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## Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology

 To: ontolog-forum@xxxxxxxxxxxxxxxx John F Sowa Sun, 06 Jul 2014 02:31:58 -0400 <53B8ED5E.5050203@xxxxxxxxxxx>
 ```On 7/5/2014 8:51 AM, rrovetto@xxxxxxxxxxx wrote: > based on what's been said thus far, then it's possible to create > non-FOL, non-syllogistic logics, correct? And are logics without > quantifiers doable?    (01) That depends on what you mean by 'not'. What aspect of a logic do you want to negate?    (02) 1. For example, higher-order logic (HOL) is not FOL because it can express more kinds of statements than FOL. But you could also have a non-FOL logic that expresses some subset of FOL.    (03) 2. Propositional logic (i.e., Boolean algebra) is not FOL because it expresses a subset that has no quantifiers.    (04) 3. RDF is a subset of FOL that has only one Boolean operator (and) and one quantifier (a blank node that says there exists something).    (05) 4. But if you add negation to RDF, you can define all the operators of full FOL. To specify all of FOL with just 'and', 'not', and 'there exists', see http://www.jfsowa.com/talks/egintro.pdf .    (06) There are also variations of logic that deny the option of just two truth values {T,F}. A three=valued logic would have an option of unknown. Cyc has five values: True, True by default, Unknown, False by default, False. Any of these logics could use any combination of quantifiers and Boolean operators.    (07) There are also variations of fuzzy logic with a continuous range of uncertainties. Some people claim that vagueness or fuzziness is just in the degree of knowledge, because no object can be truly vague. But Peter Simons wrote an intriguing article about the possibility of vague objects. See the URL and excerpts below.    (08) But that is a problem of ontology, not of logic. Some people think that identity conditions are a big deal. I don't. I believe that similarity is more fundamental: similarity is perceptible, but identity is just a context-dependent inference.    (09) John ________________________________________________________________________    (010) Source: https://www.academia.edu/7533490/Does_the_Sun_Exist_The_Problem_of_Vague_Objects    (011) Does the Sun Exist? The Problem of Vague Objects    (012) PETER SIMONS    (013) At any time, there are considerable masses of energy and matter leaving the sun, and since there is no sharp boundary marking where the sun stops... if all the objects that exist are exactly delimited, since the sun is none of these, the sun does not exist...    (014) Each of us is in the same position as the sun: at any time there are countless molecules lurking around us, in or near us, the air, water vapor and particles we respire, the pieces of skin about to be rubbed off, the substances sticking to the skin, the nutrients about to cross cell membranes from the gut, and there is no sharp fact of the matter as when they become or cease to become parts of us...    (015) On the other hand, if all of these everyday objects like the sun and ourselves do exist, as common sense would have us believe, they are vague and fail to have determinate identity conditions: there can be an entity without identity...    (016) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (017) ```
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