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

 To: ontolog-forum@xxxxxxxxxxxxxxxx John F Sowa Tue, 24 Jun 2014 12:28:09 -0400 <53A9A719.9040207@xxxxxxxxxxx>
 ```Robert, Alex, et al.,    (01) RR > what do you mean by "closed-form definitions"?    (02) In mathematics and other fields, it's common to distinguish an explicit definition from an implicit definition.    (03) For example, following is an implicit definition of a function f:    (04) x^2 + 3*f(x) - 4 = 0    (05) And following is an explicit or *closed-form* definition:    (06) f(x) = (4 - x^2) / 3    (07) But many implicit definitions cannot be converted to closed-form: See http://www-math.mit.edu/~tchow/closedform.pdf    (08) RR > I understand Edward Barkmeyer's reservations as well, but perhaps > i'm not getting the gist of the whole context you have in mind.    (09) In another note, I clarified the point I was trying to make: the proliferation of metalevel terminology is more confusing that helpful. Whenever possible, reduce the number of metalevel terms by replacing them or defining them in terms of some version of logic.    (010) RR > Based on my studies in philosophy FOL is essentially presented as > a modern form or translation of [Aristotle's syllogisms].    (011) A's syllogisms are a subset of FOL. They are also the most widely used subset of description logics such as OWL.    (012) AS > For example OWL 2 Full is not FOL.    (013) RDF and OWL full allow quantifiers to range over relations. Classical FOL does not allow that. Common Logic is an extension of FOL that was designed to support that option.    (014) RR > Now, my concern with this is that since syllogistic logic is not > how the mind reasons...    (015) First, nobody knows the details of how the mind reasons. But one point is certain: the human mind supports *every* version of reasoning that anybody has ever used. That includes all of mathematics and logic as well as every kind of intuition, creativity, meditation, or whatever.    (016) Second, every digital computer is a logic machine. Anything that cannot be defined in some version of logic cannot be programmed in a digital computer.    (017) And third, every notation for any version of reasoning, formal or informal, can be explained in and translated to natural languages.    (018) RR > why isn't a non-syllogistic-based logic used for ontologies? > Why is FOL used?    (019) The basis for syllogisms is a statement that term A is or is not more general (applies to more instances) than term B. That's an integral part of every natural language. You use it whenever you speak.    (020) The reason for FOL is that it's a subset of every NL. Whenever you use the words 'and', 'or', 'not', 'some', and 'every', you're speaking FOL. If you just take something as simple as RDF triples and add negation, you get the expressive power of FOL.    (021) Basic point: if you try to extend RDF, it's much easier to define full FOL than it is to avoid FOL. One of the major reasons for the complexity of OWL is that they tried to *avoid* the full expressive power of FOL. That imposes many constraints on what you can say.    (022) RR > Aside from that, please continue mentioning any other logics > that are used.    (023) All other logics are subsets, supersets, or variations of FOL. Fuzzy logic, for example, assumes a continuous range of fuzzy levels from absolutely certain (true) to absolutely not certain (false). For a discussion of the relationships, see    (024) http://www.jfsowa.com/pubs/rolelog.pdf The role of language and logic in reasoning    (025) AS > non-FOL def: VPC(p)(ob) ≝ 100*Volume_in(p,ob)/Volume(ob).    (026) Any mathematical function or operator can be used in an FOL statement.    (027) For a useful survey of the many issues about definitions, see http://faculty.cbu.ca/rkeshen/Logic/Definitions,%20Dictionaries,%20and%20Meanings,%20by%20Norman%20Swartz,%20Dept_%20of%20Philosophy,%20Simon%20Fraser%20University.htm    (028) John    (029) _________________________________________________________________ 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    (030) ```
 Current Thread Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, (continued) Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, John F Sowa Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Barkmeyer, Edward J Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, John F Sowa Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Barkmeyer, Edward J Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, John F Sowa Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Barkmeyer, Edward J Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Rich Cooper Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, rrovetto Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Alex Shkotin Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Adrian Walker Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, John F Sowa <= Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Alex Shkotin Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Barkmeyer, Edward J Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, John F Sowa Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, rrovetto Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Philip Jackson Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, rrovetto Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Ali H Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, rrovetto Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Philip Jackson Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology, Ali H