Introduction – BORO Solutions Limited Chris Partridge Dagstuhl Seminar 17492 "Multi-Level Modelling" 3 rd – 8 th December 2017 About BORO - Summary BORO Solutions (BORO Engineering) - www.borosolutions.net Small company – currently 6 staff plus associates Incorporated in 2002 (2006) Research-led company Focus on radically improving information systems' semantics using ontology Made significant R&D investment (over £50m) Developed and deployed top ontology (BORO) and associated methodology ( bCLEARer ) Major Sectors Financial, Defence and Energy 2 BORO Foundation 3 Core global objects – e.g. type. Cross business objects – e.g. cost Domain specific objects – e.g. contact lens brands bCLEARer Methodology (an example) 4 Draft analysis of effort 5 Work Package Type 6 Selecting the chunks 7 An Example of Current Work MLM as higher order types have been central to the BORO Foundational Ontology since the late 1980’s. As in much MLM work, this has included an interest in other structural/compositional relations – such as whole-part or mereology. In the four or five years, largely as a result of research into Kit Fine’s work, we have been developing an inclusive framework for the family of levelling structural/compositional relations, more specifically that: There is a family of compositional relations that provide a metaphysical structure for ‘reality’ That at base these include mereology and instantiation That generalisation is (metaphysically) derivative from instantiation Position is laid out in paper: Developing an Ontological Sandbox: Investigating Multi-Level Modelling’s Possible Metaphysical Structures Overall goal is a general theory of multi-levelling "A single concretization hierarchy of m-objects (or m-relationships) combines and differentiates multiple classification- , generalization-, and aggregation-hierarchies." 8 Context - MLM Concerns in Focus Conceptual models typically have multiple hierarchies (such as classification, generalisation and whole-part); what are these, how are they linked, and how should they be organised into levels and modelled? Ontology is part of the answer: These hierarchies are (at least) sometimes ontological. We present a view that these hierarchies are all varieties of a more general whole-part hierarchy. Classification and generalisation seem to be linked; MLM often explains their differences as reflecting the different ontological natures. In the view presented here, classification is shown to be more fundamental than generalisation; that generalisation is derived from classification. Classification is levelled in a different way to generalisation and whole-part. In the view presented here, this is explained as a result of different identity principles. 9 Fine’s Constructional Ontology Framework Based upon constructors generating objects (rather than logic). Fine sees the advantage of his framework is that it naturally reveals the underlying metaphysical structure of reality. As an example, he comments on levels : “there is an intuitive distinction between wholes which are like sets in being hierarchically organised and those which are like sums in being ‘flat’, or without an internal division into levels. The distinction, under the operational approach, can be seen to turn on whether repeated applications of the operation are capable of yielding something new.” He talks about its power and beauty; its ability to provide a single and elegant account of a variety of structures. Built using Constructional Ontology framework from: Fine, K.: The study of ontology. Noûs . 25, 263–294 (1991). Fine, K.: Towards a theory of part. The Journal of Philosophy. 107, 559–589 (2010). 10 Constructional Ontology Constructional Ontology – What is it {21E4AEA4-8DFA-4A89-87EB-49C32662AFE0} Acronym Domain Names for Members B basis domain bases, givens, basic elements or given elements C constructor domain constructors E constructed domain constructs or constructed elements Constructed Domain Basis Domain Constructor Domain 11 Can characterise an ontology with just the basis and constructor domain. Construct the constructed domain. style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility Characterising Constructors (Fine) {21E4AEA4-8DFA-4A89-87EB-49C32662AFE0} C Collapse ∑(x) = x If Collapse holds then any whole composed of a single part is identical to it. L Levelling ∑(… ,∑(x, y, z,...),… ,∑(u, v, w,...),...) = ∑(… , x, y, z,… ,… , u, v, w,… , ...) If Levelling holds then when the parts of whole have parts, these parts’ parts are also parts of the whole. A Absorption ∑( … , x, x, … , … , y, y, … , … ,) = ∑( … , x, … , y, ...) If Absorption holds then the repetition of parts is irrelevant to the identity of the whole. P Permutation ∑(x, y, z, ...) = ∑(y, z, x, ...) (and similarly for all other permutations) If Permutation hold then the order of the parts is irrelevant to the identity of the whole. CLAP (formal identity) principles {21E4AEA4-8DFA-4A89-87EB-49C32662AFE0} Profile Whole Example Parts-to-Wholes Constructor Example Wholes-to-Parts Constructor CLAP Sums SUM-BUILDER SUM-DECOMPOSER CL AP Sets SET-BUILDER SET-DECOMPOSER CL AP Strings STRING-BUILDER STRING-DECOMPOSER CLAP Sequences SEQUENCE-BUILDER SEQUENCE-DECOMPOSER Some possible forms of composition 12 Ontological Sandbox: Building up the SIMPLE Ontology {21E4AEA4-8DFA-4A89-87EB-49C32662AFE0} Ontology Acronym Basis Domain SET-BUILDER SUM-DECOMPOSER Includes Analysed in Paper NULL NULL NO NO NO None NO Simple Basis only SB YES NO NO NULL YES SET-BUILDER only SET NO YES NO NULL YES SUM-DECOMPOSER only SUM NO NO YES NULL NO SET-BUILDER and SUM-DECOMPOSER SET+SUM NO YES YES SET, SUM NO Simple Basis plus SET-BUILDER SB+SET YES YES NO SB, SET NO Simple Basis plus SUM-DECOMPOSER SB+SUM YES NO YES SB, SUM YES SIMPLE SIMPLE YES YES YES SB+SET SB+SUM SET+SUM YES 13 SET E NULL U SUM P SB P U E SIMPLE P U SB+SUM P E SB+SET U E SET+SUM Ontological Space Evolution (Item Dependency) - SIMPLE 14 Ontological Space style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility SET E NULL U SUM P SB P U E SIMPLE P U SB+SUM P E SB+SET U E SET+SUM Ontological Space Evolution (Ontology Dependency) SIMPLE 15 Ontological Space style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility SIMPLE Ontology 16 SIMPLE Constructional Ontology Ontological Space Basis Domain Constructor Domain P U E {21E4AEA4-8DFA-4A89-87EB-49C32662AFE0} Domain Domain Members basis domain P = Simple Basis constructor domain U = SET-BUILDER, and E = SUM-DECOMPOSER Example: SINGLETON STRICT and TOLERANT MetaModelling 17 Definition: Strict Metamodeling Strict Metamodeling : In an n-level modeling architecture, M 0 , M 1 , ..., M n−1 , every element of an M m -level model must be an instance-of exactly one element of an M m+1 -level model, for all 0 ≤ m < n − 1, and any relationship other than the instance-of relationship between two elements X and Y implies that level(X) = level(Y). in Atkinson, C. and Kühne , T. (2002): Rearchitecting the UML Infrastructure. In: ACM Transactions on Modeling and Computer Simulation, Vol. 12, No. 4, October 2002, pp. 290-321 18 Varieties of Violations of Strictness 19 Gitzel , R. and Merz , M. (2004), How a Relaxation of the Strictness Definition Can Benefit MDD Approaches With Meta Model Hierarchies, In: Proceedings of the 8th World Multi-Conference on Systemics , Cybernetics and Informatics (SCI2004) , 19-21 July, 2004, Orlando, USA, International Institute of Informatics and Systemics (IIIS), 62-67. style.visibility SINGLETON Ontologies 20 GENERATION-SINGLETON Constructional Ontology Ontological Space Basis Domain Constructor Domain 0 G {21E4AEA4-8DFA-4A89-87EB-49C32662AFE0} Domain GENERATION-SINGLETON Domain Members STAGE-SINGLETON Domain Members basis domain 0 = Singleton Basis 0 = Singleton Basis constructor domain G = GENERATION- SET-BUILDER S = STAGE- SET-BUILDER STAGE-SINGLETON Constructional Ontology Basis Domain Constructor Domain 0 S Ontological Sandbox: Generation versus Stage SET-BUILDER {21E4AEA4-8DFA-4A89-87EB-49C32662AFE0} Level 0 1 2 Singleton Basis plus GENERATION-SET-BUILDER 0 A = {0} B = {A} Singleton Basis plus STAGE-SET-BUILDER 0 0 + A’ = {0} 0 + A’ = {0} + B’ = {A’} + M = {0, A’} Singleton Basis plus GENERATION-SET-BUILDER Singleton Basis plus STAGE-SET-BUILDER 0 Level 0 Basis 0 M Level 2 B B’ Level 1 A A’ G S G S S 21 style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility style.visibility Hierarchy View: Generation versus Stage SET-BUILDER 0 A B 0 A’ B’ M Note: instantiation will ALWAYS cross ALL lower levels Level 0 Basis Level 1 Level 2 22 Singleton Basis plus GENERATION-SET-BUILDER Singleton Basis plus STAGE-SET-BUILDER Reasons for choosing one of the approaches: Pragmatic - GENERATION-SET-BUILDER provides a more componentised structure. Foundational - STAGE-SET-BUILDER has a simpler, less ad hoc, generation. How to motivate the restriction of application from stages to generations? style.visibility Look In The Paper See how: one can use this sandbox to build up an understanding of the target ontology in steps through ontological space, the constructional approach exposes the underlying compositional metaphysical structures of ontologies; for example how set-inclusion hierarchy is derived from the fundamental set-membership hierarchy’s constructor, familiar hierarchical structures, such as taxonomies and component breakdowns, can be derived from more fundamental structures. 23 Summary Constructional ontologies New, more explanatory way of formalising ontologies by generation from constructors. Ontology sandbox Tool for analysing a range of constructional ontologies. Good at exposing the nature of ontological levels. Strict or tolerant metamodelling SINGLETON example We have provided a clear picture of the trade-off between order and expressiveness that drives the choice of strict metamodelling (effectively a generation level hierarchy) – as well as an alternative – stage level hierarchy. 24 Questions 25