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more-general-than In 2, we defined the more_general_than_orequal20 relation (z,) as follows: Given two boolean-valued functions hj(x) and hk(x), we say that hj 2, hk if and only if (Vx)hk(x) + hj(x) This > , relation is used by many learning algorithms to guide search through the hypothesis space 8-subsumption Consider two clauses Cj and Ck, both of the form H v L1 v L,, where H is a positive literal, and the Li are arbitrary literals Clause Cj is said to 8-subsume clause C if and only if there exists a substitution k 0 such that CjO G Ck (where we here describe any clause C by the set of literals in its disjunctive form) This definition is due to Plotkin (1970) Entailment Consider two clauses Cj and Ck Clause Cj is said to entail clause Ck (written Cj k Ck) if and only if Ck follows deductively from C,

Listing 9 1. Setting the Storage Options for the DailyJournal Application url = [NSURL fileURLWithPath: [applicationSupportFolder stringByAppendingPathComponent: @"storedata"]]; persistentStoreCoordinator = [[NSPersistentStoreCoordinator alloc] initWithManagedObjectModel: [self managedObjectModel]]; if (![persistentStoreCoordinator addPersistentStoreWithType:NSXMLStoreType configuration:nil URL:url options:nil error:&error]){ [[NSApplication sharedApplication] presentError:error]; }

What is the relationship among these three definitions First, let us re-express the definition of 2, using the same first-order notation as the other two definitions If we consider a boolean-valued hypothesis h(x) for some target concept c(x), where h(x) is expressed by a conjunction of literals, then we can re-express the hypothesis as the clause

Here we follow the usual PROLOG interpretation that x is classified a negative example if it cannot be proven to be a positive example Hence, we can see that , our earlier definition of 1 applies to the preconditions, or bodies, of Horn clauses The implicit postcondition of the Horn clause is the target concept c(x)

The first bold section shows the filename used to store your data. You can actually give this any name you like: a.b, for example. The second bold section is where you choose the storage format. Your choices are NSXMLStoreType (the default, as an XML file), NSSQLiteStoreType (for a SQLite database), or NSBinaryStoreType (for the more traditional binary data format used for Mac OS X data stores before the days of Core Data). Generally speaking, the XML format is the best option to use during development, as it is easy to make changes to your data model and also to inspect the data file using external tools such as XML editors. When you go into production you may want to change over to one of the other storage formats SQLite is more scalable than XML if your database is likely to grow.

What is the relationship between this definition of 2, and the definition of 8-subsumption Note that if hl p, h2, then the clause C1 : c ( x ) t h l ( x ) 8-subsumes the clause C2 : c ( x ) t h2(x) Furthermore, 8-subsumption can hold even when the clauses have different heads For example, clause A 8-subsumes clause B in the following case: A:

Mother(x, y )

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The main user interface for this application is going to display a list and detail view of journal entries. So there will be a list of the entries probably by name. For each entry selected, the detail part of the interface will show the other information. We will want a way to add and remove entries, too. Start by giving the main user interface window a more useful name (it s just called Window in the Document window) I usually begin the names of windows with a lowercase w, so I called this one wJournalEntries. It is not actually necessary to rename objects in the Document window, but you will be creating several windows and controllers during this project, and it is a good practice to give meaningful names to such objects.

Father(x, z ) A Spouse(z, y ) Father(x, Bob) A Spouse(Bob, y ) A Female@)

B : Motker(x, Louise)

Now open the window and drag a Core Data Entity object into it from the Library. This brings up the New Core Data Entity Interface assistant. Choose the DailyJournal project, then the DailyJournal_DataModel.xcdatamodel model these are the only options, but in more complex projects you may have a variety of models to choose from. In the last column choose the journalEntry entity, then click Next (see Figure 9 5).

because A8 G B if we choose 8 = {ylLouise, zlBob) The key difference here is , that > implicitly assumes two clauses for which the heads are the same, whereas 8-subsumption can hold even for clauses with different heads Finally, 8-subsumption is a special case of entailment That is, if clause A 8-subsumes clause B , then A k B However, we can find clauses A and B such that A F B, but where A does not 8-subsume B One example is the following pair of clauses

Elephant(father_of ( x ) )