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## Re: [ontolog-forum] Constraint Solving versus Inferencing

 To: ontolog-forum@xxxxxxxxxxxxxxxx John F Sowa Sat, 11 Oct 2014 02:14:17 -0400 <5438CAB9.3090107@xxxxxxxxxxx>
 ```I just wanted to clarify some points in this thread.    (01) > For a constraint to be expressed in Boolean logic, aren't you then > moving out of the realm of propositional logic and into the realm > of first order predicate logic?    (02) No. Boolean logic is usually used as a synonym for propositional logic.    (03) But it's important to note that Boolean algebra is actually more general than propositional logic, since George Boole himself applied the algebra to several different domains:    (04) 1. If the letters represent propositions, you get propositional logic: 1 represents truth, 0 falsity, AxB is AND, A+B is OR, -A is NOT. Peirce observed that if A implies B, the truth value of A must be less than or equal to the truth value of B. Therefore, A≤B can be used to represent "If A, then B."    (05) 2. But GB also used the letters to represent a Boolean algebra of monadic predicates: 1 is the predicate that is true of everything, 0 is true of nothing, AxB is the predicate that is true of everything for which A and B are both true, etc.    (06) 3. GB also used the letters to represent sets: 1 is the universe of discourse, 0 is the empty set, A+B is the union of A and B, AxB is the intersection, and -A is the complement of A. But Boole's version of set theory was actually a version of mereology: he did not distinguish a single value x from the set {x}.    (07) Description logics take advantage of points #2 and #3 by treating a class a pair: a set and a predicate that is true of everything in the set. The same Boolean operators apply to both the sets and the predicates that determine them.    (08) > Even if you only use equality (=), and non-equality ('=) > to express your constraints, don't those two act as predicates?    (09) Well, yes. But you don't get predicate calculus without quantifiers. If you only have constants as the arguments of the predicates, the expressive power is limited to propositional logic.    (010) You can have constraint logic programming (CLP) with just equality. If you extend the notation to support inequalities, the solution to a CLP problem may consist of a family of possible options.    (011) John    (012) _________________________________________________________________ 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    (013) ```
 Current Thread [ontolog-forum] Constraint Solving versus Inferencing, David Whitten Re: [ontolog-forum] Constraint Solving versus Inferencing, Simon Spero Re: [ontolog-forum] Constraint Solving versus Inferencing, Rich Cooper Re: [ontolog-forum] Constraint Solving versus Inferencing, David Whitten Re: [ontolog-forum] Constraint Solving versus Inferencing, Rich Cooper Re: [ontolog-forum] Constraint Solving versus Inferencing, John F Sowa <= Re: [ontolog-forum] Constraint Solving versus Inferencing, Philip Jackson Re: [ontolog-forum] Constraint Solving versus Inferencing, Rich Cooper