You think there is more than one possible set of semantic primitives? If interpreted as saying that there are several sets of things that can be used as primitives, and that these alternative “primitives” can be **constructed from either base**, I would not disagree. For example, the notion of a “birth mother” can be represented as a type of woman who has born a child, or may be represented by a relation “isTheMotherOf” , with the same logical implications resulting from being an instance of the type or from being the subject of the relation. This is mentioned in the documentation for the COSMO ontology. Similar alternatives of type or relation can be found for other types. It is common to find some “faceted terminologies” in which different root taxons of types are defined as those having known values for certain properties. (e.g. “persons by nationality” etc). If the properties are themselves defined, such types are superfluous, but can be immediately generated from the relations. If desired. When types can be constructed from relations, I prefer to just include the relations unless the types are very common or used often in language, or just convenient for representing other elements (so COSMO does have a “BirthMother”). But one could have both kinds of primitive representation in the ontology, or, if one was concerned to keep the ontology elements numerically small (a tactic followed by SUMO), one could use one type of primitive and a generator function to automatically create the other type of primitive when desired, and it would make no difference at all which was used. Since one function of a primitives-based foundation ontology is to enable semantic interoperability, it is important to allow users to use any terminology locally, as long as it can be translated into alternative terminologies. My inclination is to include whatever users think they need in the foundation ontology, and to winnow the size of the ontology when used for specific practical applications by selecting out only those elements required for the application, with an automatic selection mechanism. So, a foundation ontology with only one or both alternative sets of primitives will have (directly or by logical implication) *all* of those basic elements required to define anything anyone wants to define. But these kinds of alternations in primitive representation are, I believe small in number, and as long as the alternative “primitives’ can be generated from either set, the choice will have no practical effect on the project to create a foundation ontology broadly useful for semantic interoperability.
One principle I use in constructing the COSMO ontology is to include all the elements that people are likely to want to use to describe things, even if they are not themselves primitive. But there has to be limit, and that will be about 10,000 elements. The goal, as I have mentioned is a very practical one, and I am not concerned to find the actual final minimal set of indispensable primitive, rather to try not to leave any out and not worry about including common concepts that are likely to be needed for rapid work, even if they are not primitive. Usability is an important design principle.
That said, the number of such “alternations” in primitive representation that I have encountered is small. As for “NOR”, I would *not* expect any practical terminology of logic to leave out the AND, NOT, OR, XOR, etc. just because they can be constructed from other primitive elements. Likewise with other commonly used arithmetic functions. A foundation ontology is not a “foundations of mathematics” research program. Do you have other examples that you think might actually be problematic and explode the number of alternative primitive elements beyond the 10,000 range?
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of William Frank
Sent: Sunday, August 11, 2013 8:55 AM
Subject: Re: [ontolog-forum] Practical Semantic Primitives
The problem I am attempting to raise is not about whether it is reasonable to look for a set of primitives from which to derive through definition all the other concepts in a corpus of concepts. In fact, I happen to agree with you that this is an essential part of ontology in computer science.
The problem I am raising is that, in a deductive system, there is no ONE set of primitives that is the 'right' one. There will be MANY, just as in the examples I gave. For example, even with a dozen Boolean connectors, I can reduce them to primitives in about a half dozen ways.
>On Sat, Aug 10, 2013 at 12:29:27PM -0400, Patrick Cassidy wrote:
>> Concerning a comment of William Frank:
>> [WF] > One of the problem with the "Leibnizian dream" of a universal
>semantics based on primitives is the unstated assumption that there is at
>most ONE set of primitives from which all other concepts can be derived.
>> I???m not Leibniz. My concern is to find a set of primitives for those
>cooperative (informative) communications that people have found
>significant enough to spend some effort to get their computers to
>understand. For any given set of ontologies, or of linguistic
>there will indeed be one set of primitives that can represent all of the
>concepts included. Even if there were no overlap, the set of primitives
>would be the sum of all of the primitives in the individual
>> Patrick Cassidy
>> MICRA Inc.
>> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of William
>> Sent: Saturday, August 10, 2013 9:09 AM
>> To: [ontolog-forum]
>> Subject: Re: [ontolog-forum] Practical Semantic Primitives
>> One of the problem with the "Leibnizian dream" of a universal semantics
>based on primitives is the unstated assumption that there is at most ONE
>of primitives from which all other concepts can be derived. In fact, if
>at least one, for a set of N concepts, then there will be plenty more
>sets of primitives from which all the other concepts can be derived. (My
>guess would be something on the order of N factorial).
>> People who discover one of these, or are looking for one and making
>progress, so often think that theirs is the "real" one. (Just as, more
>people who are taught in a logic class that one can derive all the other
>operators from NOR sadly often come away thinking that NOR is the real
>primitive, or from the foundations of mathematics, that sucessor and zero
>more primitive that plus, zero, and one, just because it is a smaller set,
>though if I define sucessor in terms of plus and 1, I have the same
>> More generally, mediocre engineers who discover one solution to a
>> programming problem think they are done, and defend it to the death.
>> The key is to determine among a set of solutions, which will be the
>> most useful, for a give set of purposes. (Purposes being something
>> else few people seem to want to state explicitly.)
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