{"id":1202,"date":"2018-11-12T20:56:15","date_gmt":"2018-11-12T15:26:15","guid":{"rendered":"https:\/\/www.rangakrish.com\/?p=1202"},"modified":"2018-11-13T07:11:50","modified_gmt":"2018-11-13T01:41:50","slug":"simulating-possible-worlds-in-flora-2","status":"publish","type":"post","link":"https:\/\/www.rangakrish.com\/index.php\/2018\/11\/12\/simulating-possible-worlds-in-flora-2\/","title":{"rendered":"Simulating Possible Worlds in Flora-2"},"content":{"rendered":"

The idea of encountering different worlds<\/strong><\/em> with varying truths<\/strong><\/em> is an interesting one. It has deep connections to philosophy and logic. For a nice discussion, see this article<\/strong><\/em><\/a>.<\/p>\n

Today, we are going to take advantage of Flora-2<\/a><\/strong><\/em>‘s module system to simulate possible worlds<\/strong><\/em>. Flora-2<\/strong><\/em> allows us to dynamically associate any knowledge base (KB) with any module; when loading a KB, we can specify the module name to be associated with that KB (this approach is different from most conventional programming languages such as C++<\/strong><\/em> and Java<\/strong><\/em>, where the namespace<\/strong><\/em> or package<\/strong><\/em> name is statically associated with the file). If module name is not specified, it is assumed to be the main<\/strong><\/em> module.<\/p>\n

We can thus partition a huge knowledge base into manageable chunks and work with them as needed. This can facilitate efficient reasoning as well.<\/p>\n

For our discussion, we are going to consider two possible worlds<\/strong><\/em>:<\/p>\n

1) A child’s world<\/strong><\/em>, where all living beings are friendly with one another<\/span>
\n2) An adult’s world<\/strong><\/em>, where discrimination exists<\/span><\/p>\n

We also have some common knowledge<\/strong><\/em> that is shared<\/strong><\/em> by adults and children.<\/p>\n

[text]
\n\/\/ Rangarajan Krishnamoorthy – 12\/11\/2018<\/p>\n

\/\/ This KB contains world knowledge (common knowledge)
\n\/\/ [‘G:\/Flora-2\/Examples\/ModuleExample\/Common-knowledge.flr’].<\/p>\n

{Man, Woman} :: Human :: LivingBeing.
\n{Bird, Animal} :: LivingBeing.<\/p>\n

{Lion, Tiger, Cat, Dog} :: Animal.
\n{Parrot, Pigeon} :: Bird.<\/p>\n

\/\/ Instances of Birds
\nParrot1 : Parrot.
\nPigeon1 : Pigeon.<\/p>\n

\/\/ Instances of Animals
\nLion1 : Lion.
\nTiger1 : Tiger.
\nCat1 : Cat.
\nDog1 : Dog.<\/p>\n

\/\/ Men and Women
\n{Peter, Joe, Phyllis} : Man.
\n{Sylvia, Mary, Teresa} : Woman.<\/p>\n

\/\/ Predicate must be true in all the worlds
\nNecessarily(?p) :- ?p@child, ?p@adult.<\/p>\n

\/\/ Enough if the predicate is true is any one world
\nPossibly(?p) :- ?p@child; ?p@adult.<\/p>\n

[\/text]<\/p>\n

In the above, we define a hierarchy and various instances of classes that belong to the hierarchy. For instance,<\/p>\n

Joe is a Man.<\/span>
\nMary is a Woman.<\/span>
\nDog1 is a specific Dog.<\/span><\/p>\n

Let us now peek into the child<\/strong><\/em> world:<\/p>\n

[text]
\n\/\/ Rangarajan Krishnamoorthy – 12\/11\/2018<\/p>\n

\/\/ This should be loaded into a module called "child"
\n\/\/ [‘G:\/Flora-2\/Examples\/ModuleExample\/World-of-Child.flr’ >> child].<\/p>\n

\/\/ World knowledge is assumed to be available in "main" module<\/p>\n

\/\/ All living beings are friendly with one another
\nfriendly(?x, ?y) :- {?x, ?y}:LivingBeing@main.<\/p>\n

[\/text]<\/p>\n

We see that according to the child, everyone is friendly with everyone else. No discrimination at all. What an ideal situation!<\/p>\n

Notice how I have referenced the class LivingBeing<\/strong><\/em> defined in main<\/strong><\/em> module while defining the friendly<\/strong><\/em> predicate.<\/p>\n

Now let us look at the adult<\/strong><\/em> world:<\/p>\n

[text]
\n\/\/ Rangarajan Krishnamoorthy – 12\/11\/2018<\/p>\n

\/\/ This should be loaded into a module called "adult"
\n\/\/ [‘G:\/Flora-2\/Examples\/ModuleExample\/World-of-Adult.flr’ >> adult].<\/p>\n

\/\/ World knowledge is assumed to be available in "main" module<\/p>\n

friendly(?x, ?y) :- ?x \\in [Peter]@main, ?y \\in [Joe, Mary, Teresa]@main.
\nfriendly(?x, ?y) :- {?x, ?y}:Bird@main.<\/p>\n

\/\/ "Friendship" is a bi-directional relationship.
\nfriendly(?x, ?y) :- friendly(?y, ?x).<\/p>\n

[\/text]<\/p>\n

In this world, all Birds<\/strong><\/em> are friendly with one another. Among Humans<\/strong><\/em>, the only set of friends are Peter, Joe, Mary, and Teresa. There are no other friends<\/strong><\/em>.<\/p>\n

Let us check these possible worlds in Flora-2<\/strong><\/em>. First we have to load the different KBs into their respective modules:<\/p>\n

\"Loading<\/a>
Loading Modules<\/strong><\/figcaption><\/figure>\n

If a module name is not specified while loading a KB, it is assumed to be main<\/strong><\/em>, the default module.<\/p>\n

Let us pose a few queries based on these possible worlds<\/strong><\/em>. Look at the Child’s<\/strong><\/em> world first:<\/p>\n

\"Querying<\/a>
Querying Child’s World<\/strong><\/figcaption><\/figure>\n

Here is the adult’s world:<\/p>\n

\"Querying<\/a>
Querying Adult’s World<\/strong><\/figcaption><\/figure>\n

What this clearly demonstrates is that different truth conditions can prevail in different worlds. For example, Dog1<\/strong><\/em> and Cat1<\/strong><\/em> are friends in the world of the child, but not in the world of the adult!<\/p>\n

Modal Operators<\/h2>\n

Modal logic includes two additional operators namely,\u00a0Necessarily<\/strong><\/em> and Possibly<\/strong><\/em>. Something is necessarily<\/strong><\/em> true if and only if it is true in all possible worlds<\/strong><\/em>, and something is possibly<\/strong><\/em> true if and only if it is true in some possible world<\/strong><\/em>.<\/p>\n

I have tried to model these operators thus:<\/p>\n

[text]
\n\/\/ Predicate must be true in all the worlds
\nNecessarily(?p) :- ?p@child, ?p@adult.<\/p>\n

\/\/ Enough if the predicate is true is any one world
\nPossibly(?p) :- ?p@child; ?p@adult.<\/p>\n

[\/text]<\/p>\n

These operators are defined as part of common knowledge<\/strong><\/em>.<\/p>\n

Let us check these operators:<\/p>\n

\"Modal<\/a>
Modal Operators<\/strong><\/em><\/figcaption><\/figure>\n

The operators seem to work as expected!<\/p>\n

The module system of Flora-2<\/strong><\/em>\u00a0thus allows us to elegantly partition knowledge bases and use that idea to simulate varying truth conditions across different possible worlds<\/strong><\/em>. I think this is a very useful feature.<\/p>\n

You can download the KB files here:\u00a0Common-Knowledge.flr<\/a>,\u00a0World-of-Adult.flr<\/a>,\u00a0World-of-Child.flr<\/a>.<\/p>\n

That is it for today. Have a wonderful week ahead!<\/p>\n","protected":false},"excerpt":{"rendered":"

The idea of encountering different worlds with varying truths is an interesting one. It has deep connections to philosophy and logic. For a nice discussion, see this article. Today, we are going to take advantage of Flora-2‘s module system to simulate possible worlds. Flora-2 allows us to dynamically associate any knowledge base (KB) with any […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[169,162,17],"tags":[164,163,168],"class_list":["post-1202","post","type-post","status-publish","format-standard","hentry","category-flora-2","category-knowledge-representation","category-programming","tag-flora-2","tag-knowledge-representation","tag-possible-worlds"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9OLnF-jo","jetpack-related-posts":[{"id":1109,"url":"https:\/\/www.rangakrish.com\/index.php\/2018\/10\/28\/flora-2-an-expressive-knowledge-representation-system\/","url_meta":{"origin":1202,"position":0},"title":"Flora-2: An Expressive Knowledge Representation System","author":"admin","date":"October 28, 2018","format":false,"excerpt":"I am always on the lookout for a good Knowledge Representation (KR) system that facilitates modeling and reasoning about real-world knowledge. 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