The second workstream process will be Evidence-based Conceptual Prototyping. Data examples for the three areas have been collected and examples of the core object types identified. We will use the bCLEARer approach to empirically conceptually prototype these data examples and their associated schema into a common ontological format. This will identify the implicit semantics in the source schemas as well as any implicit ontological requirements. It will also demonstrate the coverage of the FDM component. Opportunity to demonstrate semantic integration At the level of the two broad kinds of objects (see above) there is substantial overlap between the two source areas in terms of content - though not in structure. This will enable us to demonstrate how the mapping to the FDM component enables similar content embedded in disparate schemas can be semantically integrated into a single schema. Mapping General : Spatial Objects Background There are many standards for the CAD Geometry and geographical information space Mostly, they have no formal unpinning They do not directly map to one another Working out how they map (with no formal underpinning) relies on guesswork and experience General: Core Spatial Objects {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} Core Spatial Object Homology zero-dimensional object one-dimensional object connected, finite, non-intersecting one-dimensional object connected, finite no end-points two-dimensional object connected, finite, non-intersecting three-dimensional object connected, finite, non-intersecting boundary of a three-dimensional object connected, finite, non-intersecting These are the proposed core spatial objects. Simplifying initial assumption, that space-time is four dimensional and hence spatial objects have three or less dimensions. Start with relatively simple ‘shapes’ (homology) as these cover the majority of interesting cases. Part 42 – Mapping: Spatial Objects Mapping Process Identify core spatial objects (see next slide) the basis for the initial mapping Map two transformations (on the basis) Shift from representation to models Remove geometry and topology redundancy Reorient geometry and topology – as classification Collapse redundant geometrical and topological objects ISO 10303 Part 42 core spatial objects {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} Core Spatial Object Geometry Link Topology point point [clause 4.5.3] vertex_point [clause 5.5.4] vertex [clause 5.5.2] curve curve [clause 4.5.23] edge_curve [clause 5.5.7] edge [clause 5.5.5] loop loop [clause 5.5.14] plane (face) surface [clause 4.5.57] face_surface [clause 5.5.21] face [clause 5.5.20] volume solid_model [clause 6.4.1] volume [clause 4.5.89] sphere [clause 6.4.14] volume with faces [clause 5.5.33] closed shell closed shell [clause 5.5.29] In ISO 10303, there are geometric entities ( geometric_representation_item [clause 4.5.2]) and topological entities ( topological_representation_item [clause 5.5.1]). The corresponding core objects are shown in the table below. As is shown some of the core objects typically have both topological and geometric variants, with a linking object . Part42 – mapping: Shift from representation to models Representation => Model Refactoring Part 42 Shift from representation to models Issues Current language talks (mainly) about representations There is informal mention of domains, which are presumably what is being represented, with not much explanation. The definitions do not make clear which constraints arise as a result of the domains and which are introduced to manage the representations. Though some are clearly constraints on the representation not the domain. The mereology (and mereotopology) is implicit The onomatology is also vestigial and implicit – but not such a big issue Goal Eliminate the need to talk of representations Talk instead of models as subsets of objects in the real world. Three representational definitions of one-dimensional objects 5.5.5 edge An edge is a type of topological_representation_item , corresponding to the connection between two vertices. … 5.5.10 subedge A subedge is a type of edge, whose domain is a connected portion of the domain of an existing edge. The topological constraints on a subedge are the same as those on an edge. … Attribute definitions: parent_edge : the edge , or subedge , which contains the subedge . 5.5.11 path A path is a type of topological_representation_item , consisting of an ordered collection of oriented_edges , such that the edge_start vertex of each edge coincides with the edge_end of its predecessor. The path is ordered from the edge_start of its first oriented_edge to the edge_end of its last oriented_edge . … Attribute definitions: edge_list : the list of oriented_edge entities which are concatenated together to form this path .; mereotopology Mapping the definitions to the real-world A simple mapping does not work. A real-world definition A curve is a connected, finite, non-intersecting one dimensional object Then, (in Euclidean space) every curve is an edge, a subedge and a path as: Every curve can be extended so a longer curve, which can be nominated an ‘edge’. Then the initial curve is a ‘ subedge ’ of the extended ‘edge’ curve Every curve can be segmented into ‘edges’ whose fusions is a ‘path’ So the distinctions between the three definitions do not make sense c2 c3 b3 a1 b2 b1 c1 a2 a3 a b c 1 2 3 Two ‘representations’ of the same curves curves real-world view representations real-world path edge subedge edge One Two We take a simple discrete universe, with easily identifiable atoms for our example. The definitions allow the same ‘real-world’ objects to play different roles in different representations. So, they are NOT just about the way real-world is, they are also about the ‘representation’ role the objects play. The curves a2-a3 and c1-b1-a2 are subedges in One and edges in Two. The curve c1-b1-a2-a3 is an edge in One and a path in Two. c2 c3 b3 a1 b2 b1 c1 a2 a3 a b c 1 2 3 One Two Models select objects and allocate them roles (in that model). The same object can play different roles in different models Two ‘models’ of the same curves curves real-world view models mappings … real-world path edge subedge edge A better way to characterize this is using models subedge edge c2 c3 b3 a1 b2 b1 c1 a2 a3 a b c 1 2 3 Models as (mere) subsets of the real-world curves real-world view real-world Let’s add some mereotopology to our universe: mereology - wholes-parts topology - connections If we explicitly recognize the mereotoplogical objects, we can include them in the model. Then there is no need to type the roles/mapping. This reveals that models one and two have, in fact, as they stand, the same content. More generally, with some work, Part 42 representations can be refactored (mapped) into models as subsets of the real-world. connections wholes-parts One Two models For readability, the mappings of the mereotopological objects are not shown. Part42 – mapping: Remove geometry and topology redundancy Remove geometry and topology redundancy Issues Unsubtle separation of geometry and topology Leads to duplication of entities in ‘real world’ Solution Reorient geometry and topology – as classification Collapse redundant geometrical and topological objects vertex-point - schema Representation items have separate classifications for their topological and geometrical properties. What is odd is that the higher levels of the classification (for instance, point and vertex ) have pretty much the same content. vertex-point - data The way the separate classifications are implemented leads to duplication of objects in the model. Part42 – mapping: Reorient geometry and topology – as classification Remove geometry and topology redundancy Make topology and geometry classifications Part42 – mapping: Collapse redundant geometrical and topological objects Remove geometry and topology redundancy Collapse – remove – redundant objects OS Open Names: Mapping Look at two mapping tasks General naming pattern Introducing mereology OS Open Names: Mapping - Names Adding a general names layer New General Names layer OS Open Names: Mapping Mereology Ontological Framework Assessment No explicit abstraction to mereology Mereology (and mereotopology) examples OS Postcode ontology classes Postcode Area http://data.ordnancesurvey.co.uk/ontology/postcode/PostcodeArea An area given a unique alphabetic coding by Royal Mail to facilitate the delivering of mail. The area is identified by one or two alpha characters at the start of the full postcode Postcode District http://data.ordnancesurvey.co.uk/ontology/postcode/PostcodeDistrict A sub-area of the postcode area, specified by the character sub-string within the first half of a full postcode, which may be numeric, alphabetic or alphanumeric; for example, 42 from MK42 6GH or 1A from W1A 4WW. Postcode Sector http://data.ordnancesurvey.co.uk/ontology/postcode/PostcodeSector A sub-area of a postcode district, whose area is identified by the number third from the end of a full postcode. There are approximately 9000 postcode sectors in Great Britain. An example of a postcode sector code is 3, from GU12 3DH. Postcode Unit http://data.ordnancesurvey.co.uk/ontology/postcode/PostcodeUnit An area covered by a particular postcode. Postcodes are an alphanumeric abbreviated form of address. Can infer mereological relations, but these are not modelled OS Open Names: Mapping Coordinates Mapping GM Point and DirectPosition Mapped GM Point and DirectPosition Reify Easting and Northing Coordinate Lines – and recognize the numerals that name them as names. The DirectPostion coordinates are a composite name built out of these. See https://www.academia.edu/39988229/ - https://www.academia.edu/27433806/ - https://www.academia.edu/40373119/ Relations (Foundation Extension) Background The formal unpinning for relations share a common trait with standards in many areas There are many of them The details are not mutually comprehensible They incorporate ‘known’ features Though they may not say they do pima facie Starting issues {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} Feature Description Comment Conversality One relation is the converse of another, when the order of the elements is switched. For example, the converse of the relation 'child of' is the relation 'parent of’ Also called ‘ transposality ’ over-generates – too many relations Symmetricity A relation is symmetric if it remains the same relation when the order of the elements is switched (in other words, it is the same as its converse) over-generates – too many relations Reflexivity A relation is reflexive if, for every element it relates, it relates that element to itself differentiates relations from sets Three features of relations General terminology – binary relations Informally, a binary relation is a relation with two places. For example, ‘x is the father of y’ is a binary relation it can more formally be written as Father (x, y) or F (x, y) or Fxy . We informally talk about the relata as occupying the relation’s places We informally differentiate the places in a binary relation as the left-place and the right-place So, in F (x, y), x occupies the left-place and y the right-place For each place, there is a set of objects that occupy that place – the place domains. More formally, ∀y ∀x Rxy → x ∈ R-Left-Domain ∧ y ∈ R-Right-Domain The union of all the place domains is the relation’s domain. More formally, ∀x ∀y Rxy → x, y ∈ R-Global-Domain General terminology – finitary n- ary relations Informally, a finitary relation (often called an n- ary relation) is a relation with a finite number of places – greater than 1. Binary and tertiary relations are finitary, n- ary relations. We informally talk about the relata as occupying the relation’s finite places If we index the places with numbers, we can say x occupies the n th place in the relation For each place, there is a set of objects that occupy that place – the place domains. More formally, ∀x 1 ∀x 2 … ∀ x m R (x 1, x 2 … x m ) → x 1 ∈ R-1-Domain ∧ x 2 ∈ R-2-Domain … ∧ x m ∈ R-M-Domain. The union of all the place domains is the relation’s domain. More formally, ∀x 1 ∀x 2 … ∀ x m R (x 1, x 2 … x m ) → x 1 , x 2 , x m ∈ R-Global-Domain. More formal definitions {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} Feature Informally More formally (binary) Conversality One relation is the converse of another, when the order of the elements is switched. ∀x ∀y R ( xy ) ↔ R-Converse ( yx ) Symmetricity A relation is symmetric if it remains the same relation when the order of the elements is switched ∀x ∀y Rxy → Ryx Reflexivity a binary relation is reflexive if, whenever it relates an object, then that object is related to itself. ∀x ∀y Rxy → Rxx ∧ Ryy Overgeneration: an issue for interoperability In a single system, where one has governance, one can have conventions to avoid overgeneration (, but in multiple systems, where there are multiple independent governances, it will almost certainly arise For conversality, within a system, one might agree on a particular order for a relation. But this is an arbitrary decision Try guessing a natural order for a selection of relations if you think otherwise System 2 System 1 {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} mother daughter Queen Elizabeth The Queen Mother Queen Elizabeth II Queen Elizabeth The Queen Mother Princess Margaret, Countess of Snowdon {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} daughter mother Queen Elizabeth II Queen Elizabeth The Queen Mother Princess Margaret, Countess of Snowdon Queen Elizabeth The Queen Mother x is mother of y ↔ y is daughter of x Examples Royal Family Blocks Royal Family Examples Scope – Royal Family Example {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} King George V King George VI Prince Edward, Duke of Kent Mary of Teck Prince John of the United Kingdom Katharine, Duchess of Kent Wallis Simpson George Lascelles Princess Alexandra, The Honourable Lady Ogilvy King Edward VIII Patricia Lascelles Angus Ogilvy Mary, Princess Royal and Countess of Harewood Marion Stein Prince Michael of Kent Henry Lascelles Gerald David Lascelles Princess Michael of Kent Princess Alice, Duchess of Gloucester Angela Dowding Queen Elizabeth II Prince Henry, Duke of Gloucester Elizabeth Colvin Prince Philip, Duke of Edinburgh Princess Marina of Greece and Denmark Prince William of Gloucester Princess Margaret, Countess of Snowdon Prince George, Duke of Kent Prince Richard, Duke of Gloucester Antony Armstrong Queen Elizabeth The Queen Mother Birgitte, Duchess of Gloucester Conversality – Royal Family Example System 2 System 1 {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} mother daughter Mary of Teck Mary, Princess Royal and Countess of Harewood Princess Marina of Greece and Denmark Princess Alexandra, The Honourable Lady Ogilvy Queen Elizabeth The Queen Mother Queen Elizabeth II Queen Elizabeth The Queen Mother Princess Margaret, Countess of Snowdon {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} daughter mother Mary, Princess Royal and Countess of Harewood Mary of Teck Princess Alexandra, The Honourable Lady Ogilvy Princess Marina of Greece and Denmark Queen Elizabeth II Queen Elizabeth The Queen Mother Princess Margaret, Countess of Snowdon Queen Elizabeth The Queen Mother Conversality – Mother/Daughter Example x is mother of y ↔ y is daughter of x Overgeneration: two relations for the same single state of affairs Conversality – Mother/Daughter Visualisation Mother/daughter father/daughter Symmetricity – Royal Family Examples Symmetricity – Married To Example {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} spouse# spouse* King Edward VIII Wallis Simpson Prince George, Duke of Kent Princess Marina of Greece and Denmark King George VI Queen Elizabeth The Queen Mother Wallis Simpson King Edward VIII Princess Marina of Greece and Denmark Prince George, Duke of Kent Queen Elizabeth The Queen Mother King George VI … … x is married to y ↔ y is married to x Symmetricity - Married To Visualisation married to married to King George VI Queen Elizabeth The Queen Mother Overgeneration: two relations for the same single state of affairs Symmetricity – Sibling Example System 1 {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} sibling# sibling* Prince Michael of Kent Princess Alexandra, The Honourable Lady Ogilvy Prince Michael of Kent Prince Edward, Duke of Kent Princess Alexandra, The Honourable Lady Ogilvy Prince Michael of Kent Princess Alexandra, The Honourable Lady Ogilvy Prince Edward, Duke of Kent Prince Edward, Duke of Kent Prince Michael of Kent Prince Edward, Duke of Kent Princess Alexandra, The Honourable Lady Ogilvy x is sibling of y ↔ y is sibling of x r1 r3 Princess Alexandra, The Honourable Lady Ogilvy Prince Edward, Duke of Kent Prince Michael of Kent siblings siblings siblings Symmetricity – Sibling Visualisation Overgeneration: two relations for the same single state of affairs s ibling# s ibling* r1 r3 Reflexivity – Royal Family Example Reflexivity – Same Parent Example {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} same parent# same parent* Queen Elizabeth II Princess Margaret, Countess of Snowdon Princess Margaret, Countess of Snowdon Queen Elizabeth II Queen Elizabeth II Queen Elizabeth II Princess Margaret, Countess of Snowdon Princess Margaret, Countess of Snowdon … … x has the same parent as y x has the same parent as y → x has the same parent as x AND y has the same parent as y Reflexivity – Same Mother Visualisation mother/child same mother Princess Margaret, Countess of Snowdon Queen Elizabeth II mother/child same mother as Note: similar to siblings in that it is symmetric but also different in that it is reflexive same mother as same mother as Block Examples Block 1 Scope – Block Example Block 2 Block 3 Block 4 Block 5 Block 6 Block 7 Conversality – Blocks Example System 2 System 1 {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} above below Block 1 Block 2 {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} below above Block 2 Block 1 Conversality – Above/Below Example x is above y ↔ y is below x Conversality – Above/Below Visualisation Block 2 Block 1 above / below Block 1 Block 2 Overgeneration: two relations for the same single state of affairs below / above Symmetricity – Block Examples Symmetricity – Next To Example System 1 {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} next# next* Block 3 Block 4 Block 4 Block 3 x is next to y ↔ y is next to x Symmetricity – Next To Example {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} x x Block 3 Block 4 Block 4 Block 3 x is next to y ↔ y is next to x Symmetricity cancels out conversality Hidden - Needs to be explained Symmetricity – Next To Visualisation Block 3 Block 4 next to Block 3 Block 4 Overgeneration: two relations for the same single state of affairs N- Ary – Block Example N- Ary – Between Example System 1 {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} inside one side other side Block 6 Block 5 Block 7 Block 6 Block 7 Block 5 System 2 {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} one side inside other side Block 5 Block 6 Block 7 Block 7 Block 6 Block 5 System 3 {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} one side other side inside Block 7 Block 5 Block 6 Block 5 Block 7 Block 6 x is between y and z ↔ y and z surround x ↔ y is on one side of x AND z on the other side of x The places ‘one side’ and the ‘other side’ are symmetric. The non-symmetry of the ‘inside’ place and the other places, allows conversality to arise, as is demonstrated in multiple systems. N- Ary – Between Visualisation – System 1 Block 5 Block 6 inside / one side / other side Block 7 Block 5 Block 6 Block 7 Overgeneration: two relations (due to symmetricity) for the same single state of affairs N- Ary – Between Visualisation Block 5 Block 6 inside / one side / other side Block 7 Block 5 Block 6 Block 7 Overgeneration: six relations for the same single state of affairs (due to symmetricity and conversality ) one side / inside / other side one side / other side / Inside