Re: [ontolog-forum] Semantic Systems

["Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>]

Frank,

 

Thanks for the glossary of folding operations.  I think your exploration of reality proceeds in a different way than mine does, however.  I can’t quite identify with the word “folding” without more formal definitions, i.e. I would like to see the mathematical underpinning of whatever a “folding” is. 

 

Thanks,

-Rich

 

 

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

 

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From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of FERENC KOVACS
Sent: Saturday, July 11, 2009 11:38 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Semantic Systems

 

Rich,

Let me answer some of the questions economically from my point of view. I know that it is difficult to align thinking especially between you equipped with the knowledge and terminology of Formal Logic and me coming from a different background but very keen on alignment of thinking  done along different disciplines

I have written a pamphlet on folding operations and I am pasting a glossary of the terms that I am using that need some pondering. I hope we are getting closer that way.

Sincerely,

 Frank

http://www.firkasz.com/e107_files/downloads/semantics.pdf

Originally the list of words defined below and used in science are meant to indicate compartments in separate branches of interests/fields of study on cognition or thinking and thoughts, but they appear to have no such boundaries of application, as they all can be attributed to some mental function, such as reasoning, feeling emotions, exercising free-will or otherwise. So in fact, we are likely to end up with a unified or harmonised picture of the workings of the brain as opposed to seeing it as being active in various disparate areas all performing independent or distinct functions, compared to a hierarchically structured computer.

The words or the vocabulary to be used here in order to define the words or concepts listed below will rely on the definition of meaning to be read first. From that on all definitions will be obvious and even easy to remember.

Abstraction is a folding operation from an O going to P

Association: is an unqualified connection. Very close to perception level and emotional overtones.

Classifying objects: Objects have many properties, none of them will describe an object entirely. If a property is typical of an object and makes it possible to identify the object from the rest of the objects, then it is called a quality. Each object has one such quality, it is specific, not typical of any other object.

Classifying properties: a) Each property is typical of a set of objects. That set will define the extensity, or the extentionality of the property. The very same property in different objects differs in terms of intensity. This is called intensity and is expressed as a figure/number or a quantity/plurality. b) A property may have more than one dimensions. A property with linearity such as length, weight, etc. will change along that line only in intensity. A property with two dimensions will change in terms of two relationship/aspects. Example is a vector that can change in terms of its direction and its absolute value. A property with three dimensions or n dimensions is capable of changing in three aspects. A property with n dimensions may be broken down into single dimension properties. Some properties may not have dimensions at all – they display a point like or null dimension property. such property have no quantitative features.

Classifying relations:  a) The number of objects that may feature a relationship may be either indefinite, or definite. b) Relationships may be point-like (zero dimension), linear and n-dimensional. c) There are internal and external relationships. On the basis of qualities you have internal relationship, on the basis of minor features you have external relationship. d) A  relationship is a property. As a property it may have intensity. Not all of them have intensity, like in a relationship between a father and a son. e) There are also total and partial relationships. There are a set of relationships between two objects. If the properties that form the basis of a relationship covers all the properties of the objects in relationship, then this relationship is specific for that object. This relationship is called a total relationship. f) Relationships may have many properties. None of them will describe a relation entirely. If a property is typical of a relationship, then it is a quality of relationship. Each relation has such a quality.  g) Relationships are classified in terms of meeting the criteria of Reflexivity, Symmetry, Transitivity, Functionality, and Inversion.  h) Relationships may have/feature two variables, three variables, etc.

Concrete concepts: (a misnomer) there is no such thing as a concrete concept. All concepts are abstract, and in any case, they are always named by a label or a name (in the end a noun of some sort.)

Connection: the assumption that ideas are connected, without knowing the actual (neurological) nature of such connections that look pretty stable and allow us to build up trains of thoughts, for instance. Now it is not immaterial what sorts of connections a man is engaged in constructing. Temporal and causal connections, for instance present problems. Temporal connections do not seem to be supported by perception, while causal connections are not obvious at all, especially if no direct experience is involved. Connectedness and connectivity are important properties, For their meaning, see the relevant entry words.

Context: a relation of the object (meaning) with a property of variable content. Context is often deemed to be a background, a frame of reference, pragmatics, or anything that completes the meaning of a verbal phrase. If you think of anything devoid of any context, that is if you consider something as a non tangible (abstract) and unique entity, then you end up with the concept of one, a totality, or a whole or a number, in other words a form without content.

 

Creation: is a folding operation.

Direction: a property of an object called order. Also a linear property. (It has a property called linearity, or one dimension. It is the property of a directed graph.)

Exposition is a folding operation starting from a special object called nothing and going to an object.

Existence is a relation between any object and its properties

Extension is the quantity or  extent (determining the specific classes or individual instances) indicated by or related to the object

Formalisation is a folding operation starting from R and ending in O.

Idea: a triplet (ORP) , or the smallest unit of articulated abstraction in the mind. A triplet consists of an object, a relation and a property, that is ORP for short. All those entities are abstract beings and therefore need to be visualised in some familiar form. I have chosen the vertexes and the edges of a triangle. Another possible visualisation is a water molecule with one Oxygen atom and two Hydrogen atoms closely bundled together. The vertexes are called O, R and P respectively, whereas the edges are called various mental operations on the triplets, and are not abbreviated. See the meaning of (Folding) Operation 

Illustration: is one of the folding operations of the mind starting from the vertex O and arriving at the vertex R. Its meaning is parallel with that of Formalisation and Examplification.

Intelligence: the capability, principle and strategy of a living being to proceed on non collision course, such as in communication, thinking, etc. Also called as adaptation to the environment as the practical application of such behaviour  has the property of adaptation or continuous adjustment while moving in space (living)

Intension of an object is a way of measuring or enumerating all the properties of an object.

Interpretation is a folding operation starting from R going to O, the reverse, the opposite or the counterpart of Formalisation

Isolation is a folding operation starting from P and ending in O.

LORP[1][1] is a set of ontology language elements called lean that solves the problem of foundation ontology, it has in its core a triplet, that of object, relation and property defined in relation to one another in a recursive fashion. The purpose of this language, however is to provide a menu of what is known, a device to continuously update this body of knowledge representations, and to serve as a retrieval system for those, who do not know a subject well enough, or want to make progress and at the same time record a copy of their advance in a subset or replica of the total LORP ontology system. Since the knowledge constituents are interconnected and comprise an open system the boundary of which the state of the art knowledge in any field or discipline covered by the system, this system, if and when implemented is at the same time a repertory of the consolidated knowledge of humankind similarly to a Bill of Materials processing system used in manufacturing. In manufacture, similarly to composition. you start off from materials that need to be used as is, parts and assemblies to build a family of products where such elements are identified by numbers, making it thereby possible to have different textual language mutations of the same product structure and its variations, and to serve as a multilingual dictionary arranged in a thesaurus pattern and also reflecting at the same time the process of thinking and capable of producing, recording, etc. new concepts as the need arises. The difference in various language mutations will show where reality is chunked in a different manner, where the formation of words and naming practice are lagging behind current need, or where other problems of translation or I should rather say, conversion between languages based on LORP triplets and twin concept chains (e.g. form and content, specific and generic) as connected to various syntax level implementations needs fixing or enhancement.

How does an object, a property and a relation become its counterpart? Well, they are all related, and they become the other one as a special case. All the three categories are relative, quality defined, and have the nature of an object. Objects are relative, because they do not exist without being in relation to other objects. You cannot isolate an object from its relations. Changing the relations will change the object itself. This is due to the fact that objects have properties and properties are a special case of relation. Relations describe a set of objects, relations being a system together (see synergy). (The same is true of properties.) Thus relation may also be conceived as an object. Relations may be broken down into (other) relations, hence they are a system of relations, but in an extreme case a relation is a single element (singularity). Since a relation is a property, a system of relations is nothing, but a system of properties. A relation as a system of other relations is then a special case of objects. A relation as an object is described as something with specific features/properties. Quality may be deemed of as an object. We know that every object has properties. Those properties again have properties. When you name a property, you use/make a noun: whiteness, prudence, etc. so a particular property taken on its own is an object. Thus a property is a special object, a special case of relation. There are no relations outside, or independent of objects. Neither are properties possible without objects. And even objects cannot be deemed without other objects (including themselves).

The indication of a relation is a verb, or in other words a verb is a relation symbol. (There is a special verb called copula that is often omitted.) But some say that in NL relations are usually expressed by adjectives: Examples: Equal, friendly, concurrent, and any number can be generated. This is not true, because the relation expressed with those adjectives is existence (may be or may not be indicated by a copula), and those adjectives are the properties of the object(s) or their relation (existence). Nouns are also used to describe relations, but this vocabulary is not rich, and uses circumvention. E.g.  A rabbit and a wolf relation.

When a noun is in focus, you have cardinality one. When a verb is in focus, you associate it with a subject and an object (cardinality 2) as well. The subject and/or the object are called argumentum. See more under the relevant entry words.

 

Meaning: the meaning of an object as identified by a word or longer phrases or clusters) is a fully fledged LORP, plus context. A fully fledged LORP would have several relations, and in turn, each relation would have several properties attached to it. An object (as a concept) has intension and extension, which are inversely related, they are the particulars that constitute the meaning (specification) of the object complete with context. The meaning of the meaning is a relation between the form of an object (the name, the word) and its content (context). The more context is available to the speakers, the shorter the name of the object should be to remind the speakers of the object (of reality) in question, and vice versa.

Object: An object is a substantial, or abstract entity (singularity) in your focus of attention created by “zooming” on a particular singularity. An object may also be termed as a “system” of qualities. a) The one and the same object is the one and the same system of qualities. Different objects are different systems of qualities. b) Two objects are identical, if any change in the quality in one object will induce the other object change likewise. c) Objects seem to have greater autonomy than properties or relations. You can always talk about an object on its own, but a property shall always be the property of some other entity (object), and a relation will always be a relation between two entities (such as objects).

It is interesting that the word “object” means something that obstructs your sight, by being on your mind. And in the word “reality” you have the Latin stem “res” meaning a thing, or an object… (Obviously, we have spatial relationship in the working revealed here.)[2][2]

 

d) The interrelation of properties with objects and relations is seen in the fact that objects and relations are of quality type, or they feature a quality. An object cannot be separated from its qualities. An object has no foundation without qualities. By removing all the properties of an object, you will destroy the object itself. The claim that an object is of quality nature follows from the fact that an object is a system of qualities. But this quality of the object itself is an object, and thus it has qualities. This generates infinite regression, which should be no problem. e) It is false to assume that a part of a whole will have fewer properties than the whole. Every object has an unlimited number of different qualities. f) An object has a property to cause another object to display one feature or another, and that capability is also a property.  It is a property that causes various objects to become a system, making it thereby a relation. Thus an object may also be conceived as a relation. g) An object being of quality nature means that a relation is also of quality nature. A relation is said to be of quality nature, because it is a special case of an object. There are no relations without properties. This is why there are sciences out there studying the properties of relations. h) An object (a system of properties) conceived as a property (Properties are features or attributes) is itself a property. i) Object=>system of properties=>property: a special case of property. j) If an object is the totality of an infinite number of properties, then the class of objects characterised by the object is a single entity, or an object of its own class. k) An object may be the property of another object means that the subject of a proposition VP be reversed, and the subject will become the predicate. This is seen when an adjective is used as a noun (the poor) or in other examples. Poverty expresses a property as an object, poor expresses an object as a property. l) You can focus on a property and a relationship and conceive them as separate entities, but when you treat them that way, you treat them as objects. This means, that conceiving reality has something to do with conceiving “something” as one entity (a whole), a thing existing on its own, standing alone, or in fact a synergy. To put it in other words we have a tendency to deal with one thing at a time (object in focus), although we are aware of its dual nature (context, or domus around the focus) and can shift between the two, if they are in proximity relationship. If they are wide apart, then it is difficult to have two objects in focus, or more precisely, to have two focuses. (Despite the fact that our eyes seem to work that way, each with a slightly different point to focus on when reading)

 

Ontology: a field identified by the way of analogy as a model of the world and human knowledge devised to make a computer behave or act as an intelligent man in a particular area of practice or field of study. Now it is also a part of an effort to replace nomenclatures and the system of descriptors as well as to process NLs.

Operation (folding): a short mental activity, “a kind of step taken by the brain” by folding from one vertex to arrive at another vertex. An operation is a triplet itself, as long as it is a word that is three faceted. Three faceted means that the name of an operation indicates an embedded object, relation and a property.

Origo: a reference point for an object to come into existence in space described in terms of coordinates

Order is - as a relation between two non-equal quantities, such as two real numbers. As an object, it has the property of direction. As a property it is the quality of order as opposed to unsorted, chaotic, or disorderly.

Proposition: A proposition is an idea, containing an object, a relation called existence and a property. So in place of the traditional SP and the truth tables in formal logic, you have a more flexible formula with a number of other properties to test for existence, such as:  authentic, complete, correct, credible, equivalent, faithful, fit for the purpose, genuine, professional, reliable, relevant, suitable, timely, to the point, true, valid, valuable, you name it.

Projection: a parallel operation with illustration

 

Property: a) A property is common in all members of a class. b) Properties are of two kinds:

Group 1 properties show the limits (contain constraints). If they disappear, the object itself will disappear.  So they are substantial (not substance) properties. The constraints here are not the same as the specifics of an object, though.

Group 2 properties are simple properties. They do not delimit objects. c) Properties are relative. The relative nature of properties is clear, if they are considered to be a relation. Property as a relation is a special case of relations. The same thing will display different properties, if it is in a different relation. Properties are also relative, because they are related to a relation. Properties are impossible without their relation to other properties and objects. This follows from the fact that a property is deemed to be an object, and an object is relative. All properties of an object are relative (even mass is).

 

Quality: a) Quality is the essence (substance) that makes an object (entity) what it is. b) Quality is absolute. c) The number of qualities of an object is endless. d) An object can survive without some properties, but cannot without its quality. e) A quality is typical of the whole, a property is typical of a part. f) A quality is inherent, a property is relative. g) A quality itself is a property, and it is relative just as any other property, i.e. it does not depend on the object that it is a quality of, but on other objects associated with that object. g) A particular quality may be the property of different objects, and vice versa. It is quality that makes a difference among objects.

Or, what quality is for one object, it is a property for another. (Example: a particular competence to do something may be different subject to who has that competence: an amateur or a professional. h) A quality is not complete specifics. The complete set of qualities is what you call the specifics. h) Therefore quality has another sense too. If two substantial properties make up a quality, then the two properties combined will again be a substantial property. i) The quality nature of a relation is visible in the quality of a form, which is identical with all the relations among the elements of the content. j) It is the quality of the relations that explains the impact of content on form, and vice versa. The interaction between an object and a relation is different from the interaction between two objects. k) A quality of properties is also of quality type, hence a quality, just like an object has properties, and its not possible to conceive it without such properties.

 

Procedural knowledge: Procedural knowledge is the knowledge exercised in or required to the performance of some tasks. If such knowledge involves muscle movements and the process is repetitive and not too long, then making use of such knowledge becomes a skill, the level of which may vary from nearly reflex, automated to planned, consciously and carefully exercised. Procedural knowledge is similar to know-how, which is a description of a new procedure in hard copy, but not necessarily exercised or tested. In either case this type of knowledge is more important than the others as it usually addresses the future and leads to skills, whereas the others do not. Procedural knowledge is usually broken down into a sequence of operations, where operations may call for further procedural knowledge in the course of performing a job task. Procedural knowledge may be measured by the time it takes to complete a task and the number of mistakes made in the procedure. Since thinking may also be a part of procedure, thinking skills are best acquired and assessed as procedural knowledge.

 

Relation: is an “idea”, where relation means the verb, the resulting object and the quality, or property “relation” (like in relation algebra). With some words, like relation the original forms to express the three facets have been replaced by new forms such as relating and relative, with the last one made more ambiguous as it is also a nounad. But the main issue is that you can look at them by using in three different templates, i.e. LORP.

a) Relations are a special case of a property. They characterise the things (objects) among which they exist. For example A is greater than B.  A is a sibling of B. A is to the north of B, etc. b) The same relation may exist between different things. If the objects among which a relation exist is complex, you may call it a system, or a single entity, where the relation is shared or common to the constituents. b) In one class of objects in a special case it is one object = individual 83 a) A relation is in conformity with the definition of a property, therefore it is considered to be a special case of property. How does it differ from other properties then?  An object characterised by a relation is not seen as a complete entity, just a variety, or a totality of its own constituents (such as other objects). d) A relation is a singularity to be examined as multiplicity. e) A relation is an object created from its elements, or components. Such elements may be properties or objects. f) Some believe that categories (of relations?) are usually duplets, pairs, but not triplets or multiplets. g) Relations are also relative. No relation is deemed to be existing without other relations. Changing other relations will change the relation in question. This follows from the fact a relation is a property, and a property is relative (or from the fact that a relation is an object) h) Relations are characterised by transitivity, symmetry and reflexivity. i) Examples of another classification of relation is: kinship, spatial, temporal, causal, etc. j) What makes a property different from any other relation? A relation may be thought of in itself, disregarding what it is that is identified by a relation. A property as a relation cannot be thought of as a relation in general, because a property relates to specific objects: aRb k) Every relation is a system of other relations. If you add another relation, the system of relations will be more complex, but will still remain a relation, hence a property, which remains a property despite that you may add new properties to it. l) A system with a single property is a relation again. (Every object is united with other objects to form a system.) m) If you transfer the relations of an object to other objects, you will change the object. n) The difference between an object as a relation from other relations is that relations are specific relations to other objects.

 

Specification: is a folding operation staring from P and going to O. By specifying properties you get an object (see intensionality ((of a concept))

 

Note:

 

The above material has never been published, yet some of the ideas are explained in more details than above. Especially with regard to meaning, context, mental operations and semantics here:

 

http://translationjournal.net/journal/46meaning.htm 

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----- Original Message -----

From: Rich Cooper

To: '[ontolog-forum] '

Sent: Sunday, July 12, 2009 1:23 AM

Subject: Re: [ontolog-forum] Semantic Systems

 

FK>   RC> Objection!  Contrast is by definition a comparison.  Ordinarily, it means comparison with neighboring pixels, against frequency buckets, comparison against memory settings, all forms of identity (IMHO) resulting from a comparison function's unique positioning of that identity within a domain of all such identities. 

 

FK:>    This is why now it was high time to see that no ontology is correct without mental operations identified within the FO language system, of which abstraction is one operation that results in a property. 

 

Whoah – why does ABSTRACTION result in a “property” of the thing so abstracted, instead of in another abstraction slightly more smudged than the first abstraction from the original?  Why not choose a property only after at least three repeats of the same absractions, or best two out of three double abstractions?  Please justify this construction.  But it sounds interesting!

 

-Rich

 

Comparison is done on two objects which may be either a hit or a match output with respect to each other.

 

Set ordering aficionados out there would also like to have at the very least a LessThan and a GreaterThan result from comparisons, but the more expressive constants (JustNotEqual, PlausiblyEqual, FuzzilyLike, CouldPossiblyBe, …) would also be useful to some researchers.  The point is that the COMPARISON function you choose impacts whether you enable a single ordering, multikey ordering, the choice of ascending or descending ordering, and other considerations that are of prime interest in very many practical applications. 

 

-Rich

 

If they are a hit, then they have a property in common in terms of form, and they are a match, if their content is also common. 

 

Just the few comparison result constants used here - LessThan, Equal, GreaterThan, NotLessThan, NotEqual, NotGreatThan - and their logical combinations – JustNoMore - exhaust my vocabulary but shades of preferences based on multiple property-value comparisons can lead to arbitrarily subtle distinctions.  For every dimension, for every pair of dimensions, and probably for every triple of dimensions, there are pluralities of comparison functions that establish unique, monotonic gradients on objects based on the objects’ immutable properties. 

 

But this is a cause for ordering.  If they match, they are equal, but if they don’t, is one “>” or “<” the other?  Property value pairs for the same property may (OR MAY NOT) be ordered in some rational way.  Any rational ordering implies that there is a comparison function which calculates the basis property value pair for each of the two Things. 

 

FK> The operation caled abstraction is a folding operation which enables you to see the same thing or object as an association on the level of two existences, namely specific and abstract, and you can switch between the two aspects, as you can transfer across the existing connections as you like. <snip/> Folding means that we transfer something or some person in focus from one place to another. It also means the change itself, when or where something is moved from one person or place to another, that is the operation that happens when something is transferred. We do not know what is happening in reality in our brains, therefore we call for an analogy, as a usual device in any similar situation @ontolog.cim3.net

 

 

 

 

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

 

 

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[1][1] Lean ORP, - lean in the sense it is used in Lean Six Sigma – leaving everything out that does not contribute any value directly to the product

[2][2]  [Middle English, from Old French, from Late Latin relis, from Latin rs, thing. See r- in Indo-European Roots.]

 

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