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## Re: [ontolog-forum] Logic, Datalog and SQL

 To: "[ontolog-forum] " , Charles D Turnitsa , Chris Menzel "[ontolog-forum] " Kathryn Blackmond Laskey Fri, 09 Feb 2007 18:22:15 -0500
 ```> On the other hand, in order to >satisfy the axioms, the 'model' must contain all >the structure that these axioms explicitly >describe, so in a very precise sense it cannot be >of lower fidelity than the axioms, but it can >well be of much higher fidelity.    (01) That statement could be very misleading, because the referent of "fidelity" is unclear. Tarski interpretations must be faithful to the axioms, but may be wildly unfaithful to the intention of the modeler, and to the world we are trying to represent with the axioms.    (02) Let me give an example to make things concrete.    (03) Consider the set of axioms: All men are mortal. Pat is a man. John is a man. Kathy is a woman.    (04) There are Tarskian interpretations of this set of axioms in which Kathy is immortal. The axioms say men are mortal, but don't pin down whether or not women are mortal. There are also Tarskian interpretations of this set in which Kathy is a man. That's because the axioms don't say whether women and men are mutually exclusive categories. In the Tarskian interpretations in which Kathy is a man, though, she has to be mortal, because all men are mortal.    (05) All the Tarski interpretations are faithful to the axioms, in the sense that the axioms are true in every interpretation. The ones in which Kathy is immortal or Kathy is a man are very unfaithful to the actual world, and presumably to the intentions of anyone who would write down these axioms. There's a sense in which we might call them unfaithful to the axioms, because they define truth-values for things the axioms leave open.    (06) I think it is less misleading to say that Tarskian models are more specific than the axioms, in that any given Tarski model pins down the truth-value of every sentence. But this specificity comes at the cost of assigning definite truth-values to sentences whose truth-value is left open by the axioms.    (07) Kathy    (08) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: 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 Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (09) ```
 Current Thread Re: [ontolog-forum] Logic, Datalog and SQL, (continued) Re: [ontolog-forum] Logic, Datalog and SQL, Ed Barkmeyer Re: [ontolog-forum] Logic, Datalog and SQL, Adrian Walker Re: [ontolog-forum] Logic, Datalog and SQL, Pat Hayes Re: [ontolog-forum] Logic, Datalog and SQL, John F. Sowa Re: [ontolog-forum] Logic, Datalog and SQL, Pat Hayes Re: [ontolog-forum] Logic, Datalog and SQL, John F. Sowa Re: [ontolog-forum] Logic, Datalog and SQL, Pat Hayes Re: [ontolog-forum] Logic, Datalog and SQL, Christopher Menzel Re: [ontolog-forum] Logic, Datalog and SQL, Charles D Turnitsa Re: [ontolog-forum] Logic, Datalog and SQL, Pat Hayes Re: [ontolog-forum] Logic, Datalog and SQL, Kathryn Blackmond Laskey <= Re: [ontolog-forum] Logic, Datalog and SQL, Ed Barkmeyer Re: [ontolog-forum] Logic, Datalog and SQL, Pat Hayes Re: [ontolog-forum] Logic, Datalog and SQL, Christopher Menzel Message not availableMessage not availableRe: [ontolog-forum] Logic, Datalog and SQL, Adrian Walker Re: [ontolog-forum] Logic, Datalog and SQL, Pat Hayes Re: [ontolog-forum] Logic, Datalog and SQL, Christopher Menzel Re: [ontolog-forum] Logic, Datalog and SQL, Pat Hayes Re: [ontolog-forum] Logic, Datalog and SQL, John F. Sowa Re: [ontolog-forum] Logic, Datalog and SQL, Charles D Turnitsa Re: [ontolog-forum] Logic, Datalog and SQL, Pat Hayes