Development of a Background Knowledge-Base about Transportation and Smuggling

Transcription

1 Development of a Background Knowledge-Base about Transportation and Smuggling Richard Scherl Computer Science Department Monmouth University West Long Branch, NJ rscherl@monmouth.edu Abstract This paper demonstrates how one can base a theory of transportation and smuggling on a more general theory of travel. The language of the axiomatization is AnsProlog (Answer Set Programming) which is particularly suitable for representing defaults. It is shown how given an AnsProlog theory of travel (including a basic theory of actions and intentions) a theory of transportation and smuggling can be derived in a natural fashion. Both the initial and the resulting theories have been implemented in Smodels and can be used to answer queries about scenarios over the intended domain. Introduction and Motivation The goal of this paper is to demonstrate how one can derive a theory of transportation and smuggling on a more general theory of travel. The language of the axiomatization is AnsProlog (Answer Set Programming) which is particularly suitable for representing defaults. It is shown how given an AnsProlog theory of travel (including a basic theory of actions and intentions) a theory of transportation and smuggling can be derived in a natural fashion. Both the initial and the resulting theories have been implemented in Smodels and can be used to answer queries about scenarios over the intended domain 1. Consider the following examples 2 : Example 1 John drove 200 crates of cds from Florida to Toronto. We can ask the following questions: 1. Did the cds arrive in Toronto? 2. Did John arrive in Toronto? The answer to both questions is yes. But if we then add the following statement, The truck had an accident in Maryland. Copyright c 2006, American Association for Artificial Intelligence ( All rights reserved. 1 The inteded application is a question/answering system as described in (Baral, Gelfond, & Scherl 2004). 2 Many of the examples are borrowed from or inspired by the CNS (Center for Nonproliferation Studies) data corpus. The CNS data corpus contains news articles relevant to the proliferation of nuclear technology and materials. then the answer to both queries has to be unknown. Example 2 John shipped 200 crates of cds from Florida to Toronto. We might ask the following questions: 1. Did the cds arrive in Toronto? 2. Did John arrive in Toronto? Now the answer to the first question is yes and the answer to the second question is no. Again if we add, The shipment was stopped at Canadian customs. the answer to the first question becomes no. Additionally if we ask, Are the authorities looking to arrest John? the answer is no. Example 3 Viktor smuggled a container of radioactive material from Novogorod to Finland. We may ask the following questions: 1. Did the radioactive material arrive in Finland? Yes. 2. Is Viktor in Jail? No The answer to the first question is yes and the answer to the second is no. We could decide that smuggling is a risky activity and therefore the smuggler is likely to get caught. The English sentence implies (nonmonotonically) that the smuggling was successful, though. So, we do assume that the smuggling activity was successful without any information to the contrary. Now if we add: Russian Customs officials discovered the container at the Brusnichniy check point on the Russian-Finnish border. then the answer to the first question is no and the answer to the second question is yes. But if instead we add that Finnish customs officials discovered the container at the Brusnichniy check point on the Russian-Finnish border. then the answer to the first question becomes yes while the answer to the second question is still yes. We can also ask

2 Was the radioactive material received by the intended recipient? and the answer is no. Example 4 Fred smuggled a case of Molson from Toronto to Buffalo. But the U.S. customs agent found the case. We may ask the following questions: 1. Does Fred still have the Molson? Yes. 2. Is Fred in Jail? No The answer to the first question is unknown and the answer to the second is no. The above scenarios and questions are relatively simple, but determining the correct answer depends upon correctly axiomatizing the common-sense meaning of several concepts involving smuggling and transportation. The next section discusses the basics of AnsProlog. Section 3 covers the representation of action and change in AnsProlog. The theory of travel is discussed in Section 4. The theory of transportation and smuggling is developed in Section 5. Section 6 concludes and outlines future work. Syntax and Semantics of AnsProlog An AnsProlog(Gelfond & Lifschitz 1988; Baral 2003) knowledge base consists of rules of the form: l 0 l 1,..., l m, not l m+1,..., not l n (*) where each of the l i s is a literal, i.e. an atom, a, or its classical negation, -a and not is a logical connective called negation as failure or default negation. While -a states that a is false, an expression not l says that there is no reason to believe in l. The answer set semantics of a logic program Π assigns to Π a collection of answer sets consistent sets of ground literals corresponding to beliefs which can be built by a rational reasoner on the basis of rules of Π. In the construction of these beliefs the reasoner is guided by the following informal principles: He should satisfy the rules of Π, understood as constraints of the form: If one believes in the body of a rule one must belief in its head. He should adhere to the rationality principle which says that one shall not believe anything he is not forced to believe. The precise definition of answer sets is first given for programs whose rules do not contain default negation. Let Π be such a program and X a consistent set of ground literals. Set X is closed under Π if, for every rule (*) of Π, l 0 X whenever for every 1 i m, l i X and for every m + 1 j n, l j X. Definition 1 (Answer set part one) A state X of σ(π) is an answer set for Π if X is minimal (in the sense of set-theoretic inclusion) among the sets closed under Π. To extend this definition to arbitrary programs, take any program Π, and consistent set X of ground literals. The reduct, Π X, of Π relative to X is the set of rules l 0 l 1,..., l m for all rules (*) in Π such that l m+1,..., l n X. Thus Π X is a program without default negation. Definition 2 (Answer set part two) X is an answer set for Π if X is an answer set for Π X. Given, the translation of a text and a background theory, the initial task of inferencing in AnsProlog is to compute all of the answer sets or models of the text and background theory. To determine whether a fact follows from our text and background theory, it is necessary to have a definition of entailment. Definition 3 (Entailment) A program Π entails a literal l (Π = l) if l belongs to all answer sets of Π. The Π s answer to a query l is yes if Π = l, no if Π = l, and unknown otherwise. Given an AnsProlog program Π, the output of an implementation of AnsProlog such as SMODELS is a set of the answer sets of the program Π. Each of the answer sets is represented by a listing of the ground literals true in that answer set. The output can be quite large, but the user can restrict the output to see the specific results that are relevant to his/her purposes. Note that the language of AnsProlog includes both negation as failure (not), and logical negation (-). This is important as the two together are used to represent defaults. Many examples of this combination occur in the next sections. The goal here is to the rest of this paper is to first encode a background theory concerning transportation and smuggling in AnsProlog. Additionally the scenarios from section 1 need to be translated into AnsProlog. The answer sets of the combination of the background theory and the scenarios can be generated with Smodels. If the translation of the query holds in each of the answer sets then the answer is yes, if it does not hold in any of the answer sets then the answer is no, and otherwise the answer is unknown. Automating the translation of the scenarios from English to AnsProlog is an important topic, but is outside of the scope of this paper. Representing general knowledge This section describes the basic axiomatization of a dynamic world, actions, sequences of actions, and intentions within AnsProlog. Actions We have an ontology consisting of actions, fluents, and steps. These are represented in Smodels notation as follows: #const n=5. #step(0..n). #domain action(a;a1;a2;a3). #domain step(i;i1;i2;i3). #domain fluent(f1;f2;f3).

3 Time steps, here limited to the integers 0 through 5, are used to represent change over time. The binary predicate h is used to indicate that a particular fluent f holds at a particular time step as in h(f,0).the binary predicate o is used to indicate that an action a occurs at a particular step as in o(a,1). The ontology may contain various types of things: #domain container(c). #domain object(o). #domain person(p). object(p) :- person(p). object(c) :- container(c). Here we have specified containers, objects, and people. People and containers are objects. Causal laws specify the effects of actions on fluents. For example: action(pack(p,o,c)). fluent(contains(c,o)) :- neq(c,o). h(contains(c,o),i+1) :- o(pack(p,i,c),s). The effect of packing is that the container now contains the object. We have the inertia axioms: h(f1,i+1) :- h(f1,i), not -h(f1,i+1). -h(f1,i+1) :- -h(f1,i), not h(f1,i+1). These rules deal with the frame problem and ensure that as little as possible changes from step to step. Intentions We also utilize a representation of intentions(baral & Gelfond 2005; Gelfond 2006). o(a,i) :- planned(a,i), not -o(a,i). planned(a,i+1) :- planned(a,i), not o(a,i), not -planned(a,i+1). The first rule states that if an action is planned, and if there is no reason for it not to occur, then it does occur. The second rule states that if a planned action does not occur, then the intention to carry out the action persists. It is also necessary to axiomatize the intention to carry out a sequence of actions. Now in addition to atomic actions, we also have sequences. #domain sequence(s1;s2;s3). sequence (X) :- component(y,k,x). Sequences are specified by ordered components with K ranging from 1 to some integer n. The axioms for planning to execute a sequence of actions are as follows: planned(v,i) :- planned(s,i), component(v,1,s). planned(v2,i1) :- planned(s,i), component(v2,k+1,s), component(v1,k,s), ends(v1,i1). When a sequence of actions is intended, the plan is to carry out the first component. Additionally, once a component of the intended sequence has ended, the intention is to carry out the next component of the plan. An atomic action ends at the next step and a sequnece ends when its last component is executed. ends(a,i+1) :- o(a,i). ends(s,i) :- length(s,n), component(v,n,s), ends(v,i). Travel The approach to axiomatizing dynamic domains forms the basis for axiomatizing a travel domain(baral, Gelfond, & Scherl 2004; Gelfond 2006). To represent the domain of traveling, we introduce a type trip or journey: #domain trip(j;j1;j2;j3). We also need to represent locations and people: #domain location(l). #domain vehicle(v). container(v) :- vehicle(v). fluent(at(o,l)). fluent(participant(p,j)). People, vehicles and containers are all objects. Additionally, vehicles are containers. A trip is an event, an event with potentially multiple participants, different legs, various means of transportation etc. Every trip has an origin and a destination. Trips have two special actions embark and disembark to mark the beginning and end of a trip. Trips may also have intermediate stops. We also introduce a location en route to represent the location of the trip between stops. action(depart(j)). action(stop(j,c). action(embark(p,j)). action(disembark(p,j)). Embarking represents the person becoming a participant in the trip. h(participant(p,j), I+1) :- o(embark(p,j),i). o(disembark(p,j),i+1) :- h(participant(p,j),i), o(stop(j,d),i), dest(j,d). Of course once the trip ends, the person is no longer a participant. This is the effect of disembark When the trip departs, movement occurs. So, at the following step the trip is en route.

4 h(at(j,en_route),i+1) :- o(depart(j),t). h(at(j,l),i+1) :- o(stop(j,l),i). Finally, in the step after a stop occurs the trip is in the location of the stop. We can complete the definition of packing given earlier with unpacking. action(unpack(p,o,c)). -h(contains(c,o),i+1) :- o(unpack(p,i,c),i). h(at(i,pos),i) :- h(contains(c,o),i), h(at(c,pos),i). People can also take objects with them. action(take,p,i)). h(attached(i,p,i+1) :- o(take(p,i),i). h(at(i,pos),i) :- h(at(p,pos),i), h(attached(i,p),i). Transportation and Smuggling Transportation Let s look at how to represent the idea of John driving some cds from Florida to Toronto. location(florida). location(toronto). person(john). item(cds). o(pack(john,cds,l1),0). o(pack(john,l1,v1),1). o(embark(john,jft),2). journey(jft). sequence(jft). h(planned(jft,2)). component(depart(toronto),1,jft). component(stop(toronto),2,jft). component(disembark,3,jft). vehicle(v1). vehicle_type(v1,truck). vehicle_used(jft,v1). origin(jft,florida) destination(jft,toronto) In this case, we have a trip in which the items being transported are packed and brought onto the trip. John is a participant in the trip. When someone has something shipped from one location to another, then the the difference is that the person doing the shipping causes the intention to have the sequence of actions take place. The example now is that John had cds shipped from Florida to Toronto. In this case John is not a participant in the trip. John causes the trip to take place. planned(s,t) :- o(have_done(p,s),t) We have: o(have_done(john,s),0). location(florida). location(toronto). person(john). person(p1). person(p2). person(p3). item(cds). journey(jft). vehicle(v1). vehicle_used(jft,v1). sequence(s). component(pack(p1,cds,l1),1,s). component(load(p2,l1,v1),2,s). component(jft,3,s). component(embark(p3,jft),1,jft). component(depart(toronto),2,jft). component(stop(toronto),3,s). component(disembark(jft),4,s). Here the p1, p2, p3 are in effect Skolem constants for unnamed people. We could stipulate that they are all not equal to john. In both of the above cases, the background theory must require that there is by default a stop at the border crossing; first on the U.S. side and next on the Canadian side. First, we have a rule specifying that two locations are in two different countries. diff_countries(l1,l2) :- in(l1,country1), in(l2,country2), neq(country1,country2). The domain theory for our examples includes: in(toronto,canada). in(florida,usa). If the trip is by land, then there are two stops required. One is at the exit border crossing and the other is at the entry border crossing. The following axioms ensure that these two stops are in all trajectories. o(stop(j,exit_border_rossing(c1,c2),t+2) :- h(at(j,c1),t), diff_countries(c1,c2), vehicle_used(j,v), vehicle_type(v,land). o(stop(j,entry_border_rossing(c1,c2),t+2) :- h(at(j,exit_border_crossing(c1,c2)),t), vehicle_used(j,v), vehicle_type(v,land). -o(stop(j,c2,t+2) :- h(at(j,c1),t), diff_countries(c1,c2). -o(stop(j,c2,t+2) :- h(at(j,exit_border_crossing(c1,c2)),t),

5 diff_countries(c1,c2). The specification for air journeys can be given in a similar fashion to require that the exit crossing be passed before departing from the origin. Smuggling How does smuggling differ from transporting? Smuggling crosses an international border. Additionally, it involves transporting a prohibited item. Furthermore, it is necessary to axiomatize that if the border police notice the prohibited item, then the act of smuggling fails and the perpetrator is arrested. prohibited(i) :- radioactive(i). o(legal_ends(j,t+1) :- o(customs_officials_find(i,j),t), h(contains(j,i),t), prohibited(i). -o(depart(j),t+1) :- legal_ends(j,t). o(confiscate(i,t)) :- h(contains(j,i),t), legal_ends(j,t), prohibited(i). o(arrest(p,t)) :- h(participant(p,j),t), legal_ends(j,t). If the trip contains a prohibited item and the customs officials notice the prohibited item, then the trip is ended through legal means. If a trip is ended in such a fashion, the prohibited item is confiscated, the participants are arrested, and the trip does not proceed on to the destination. The full specification needs to distinguish between prohibited items such as radioactive material and restricted items such as alcoholic beverages. In the case of restricted items, the default is not that the smuggler goes to jail, but rather pays a fine. Additionally, it is necessary to distinguish between participants in a trip who are responsible for the packed item (restricted or prohibited) and those who are not responsible. In the above examples, it is assumed that all the participants are responsible for the item in question. To handle Example 3, we first need to look at Victor Smuggled a container of radioactive material from Novogorod to Finland. location(novogorod). location(finland). in(novogorod, russia). in(finland, finland). person(viktor). item(i1). radioactive(i1). o(pack(john,i1,l1),0). o(pack(john,l1,v1),1). o(go_on(john,nft),2). journey(nft). vehicle(v1). vehicle_type(v1,truck). vehicle_used(nft,v1). origin(nft,novogorod) destination(jft,finland) Note that our theory ensures that the trajectory includes o(embark(viktor,nft),2). o(depart(nft),3). h(at(en_route,nft),4). o(stop(nft,bordercrossing(novogorod, finland)),4). h(at(bordercrossing(novogorod,finland)),5). Then the addition of Russan Customs officials discovered the container at the Brusnichniy check point on the Russian- Finnish border is translated as: o(customs_officials_find(i,nft),5). Conclusion and Future Work This paper has demonstrated how one can in a modular fashion derive a theory of transportation and smuggling on a more general theory of travel. The theory can be used in the Smodels implementation of AnsProlog to answer queries involving a scenario within the domain of transporting goods and smuggling. Future work involves adding the following capabilities; Adding extensions to cover the possible use of the smuggled item. Can it be used to create a nuclear bomb or a dirty bomb or to kill someone? Consider the issue of the intended recipient. In the CNS corpus, the intended recipient is usually implicit. Often there are discussions of people smuggling materials to Turkey (for example) with the intention of selling it. So, a fuller story certainly needs to involve buying, shipping/smuggling and selling. Acknowledgments This work has been supported by ARDA under award number 2004-H References Baral, C., and Gelfond, M Reasoning about intended actions. In Proceedings of the Twentieth National Conference on Artificial Intelligence (AAAI-5), Baral, C.; Gelfond, M.; and Scherl, R Using answer set programming to answer complex queries. In Workshop on Pragmatics of Question Answering at HLT-NAACL 2004 (Human Language Technology - North American Association for Computational Linguistics. Baral, C Knowledge representation, reasoning and declarative problem solving. Cambridge, UK: Cambridge University Press. Gelfond, M., and Lifschitz, V The stable model semantics for logic programming. In Kowalski, R., and Bowen, K., eds., Logic Programming: Proc. of the Fifth Int l Conf. and Symp., MIT Press. Gelfond, M Going places -notes on a modular development of knowledge about travel. In Proceedings of the AAAI Spring Symposium to appear.