 | |
#1781
 
| |||
| |||
|
Re: Guessing? -
08-01-2008
, 08:35 PM
|
"David BL" <davi... (AT) iinet (DOT) net.au> wrote in message news:dca3a676-7636-4ffa-962d-bd44f312da67 (AT) p31g2000prf (DOT) googlegroups.com... On Jul 31, 7:53 pm, "Brian Selzer" <br... (AT) selzer-software (DOT) com> wrote: "David BL" <davi... (AT) iinet (DOT) net.au> wrote in message news:c89ae2a9-5880-4b96-bf7e-adf8f2a899e1 (AT) j22g2000hsf (DOT) googlegroups.com.... On Jul 31, 10:01 am, "Brian Selzer" <br... (AT) selzer-software (DOT) com> wrote: "David BL" <davi... (AT) iinet (DOT) net.au> wrote in message Given relation r, let X(r) be the boolean valued characteristic function of r. Consider the following definitions 1. OnTheTeam_r : the relation value recorded by the DB 2. OnTheTeam_i : the internal predicate recorded by the DB 3. OnTheTeam_e : the external predicate meant to represent reality Is CWA associated with saying: a) OnTheTeam_i = X(OnTheTeam_r) or b) OnTheTeam_i = OnTheTeam_e? You appear to suggest CWA implies both a) and b). Is that right? The closed world assumption involves what can be proved rather than what something means; an external predicate involves what something means; therefore, the closed world assumption is not associated with saying b). On the other hand, it is associated with saying: c) OnTheTeam_i --> OnTheTeam_e since whenever ~OnTheTeam_e, ~OnTheTeam_i. I think you have that arse about. c) is assumed under OWA or CWA. You're right. I got it backwards: OnTheTeam_e --> OnTheTeam_i since whenever ~OnTheTeam_i, ~OnTheTeam_e And when combined with OnTheTeam_i --> OnTheTeam_e becomes OnTheTeam_i iff OnTheTeam_e Which is not the case under the OWA. If anything the CWA means that a missing tuple in the DB implies the negation of the proposition in reality. Since a database is a proposition under the closed world, domain closure and unique name assumptions, I prefer to refer to what a tuple corresponds to as a formula instead of a proposition, since it is just a small part of the whole. Also, you say CWA is concerned with what can be proved, and therefore isn’t related to an external predicate (because it is informal) and yet c) refers to an external predicate. The CWA does indeed involve what can be proved instead of what something means, but that doesn't mean that it isn't related to the external predicate. The internal predicate is related to the external predicate, and the CWA is related to the internal predicate; therefore the CWA is related to the external predicate. While the internal predicate is related to the external predicate, that doesn't mean that they are identical as is stated in b). '=' and 'iff' are different relations. In what sense do you say '=' and 'iff' are different when comparing a pair of boolean valued functions? Two functions are equal when they have the same domain and each element of the domain maps to the same value. That seems equivalent to 'iff' where all the domain variables are free and by convention would be universally quantified over their domains. Are you equating the domains of the internal predicate with those of the external predicate? |
Quote:
|
I like to think that a database relvar can be understood as an encoding of a relation value (or equivalently an internal predicate which is simply the boolean valued characteristic function) according to the RM formalism, irrespective of whether or not there exists any corresponding external predicate. The latter is informal and completely outside the formalism. A relvar is a container. A relvar is analogous to a relation schema. A relation is a value that can be contained within a relvar or conforms to a relation schema. How can a container encode that which might be contained within it? |
value. A variable normally exists in time and space, and a value is
"encoded" (ie represented) in order for a variable to "hold it".
Quote:
|
I think of a) and b) as quite independent options. Therefore it still begs the question of whether the CWA is associated with a) or b). You seem closer to a). |
#1782
| |||
| |||
|
|
"David BL" <davi... (AT) iinet (DOT) net.au> wrote in message news:dca3a676-7636-4ffa-962d-bd44f312da67 (AT) p31g2000prf (DOT) googlegroups.com... On Jul 31, 7:53 pm, "Brian Selzer" <br... (AT) selzer-software (DOT) com> wrote: "David BL" <davi... (AT) iinet (DOT) net.au> wrote in message news:c89ae2a9-5880-4b96-bf7e-adf8f2a899e1 (AT) j22g2000hsf (DOT) googlegroups.com.... On Jul 31, 10:01 am, "Brian Selzer" <br... (AT) selzer-software (DOT) com> wrote: "David BL" <davi... (AT) iinet (DOT) net.au> wrote in message Given relation r, let X(r) be the boolean valued characteristic function of r. Consider the following definitions 1. OnTheTeam_r : the relation value recorded by the DB 2. OnTheTeam_i : the internal predicate recorded by the DB 3. OnTheTeam_e : the external predicate meant to represent reality Is CWA associated with saying: a) OnTheTeam_i = X(OnTheTeam_r) or b) OnTheTeam_i = OnTheTeam_e? You appear to suggest CWA implies both a) and b). Is that right? The closed world assumption involves what can be proved rather than what something means; an external predicate involves what something means; therefore, the closed world assumption is not associated with saying b). On the other hand, it is associated with saying: c) OnTheTeam_i --> OnTheTeam_e since whenever ~OnTheTeam_e, ~OnTheTeam_i. I think you have that arse about. c) is assumed under OWA or CWA. You're right. I got it backwards: OnTheTeam_e --> OnTheTeam_i since whenever ~OnTheTeam_i, ~OnTheTeam_e And when combined with OnTheTeam_i --> OnTheTeam_e becomes OnTheTeam_i iff OnTheTeam_e Which is not the case under the OWA. If anything the CWA means that a missing tuple in the DB implies the negation of the proposition in reality. Since a database is a proposition under the closed world, domain closure and unique name assumptions, I prefer to refer to what a tuple corresponds to as a formula instead of a proposition, since it is just a small part of the whole. Also, you say CWA is concerned with what can be proved, and therefore isn’t related to an external predicate (because it is informal) and yet c) refers to an external predicate. The CWA does indeed involve what can be proved instead of what something means, but that doesn't mean that it isn't related to the external predicate. The internal predicate is related to the external predicate, and the CWA is related to the internal predicate; therefore the CWA is related to the external predicate. While the internal predicate is related to the external predicate, that doesn't mean that they are identical as is stated in b). '=' and 'iff' are different relations. In what sense do you say '=' and 'iff' are different when comparing a pair of boolean valued functions? Two functions are equal when they have the same domain and each element of the domain maps to the same value. That seems equivalent to 'iff' where all the domain variables are free and by convention would be universally quantified over their domains. Are you equating the domains of the internal predicate with those of the external predicate? |
Quote:
|
I like to think that a database relvar can be understood as an encoding of a relation value (or equivalently an internal predicate which is simply the boolean valued characteristic function) according to the RM formalism, irrespective of whether or not there exists any corresponding external predicate. The latter is informal and completely outside the formalism. A relvar is a container. A relvar is analogous to a relation schema. A relation is a value that can be contained within a relvar or conforms to a relation schema. How can a container encode that which might be contained within it? |
value. A variable normally exists in time and space, and a value is
"encoded" (ie represented) in order for a variable to "hold it".
Quote:
|
I think of a) and b) as quite independent options. Therefore it still begs the question of whether the CWA is associated with a) or b). You seem closer to a). |
#1783
| |||
| |||
|
|
"David BL" <davi... (AT) iinet (DOT) net.au> wrote in message news:dca3a676-7636-4ffa-962d-bd44f312da67 (AT) p31g2000prf (DOT) googlegroups.com... On Jul 31, 7:53 pm, "Brian Selzer" <br... (AT) selzer-software (DOT) com> wrote: "David BL" <davi... (AT) iinet (DOT) net.au> wrote in message news:c89ae2a9-5880-4b96-bf7e-adf8f2a899e1 (AT) j22g2000hsf (DOT) googlegroups.com.... On Jul 31, 10:01 am, "Brian Selzer" <br... (AT) selzer-software (DOT) com> wrote: "David BL" <davi... (AT) iinet (DOT) net.au> wrote in message Given relation r, let X(r) be the boolean valued characteristic function of r. Consider the following definitions 1. OnTheTeam_r : the relation value recorded by the DB 2. OnTheTeam_i : the internal predicate recorded by the DB 3. OnTheTeam_e : the external predicate meant to represent reality Is CWA associated with saying: a) OnTheTeam_i = X(OnTheTeam_r) or b) OnTheTeam_i = OnTheTeam_e? You appear to suggest CWA implies both a) and b). Is that right? The closed world assumption involves what can be proved rather than what something means; an external predicate involves what something means; therefore, the closed world assumption is not associated with saying b). On the other hand, it is associated with saying: c) OnTheTeam_i --> OnTheTeam_e since whenever ~OnTheTeam_e, ~OnTheTeam_i. I think you have that arse about. c) is assumed under OWA or CWA. You're right. I got it backwards: OnTheTeam_e --> OnTheTeam_i since whenever ~OnTheTeam_i, ~OnTheTeam_e And when combined with OnTheTeam_i --> OnTheTeam_e becomes OnTheTeam_i iff OnTheTeam_e Which is not the case under the OWA. If anything the CWA means that a missing tuple in the DB implies the negation of the proposition in reality. Since a database is a proposition under the closed world, domain closure and unique name assumptions, I prefer to refer to what a tuple corresponds to as a formula instead of a proposition, since it is just a small part of the whole. Also, you say CWA is concerned with what can be proved, and therefore isn’t related to an external predicate (because it is informal) and yet c) refers to an external predicate. The CWA does indeed involve what can be proved instead of what something means, but that doesn't mean that it isn't related to the external predicate. The internal predicate is related to the external predicate, and the CWA is related to the internal predicate; therefore the CWA is related to the external predicate. While the internal predicate is related to the external predicate, that doesn't mean that they are identical as is stated in b). '=' and 'iff' are different relations. In what sense do you say '=' and 'iff' are different when comparing a pair of boolean valued functions? Two functions are equal when they have the same domain and each element of the domain maps to the same value. That seems equivalent to 'iff' where all the domain variables are free and by convention would be universally quantified over their domains. Are you equating the domains of the internal predicate with those of the external predicate? |
Quote:
|
I like to think that a database relvar can be understood as an encoding of a relation value (or equivalently an internal predicate which is simply the boolean valued characteristic function) according to the RM formalism, irrespective of whether or not there exists any corresponding external predicate. The latter is informal and completely outside the formalism. A relvar is a container. A relvar is analogous to a relation schema. A relation is a value that can be contained within a relvar or conforms to a relation schema. How can a container encode that which might be contained within it? |
value. A variable normally exists in time and space, and a value is
"encoded" (ie represented) in order for a variable to "hold it".
Quote:
|
I think of a) and b) as quite independent options. Therefore it still begs the question of whether the CWA is associated with a) or b). You seem closer to a). |
 |
« Previous Thread
|
Next Thread »
| Thread Tools | |
| Display Modes | |
Linear Mode
| |
Powered by vBulletin Version 3.5.3
Copyright ©2000 - 2012, Jelsoft Enterprises Ltd.
Copyright ©2000 - 2012, Jelsoft Enterprises Ltd.