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An Application of Cartesian Counterfactuals

Cartesian counterfactuals have been used to answer challenge questions in the U.S. DARPA (Defense Advanced Projects Agency) High Performance Knowledge Bases (HPKB) program. In this section briefly explain what this project does, and then we some examples of how cartesian counterfactuals are used.

The HPKB program is developing technology to build large (10 to 100 thousand axioms), reusable knowledge bases that can answer questions on a specific topic. One branch of the project considers Crisis Analysis. That is, it attempts to answer the kinds of questions intelligence analysts would ask when a crisis erupted somewhere in the world.

The HPKB project is competitive. The research groups are dividing into two groups, and build competing systems, which are tested yearly on their ability to answer newly posed questions about a chosen topic. These questions range from the (seemingly) simple, ``What is the difference between sarin and anthrax?'', to quite involved counterfactuals.

In order to even meaningfully state the counterfactuals, we need to give some background information. Here we give an extract from a scenario, modified by string substitution to be set in the world of the Lord of the Rings.

Mordor supplies a hobbit terrorist group, the Hobbit Liberation Army (HLA), with money, explosives, small arms, and advisors and offers the use of a training facility near Gondor. Mordor arranges to acquire weapons-grade anthrax from a Ranger Mafia cell. Mordor contacts an Elvish biological weapons expert, known only as Feanor, who agrees to supply Mordor with equipment and weapons-engineering skills to complete the weaponization of several small biological devices.

The orcs of Mordor, aided by the nefarious Elvish biological weapons expert, successfully build a small, hobbit-portable anthrax sprayer. Separately, arrangements are made with the HLA to begin training exercises in Mordor at the western terrorist training camp.

Although entirely hypothetical, the scenario is very detailed, running to 15 pages.

Given this scenario, (called the Y1 Phase II LOTR Scenario) the following counterfactual was posed.

How would the Y1 Phase II Lord of the Rings Scenario be affected if BW experts of Mordor did not provide advanced technology and scientific expertise aid to a terrorist group?

This question can be stated in KIF (knowledge interchange format) as follows.

    (not (occurs-in ?event (scenario-minus 
                              ?event1 Y2-scenario)))  
    (occurs-in ?event (day ?n  Y2-Scenario ))
    (supply ?event1)
    (object-acted-on ?event1 ?aid)
    (indirect-object-to ?event1 ?group) 
    (terrorist-group ?group)
    (expertise ?aid)
    (actor ?event1 ?experts)
    (citizens-of ?expert Mordor)
    (expert ?experts)
    (information-about ?aid advanced-technology)
    (actor ?event ?actor)

In the system built by the one team, to which the Formal Reasoning Group is associated, this query is sent to a theorem prover (ATP), which extracts binding from a knowledge base for the variables (the names preceded by a question mark). The binding are then translated into a natural language answer, and the proof into a natural language explanation of the answer. We will not discuss these parts further, as they do not bear on the use of cartesian counterfactuals.

The system find the correct answer, namely Mordor would not have been able to weaponize the anthrax, by reasoning that had they not received the elvish aid, then they would not have been able to weaponize the material, as biological weapon engineering skills are necessary for this task. The reasoning is about 40 resolution steps, and involves 7 rules and 30 ground facts.

In the case of this counterfactual, the frame is the facts true at the beginning of the scenario, and the events that occur before the elvish aid arrives. The events that occur later are not in the frame, as they are not independent of the earlier events.

Counterfactuals are included in the HPKB project as they are a very natural way to explore an evolving situation. When thinking about the present, past cases, and counterfactual variants of them are often employed.

next up previous
Next: Theories admitting counterfactuals Up: Useful Counterfactuals Previous: Bayesian Networks

John McCarthy
Wed Jul 12 14:10:43 PDT 2000