A Framework for Composition: A step towards a foundation for assembly An Introduction 4D SIG Workshop 19 th March 2021 Context: Paper “A Framework for Composition” is being issued soon it outlines ‘a step towards a foundation for assembly’ it : is a contribution to the Foundation Data Model (FDM), which is part of the Information Management Foundation (IMF), which is part of UK’s National Digital Twin programme ( NDTp ) https://www.cdbb.cam.ac.uk/what-we-do/national-digital-twin-programme Context: Paper’s overall aim is to ensure composition (and so the FDM) is built upon a solid foundation at the core of the notion of a component breakdown is the component as an integral (dependent) part of the composite whole this has a rich underlying formal structure – which we describe this, in turn, provides a framework for assessing how well a data model (or ontology) has captured the main elements of the structure enabling both the assessment of existing models as well as the design of new models https://www.cdbb.cam.ac.uk/what-we-do/national-digital-twin-programme Presentation goal The paper is technical with a focus on the rich formal structure of the abstract general component breakdown architecture This presentation provides a short overview of the concerns the paper addresses as such, it provides a simpler introduction to the paper Structure What is composition? How is composition modelled? What kind of formal structure is emerging? The proposed formal structure What is composition? What is a composition structure? Linguistically - some etymologies compose (v.) - … Meaning "to make or form by uniting two or more things" is from late 15c. Sense of "be the substance or elements of, make up" is from 1540s. … from 1650s as "place (parts or elements) in proper form, arrange.“ composition (n.) - late 14c., composicioun , "action of combining," also "manner in which a thing is composed," from Old French composicion (13c., Modern French composition) "composition, make-up, literary work, agreement, settlement," and directly from Latin compositionem (nominative compositio ) "a putting together, connecting, arranging," noun of action from past participle stem of componere "to put together, to collect a whole from several parts," from com "with, together" (see com-) + ponere "to place" (past participle positus ; see position (n.)). composite (adj.) - "made up of distinct parts or elements," c. 1400, from Old French composite, from Latin compositus "placed together," past participle of componere "to put together, to collect a whole from several parts," from com "with, together" (see com-) + ponere "to place" (past participle positus ; see position (n.)). … compound (v.) - late 14c., compounen , "to put together, to mix, to combine; to join, couple together," from Old French compondre , componre "arrange, direct," and directly from Latin componere "to put together," from com "with, together" (see com-) + ponere "to place" (see position (n.)). The unetymological -d appeared 1500s in English by the same process that yielded expound, propound, etc. Intransitive sense is from 1727. Related: Compounded; compounding. compound (n) - "a compound thing, something produced by the combination of two or more ingredients," mid-15c., from compound (adj.). compound (adj.) - late 14c., originally compouned , "composed of two or more elements, mixed, blended," past participle of compounen (see compound (v.)). Of flowers from 1660s; compound eye is attested from 1836; compound sentence, one consisting of two or more full clauses, is from 1772. assemble (v.) - early 14c., transitive ("collect into one place") and intransitive ("meet or come together"), from Old French assembler "come together, join, unite; gather" (11c.), … Meaning "to put parts together" in manufacturing is from 1852. Related: Assembled; assembling. … assembly (n.) - … Meaning "a gathering together" is recorded from early 15c.; that of "act of assembling parts or objects" is from 1914, as is assembly line. participate (v.) - 1530s, "to partake, to share or share in," a back-formation from participation, or else from Latin participatus , past participle of participare "to share, share in, participate in; to impart," from particeps "partaking, sharing," from parti, past participle of partir "to divide" (from Latin partire , from pars "a part, piece," …). participation (n.) - "act or fact of sharing or partaking in common with another or others; act or state of receiving or having a part of something," late 14c., participacioun , from Old French participacion (13c.) and directly from Late Latin participationem (nominative participatio ) "partaking," … also, as an adjective, "sharing, partaking," from pars (genitive partis) "a part, piece, a division" … Philosophically - some history Every individual thing is identical with its separate parts connected into one thing. For example, a man is identical with his head, chest, abdomen, feet, and other parts conjoined. Ciceronis Topica , i , 2.8; Boethius , 1988, p. 39 Boethius, 1988. In Ciceronis Topica , Eng. trans. by E. Stump. Cornell University Press, Ithaca (NY). Whoever attributes existence to this house surely concedes the same to this stone and all the other parts taken together; for this house is nothing other than this stone together with the other parts. Dialectica , v, i , 4; Peter Abelard , 1956, p. 550 Abelard, P., 1956. Dialectica , ed. by L. M. De Rijk. Van Gorcum , Assen. The parts taken together differ only in name from the whole Gottfried Wilhelm Leibniz , Specimen geometriae luciferae , 274 Allness , or totality, is nothing other than plurality considered as a unity Immanuel Kant . Critique of Pure Reason, B 111 The idea is that if there are six things then a seventh thing - the whole they are parts of - exists, and the six things collectively are the seventh thing. p. 579 , Donald L. M. Baxter , 1988. Identity in the loose and popular sense. Mind, 97: 576–582. Examples Composition/Breakdown Structures Artefactual components (my) stacking arm (my) stacking arm components Two interpretations: (1) general and (2) particular . Integral versus temporary/replaceable parts (Partridge, Business objects: re-engineering for re-use, 1996) There is a sense of a part as an integral component, in which the part belongs to the whole. There is an alternate sense of a replaceable (or temporary) part that can not only be replaced but also be used in multiple wholes. This distinction seems to rely to some extent on the notion of time; making a distinction between timeless and temporary parts. integral component replaceable (or temporary) part Consider a car where the tyre is changed Natural components Different wholes, some of the same components. (my) whole body both (my) legs (my) right hand Two interpretations: (1) general and (2) particular . Area Top Level UNICLASS - classic levelled hierarchy … Products Activity UNICLASS Item Object Section Sub group Group … … Opening products Skin products … … … … … … Formless openings products Hardware products Sealants Putties and glazing compounds Glazing joint sealants Edge sealants Ranks level 1 level 3 level 2 Engineering Breakdown Structures Equipment is classified using the EBS Equipment Breakdown Structure (EBS) (Physical) Asset Breakdown Structure (ABS) Equipment Tagging Structure One way to componentize equipment. When a system is designed, the equipment is given a tag (number) which identifies the item. The tagging classification is done at two levels; Tag Format Class, and Tag Class. A two-level hierarchy structure E.g., NORSOK Z-002-DP - DESIGN PRINCIPLES CODING SYSTEM Tag format class: sets out the format for the tag number. Different types of equipment will be tagged in different ways – e.g., instruments will need loop number. Tag class: is the level in the hierarchy you want the tag to show. Its about organising tags Functional Classes – different purpose A different way to componentize equipment. Different cut through the hierarchy for a different purpose. Functional classes are about design. Engineers specify the type of equipment in the design. Functional versus Procurement classes: different purposes Procurement classes are about what type of equipment is bought. Different cut through the hierarchy for a different purpose. Typically, manufactured equipment of a functional type. One procures to the class specified in the design i.e. the functional class. Functional classes are about design. Engineers specify the type of equipment in the design. deprecate Class constraints Disciplines are usually more general than functional classes. There are exceptions Valves can be piping or instrumentation Disciplines are allocated to taggable items For exceptions, the choice of allowable disciples is made at design time. Allocating a discipline is about allocating responsibility for the item. In the general case, the Disciplines are a thin strata through the taggable item hierarchy Manufactured equipment is not (cannot) be allocated a discipline in the exception cases. Complexity and decomposition "The different K-decompositions may or may not give spatially coincident boundaries for some or for all of the parts of the system. ... Far more interesting, however, is the relation between different K-decompositions that apply at roughly the same spatial order of magnitude. Thus, decomposition of a piece of granite into subregions of roughly constant chemical composition and crystalline form, K(T) 1 ; density, K(T) 2 ; tensile strength (for specified orientations relative to the crystal axes), K(T) 3 ; electrical conductivity, K(T) 4 ; and thermal conductivity, K(T) 5 , will produce at least roughly coincident boundaries. The granite is thus descriptively simple relative to these decompositions (see Figure 9.1). By contrast, decomposition of a differentiated multi-cellular organism into parts or systems along criteria of being parts of the same anatomical, physiological, biochemical, or evolutionary functional system into cells having common developmental fates or potentialities, or into phenotypic features determined by common sets of genes, will, almost part by part and decomposition by decomposition, result in mappings that are not 1-1. They are not even isomorphic, much less coincident. This surely involves substantial descriptive complexity." How is composition modelled? Modelling wholes, parts and composition Two formally different approaches Whole-parts typically, a binary relation Composition often a n-to-one- ary relation Wholes-parts - examples The relation is typically binary (ignoring temporalization) In mereology the conventional choice is parthood P, where “x is a part of y” is written Pxy In most TLOs – e.g. (BFO) “b occurrent_part_of c =Def. b is a part of c & b and c are occurrents.” ISO 15926-2 – see Figure 9 below - though this is an outlier in using the term ‘composition’ OPM’s one-to-many participation relation ISO19450: Automation systems and integration — Object-Process Methodology Object-Process Methodology (OPM) is a compact conceptual approach, language, and methodology for modelling and knowledge representation of automation systems. A many (components) to one (whole) relation Note: the use of ‘participation’ implying a list of participants style.visibility style.visibility ISO 16739: IFC4: IfcRelAggregates 4.4.1.2 Element Composition Provision of an aggregation structure where the element is part of another element representing the composite. … The part should not be contained in the spatial hierarchy, i.e. the concept Spatial Containment shall not be used at the level of parts. The part is contained in the spatial structure by the spatial containment of its composite. … Figure 27 — Element Composition This relies on the STEP-EXPRESS language framework for the formal structure. style.visibility UML components In Unified Modeling Language (UML), a component diagram depicts how components are wired together to form larger components The borders of the boxes and the position in the diagram reflects the (implicit) containment relations The borders of the boxes and the position in the diagram reflects the (implicit) containment relations style.visibility What kind of formal structure is emerging? Modelling wholes, parts and composition Two basic structures for wholes-parts / composing relations Structural options A very simple example c b a abc Consider a whole-abc composed of three parts; a-part, b-part and c-part whole-abc a-part b-part c-part whole-abc a-part b-part c-part n:1 approach 1:1 approach whole-first approach ((w) holology ) where a whole is composed of its components whole and part neutral approach links each part (independently) to its whole(s) Two basic formal structures There seem to be no examples of (or obvious requirements for) of a n:1 parts-first approach ( partology ) – so we do not pursue this Each relation can be taken on its own. style.visibility (possibly) heterogeneously immediate abc a b c ab bc ac a mediate part an immediate part homogeneously immediate abc b a c only immediate parts Formal structure: Homogeneously or heterogeneously immediate both mediate and immediate parts cover partial cover partial separation separation x abc x x Formal structure: n:1 approach: Components cover the composite a b c a b c a b c a b c disjoint overlapping inside b a b a b a common part Formal structure: n:1 approach: Components typically don’t overlap What kind of formal structure is emerging? Composition structure tree breakdown structure (homogeneous immediate parts) is in a context – e.g., classes or individuals within this context: nodes have single (or no) parent and many (or no) children) multiple ways to breakdown – multiple local breakdowns breakdowns are complete (components cover the composite) at each level, the components are disjoint (components don’t overlap) Seems to be a restriction of the context’s whole-part structure What kind of formal structure is emerging? {5C22544A-7EE6-4342-B048-85BDC9FD1C3A} compositions wholes-parts multiple ways to breakdown – multiple local breakdowns single global structure breakdowns are complete (components cover the composite) individual whole-part relations – no (w)holology nodes have single (or no) parent and many (or no) children) nodes have multiple (or no) parent and many (or no) children) tree breakdown structure (homogeneous immediate parts) lattice structure (homogeneous immediate parts) at each level, the components are disjoint (components don’t overlap) no levels, no constraint on overlap two compositions the same if they have the same wholes-parts two wholes-parts the same if they have the same whole and the same part Typically, compositions and wholes-parts are siblings in a context/domain – e.g., classes or individuals. Within that domain, there are these differences: composition can be seen as a restriction of whole-part structure and conversely whole-part a relaxation of the composition structure style.visibility Wholes-parts relation to composition Two complementary structures In general, if a domain has a kind of (flat) part structure then it also has the potential for a sibling (hierarchical) composition structure Or vice versa, if a domain has a kind of (hierarchical) composition structure then it also has the potential for a sibling (flat) part structure Examine the first case, starting with a (flat) part structure … Visualise a whole-part lattice structure Note: this shows the transitive reduction – to a certain granular level – to keep things manageable style.visibility style.visibility style.visibility Given a whole-part structure: How to pick out a composition Start by picking the broad levels – setting the granularity Then pick the compositions style.visibility style.visibility The proposed formal structure Quick version A simple constructional process Every operation composing some objects into a whole has an associated ‘atomic’ composition that can be dissected into corresponding set of wholes-parts relations where the fusion of the component parts is the composite whole. Relating ‘atomic’ compositions separated, transparent opaque abc a bc b c bc atop relation overlapping, transparent abc a b c bc Relations reflect compositional history an ‘atop’ directed graph The resulting ‘atop’ hierarchy The hierarchy (graph) reflects all the possible histories. The typically graph would be significantly more bushy than this. Hierarchies as particular compositional histories With the atomic compositions in place, the building of the hierarchies can start. Each hierarchy is a segment of a history for the ‘last’ atomic composition. One can visualize the history built up one atomic composition at a time – as shown on the left. Visualising possible component hierarchies/histories Or, less operationally, one can visualize it as selecting connected ‘trees’ from the atop graph – as shown on the left here. Note, one must make sure the branches are for different components. abc a ab c b ac bc abc abc+d a+b ( a+b ) +c a+b +c abc d