We are exploring an approach to a "universal upper ontology" that is defined in terms of general principles instead of specific definitions. Rather than attempt to define objects in a domain-specific list, we want to explore creating a synthesis of fundamental principles from mathematics and semantics -- on the basis of which any domain-specific ontology could be defined. We are also considering how every concept or term or object in this framework can also be defined using this same method or protocol. Definition Uses of foundational ontology Challenges to foundational ontology Top level - numbers - pure form of order The continuum and binary numbers

Definition Placeholder | Back Foundational ontologies are attempts to systematise those categories of thought or reality which are common to all or almost all subject-matters. Commonly considered examples of such categories include ‘object’, ‘quality’, ‘function’, ‘role’, ‘process’, ‘event’, ‘time’, and ‘place’. Amongst existing foundational ontologies, there is both a substantial measure of agreement and some dramatic disagreements. There is currently no uniform consensus concerning how a foundational ontology should be organised, how far its ‘reach’ should be (e.g., is the distinction between physical and non-physical entities sufficiently fundamental to be included here?), and even what role it should play in relation to more specialised domain ontologies. The purpose of this workshop is to provide a forum for researchers and stakeholders to present work on specific foundational ontologies as well as their relations to each other and to the wider ontological enterprise, but also topics related to foundational questions in ontology engineering https://foust.inf.unibz.it/foust5/ Fri, Apr 23, 2021

Uses of foundational ontology Placeholder | Back Foundational ontology is about categories of reality or thought which are common to all or almost all subject-matters. Commonly considered examples of such categories include ‘object’, ‘quality’, ‘function’, ‘role’, ‘process’, ‘event’, ‘time’, and ‘place’. There are several foundational ontologies that provide a systematic formal representation of these categories, their relationships, and interdependencies. Amongst existing foundational ontologies, there is both a substantial measure of agreement and some dramatic disagreements. There is currently no uniform consensus concerning how a foundational ontology should be organised, how far its ‘reach’ should be (e.g., is the distinction between physical and non-physical entities sufficiently fundamental to be included here?), and even what role it should play in relation to more specialised domain ontologies. The main use of foundational ontologies is as a starting point for the development of domain ontologies and application ontologies. A foundational ontology provides an ontology engineer with a conceptual framework that enables her to analyse a given domain, identify the entities in the domain as specialisations of the generic categories in the foundational ontology, and often reuse relationships (e.g., parthood) from the foundational ontology. The utilisation of foundational ontologies for the development of domain and application ontologies has two main benefits. Firstly, the ontology engineer can reuse an existing set of well-studied ontological distinctions and design principles instead of having to develop an ad-hoc solution. Secondly, if two domain ontologies are based on the same foundational ontology, it is easier to integrate them. http://ceur-ws.org/Vol-2708/preface.pdf Fri, Apr 23, 2021

Challenges to foundational ontology Placeholder | Back While the use of knowledge bases is rapidly gaining industrial interest, ontologies are by and large still a fringe technology in most industries. A major impedi9 ment for industrial uptake is often attributed to the lack of scalable knowledge engineering tools and methodologies. Moreover, the development, maintenance, and use of knowledge bases and the tools and methods that are built to support these tasks usually require considerable specialist training. Enterprises that wish to explore the benefits of using semantic technologies will likely lack the necessary competence and will find that there are a few off-the-shelf ontologies, tools, and methodologies that fit their existing system architecture and information flow. The SKALE workshop wants to attract and stimulate novel research and innovative advances of semantic technologies with the aim of making these technologies more easily accessible to and useful for modern data-driven industries. The workshop also wants to investigate where the real world problems are, and where and what are the current show-stoppers for efficient large-scale deployments of ontology-based information systems? ********** MAINTAINING MODULAR SEPARATION In the area of ontologies for Knowledge representation and reasoning, knowledge is rarely considered as a monolithic and static structure: partitioning knowledge into distinct modular structures is central to organize knowledge bases, from their design to their management, from their maintenance to their use in knowledge sharing. Moreover, keeping knowledge in separate modules is essential for representing and for reliable and effective reasoning in changing situations. Finally, evolution of knowledge resources, in terms of updates by newly acquired knowledge, is an important factor influencing the meaningfulness of stored knowledge over time. Considering these emerging needs, the International Workshop on Ontology Modularity, Contextuality, and Evolution (WOMoCoE) offers the ground to practitioners and researchers to discuss current work on practical and theoretical aspects of modularity, contextuality and evolution of ontology based knowledge resources. http://ceur-ws.org/Vol-2708/preface.pdf Fri, Apr 23, 2021

Top level - numbers - pure form of order Placeholder | Back Put this at the top -- straight line across the top line integer order analog-to-digital conversion at the edge then -- arithmetic -- then boolean descending blocks to create 1) all logical structures 2) all semantic structures (??) then the synthetic dimensional theory of semantics and word parsing for the construction of all semantic meaning Fri, Apr 23, 2021

The continuum and binary numbers Draft | Back The general thesis is Everything emerges from the continuum (real number line) when it is differentiated in its most primal way, through binary numbers -- 0's and 1's alternating as primary differentiations. The capacity to make any sort of distinction/differentiation whatsoever -- a "difference that makes a difference" -- a "jnd" -- a "just-noticeable difference" All logic, all mathematics, all numbers, all description, all construction of abstract objects, begins with this definition This project is "digital" -- which means it is inherently quantized at every point "every point" is essentially a matrix cell -- and boundary value intersection in X and Y Binary arithmetic is yin/yang Yin/yang is opposites -- how do we diagram those oppositions See Leibniz Is the continuum "one sided"? Is it "figure/ground"? It is digital and quantized It can construct every number It can construct every word We are lining up an approach for fundamental definitions, and this may be part of that. Natural number, binary number. How do they fit together as derived from or defined in terms of the continuum? From this basis we want to define all types of numbers -- and from there -- the quantization of synthetic dimensions -- qualitative dimensionality defined by stipulation. Consider the Peat/Bohm discussion of category formation, and how "birds are distinguished from squirrels" -- and how are these differences noted or symbolically represented? In what sense is the distinguishing difference binary -- or involving "opposites"? How does "figure/ground" involve "opposites"? There emerges a line of separation -- a boundary -- maybe in many dimensions (squirrels and birds are different in many ways) But maybe it starts very simple -- some fly, some only jump from branch to branch How is that cognized? Tue, May 11, 2021 Reference In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language. URL https://en.wikipedia.org/wiki/Binary_number