Automating commonsense reasoning using the event calculus

contributed articlesby Erik T. Muellerdoi: 10.1145/1435417.1435443AutomatingCommonsenseReasoningUsing theEvent CalculusCommonsense reasoning is the human abilityto make inferences about properties and events inthe everyday world. The automation of commonsensereasoning, long a goal of the field of artificial intelligence 3and an area of active research in the last decade, 8 isattaining a level of maturity. Automating commonsensereasoning allows us to build applications that are moreuser-friendly and more aware of the world. 2Several major computational approaches tocommonsense reasoning have been explored.Analogical processing implements the notion thatpeople reason about novel situations by analogy tofamiliar ones. Probability theory allows us to reasongiven uncertain knowledge of the state of the worldand how the world works. Qualitative reasoningfocuses on reasoning about physical systems. Methodsbased on natural language make use of large textualcorpora of commonsense knowledge. Society of mindapproaches stress the use of multiple interactingmethods and representations.One approach that has achieved ahigh degree of success because of itssteadfast focus on hard benchmarkproblems of commonsense reasoning,is logic. One logic-based formalismthat stands out as both comprehensiveand easy to use is the event calculus. 4, 9Problem statement. A method forcommonsense reasoning must be ableto perform various types of reasoning.Projection consists of determining whatwill happen next, or what the results ofa sequence of actions will be. Explanationconsists of determining what happened,or what the initial situation was.A method for commonsense reasoningmust be able to reason about various everydaydomains, especially time (actionand change), space, and mental states.Event calculus. The event calculusfits the bill; it handles the importantaspects of commonsense reasoning, asshown in Table 1.The entities of the event calculus areevents, properties, and timepoints. Twotypes of facts are based on these entities—thefact that an event occurs at atimepoint, and the fact that a propertyholds at a timepoint. Each fact has atruth value—it is either true or false.To perform commonsense reasoningusing the event calculus, we firstidentify an area of interest and thenprovide commonsense knowledge relatedto that area. We specify the effectsthat result from an event occurring ata timepoint. We may specify that, in agiven context, a given event initiates agiven property. This means that, if theevent occurs at some timepoint in thecontext, then the property will be trueafter that timepoint. We may similarlyspecify that an event terminates a givenproperty, which means that the propertywill be false after the event occurs.The frame problem in artificial intelligenceis the problem of representingand reasoning about what propertiesdo not change when an event occurs. Inthe event calculus, properties normallyobey the commonsense law of inertia 9 —the truth value of a property stays thesame unless the property is directlyinitiated or terminated by an event. Butjanuary 2009 | vol. 52 | no. 1 | communications of the acm 113

contributed articlesTable 1. Aspects of Commonsense Reasoning Handled by theEvent CalculusFigure 1. Discrete Event Calculus Reasonerindirect effects are also possible. For example,if a person picks up an objectand walks into another room, not onlywill the person be in the other room;the object will also be in that room. Theevent calculus allows us to specify that,in a given context, an event releases aproperty from the commonsense lawof inertia, so that the property can varyaccording to some law. For example, wemay specify that the location of an objectvaries with the person holding it.Events enable the description of discretechange. To describe continuouschange, we may specify that a releasedproperty follows a certain trajectory orfunction of time.We may specify that, in a given context,the occurrence of an event is triggered.For example, when a ball flyingtoward a wall reaches the wall, itbounces off the wall. The preconditionsfor occurrence of an event may be specified.For example, to walk through adoor, the door must be open.Default reasoning is reasoning inwhich we reach a conclusion basedon limited information, and possiblylater retract that conclusion when newinformation comes in. The event calculussupports default reasoning usingcircumscription, which can be used tominimize unexpected events, minimizeunexpected effects of events, andminimize exceptional conditions. Forexample, circumscription can be usedto represent that, unless we know otherwise,the refrigerator is plugged in.ExampleHere is an exampleof how we use theevent calculus torepresent knowledgeabout fallingobjects, and thento reason about aparticular fallingobject. We representthe knowledgeas follows:Starting falling initiates falling.Starting falling releases height.The height of a falling object ish 0– — 1 gt 22 . aFalling and a height of zero triggerhitting the ground.Hitting the ground terminatesfalling.Hitting the ground initiates aheight of zero.We can then use this knowledge toreason. Suppose we are asked to determinewhat happens given the followinginformation:The initial height of an apple is fourmeters.The apple starts falling at timepointzero.This is an instance of projection. Wereason as follows:Because starting falling initiatesfalling, after the apple startsfalling, it will be falling.Because the height of a falling1object is h 0– — gt 2 2 , the applestarts falling at timepoint zero,and h 0= 4, the height of the applewill be zero at timepoint :8/g .Because falling is subject to thecommonsense law of inertia, thea h 0is the object’s initial height in meters, g is theacceleration due to gravity (9.8 meters/second 2 ), and t isthe elapsed time in seconds.apple is falling at timepoint :8/g .Because the apple is falling andthe height of the apple is zero attimepoint :8/g , the apple will hitthe ground at that timepoint.Representing DomainsThe constructs of the event calculusenable representation of a surprisingnumber of areas.The event calculus can be used torepresent and reason about variousnotions of space, such as object-levelspace:An object is at one location at atime.Moving from L to M initiates alocation of M.Moving from L to M terminates alocation of L.An agent picking up an objectinitiates the agent holding theobject.An agent letting go of an objectterminates the agent holdingthe object.An agent picking up an objectreleases its location.If A is holding O, then O is whereA is.If A is holding O and O is at L, thenA letting go of O initiates O beingat L.The event calculus can be used to representand reason about the goal-basedbehavior of a rational agent using thefollowing knowledge:Adding a goal initiates an activegoal.Dropping a goal terminates anactive goal.Adding a plan initiates an activeplan.Dropping a plan terminates anactive plan.An active goal with no active plantriggers adding an appropriateplan.114 communications of the acm | january 2009 | vol. 52 | no. 1

contributed articlesTable 2. Four Models of a ProblemAn active plan triggers executingthe next step.An active goal that is achievedtriggers dropping the active goaland its active plan.Discrete Event Calculus ReasonerThe Discrete Event Calculus Reasoner bsolves event calculus projection andexplanation problems efficiently usingsatisfiability (SAT). 6 At its core, the DiscreteEvent Calculus Reasoner is a modelfinding program. As shown in Figure1, the program takes commonsenseknowledge and the truth values of somefacts as input, encodes a SAT problem,invokes a complete SAT solver, and decodesthe results of the SAT solver toproduce models as output. Each modelassigns a truth value to every fact.Each model produced by the DiscreteEvent Calculus Reasoner fills in facts notprovided as input. For example, supposewe know that waking up initiates beingawake, Holly is not awake at timepoint 0,and she is awake at timepoint 1. Furthersuppose that we limit the timepoints to0 and 1, and the agents to Holly and Ken.The program produces the four modelsshown in Table 2. This is an instance ofexplanation: The fact that Holly wokeup at timepoint 0 explains how it wasthat she was not awake at timepoint 0and awake at timepoint 1. Not much isknown about Ken. He might have beenawake or not awake at timepoint 0. Butif he did wake up at timepoint 0, then hewas awake at timepoint 1.ApplicationsCommonsense reasoning using theevent calculus is finding applicationb http://decreasoner.sourceforge.net/in many areas, including business systems,natural language understanding,and robotics.Business systems. The event calculuscan be used to make business systemsmore flexible and more aware ofthe human world. It is being used toincrease the flexibility of customer andmerchant applications implementingthe NetBill payment protocol. 12 Insteadof representing the protocol in a traditionalfashion as a finite state machine(FSM), the event calculus is used to representand reason about the commitmentsunderlying the protocol. An exampleof a commitment is that sendinga price quote for a product commits thesender to delivering the product if thecustomer sends a purchase request.Commonsense reasoning allows theNetBill applications to adapt to noveland exceptional situations. For example,the NetBill protocol specifies thata transaction begins with a price quoterequest from the customer. Yet by reasoningabout commitments, it is possiblefor the merchant application todetermine that it is in fact possible tosend an unsolicited price quote to thecustomer. Of course, the merchant isthen committed to deliver the productif the customer orders it at the quotedprice. Another example is that the customerapplication can determine thatit is possible to bargain hunt by sendinga purchase request at a low pricewithout having previously received aprice quote. The customer is then committedto pay if the merchant deliversthe product at that price, which themerchant isn’t committed to do.The event calculus is being used tomodel business workflows. 1 The modelof a workflow can be used for variouspurposes, such as (1) simulating theworkflow, (2) managing the executionof the workflow by participants, and(3) querying the past, present, and possiblefuture states of the workflow.Natural language understanding.The event calculus is well-suited to therepresentation of the meaning of naturallanguage, and making inferencesin natural language understandingsystems. It is being used to representtense and aspect, 11 and for inferencingin narrative comprehension systems. 7Given a commonsense knowledgebase about a domain and a narrativeconsisting of known properties andevents in that domain, the event calculuscan be used to fill in missing propertiesand events. A system for understandingterrorism news stories 7 usescommonsense reasoning to fill in suchthings as the following:After being threatened, the victim isangry at the perpetrator.After the target is set on fire, it iseventually destroyed.Although this work is in its infancy, itpoints the way to the development ofquestion answering systems with anability to understand text more deeplythan is currently possible.Robotics. The event calculus is suitablefor representation and reasoningwithin robotics systems. It is beingused within a robot’s high-level visionsystem 10 to improve object recognitionby taking advantage of reasoning aboutthe changes of the appearance of anobject over time.The high-level vision system is dividedinto three layers. The first layertakes low-level edge information andproduces hypotheses about regions.The second layer produces hypothesesabout appearance. The third layer produceshypotheses about what objectsare in view based on the changes in appearanceover time.Related WorkOther logic-based formalisms for commonsensereasoning include the situationcalculus, the fluent calculus, temporalaction logics (TAL), and actionlanguages. The situation calculus issimilar to the event calculus, but usesbranching time instead of linear time.The fluent calculus is an extension ofthe situation calculus. TAL is similarJanuary 2009 | vol. 52 | no. 1 | communications of the acm 115

contributed articlesto the event calculus. Action languagesuse specialized syntaxes rather thanfirst-order or second-order logic.Software tools are available for reasoningusing these formalisms:cKM implements the situation calculus.dFLUX implements the fluent calculus.eVITAL implements TAL.fThe causal calculator (CCALC) implementsthe CCALC action language,˲˲˲˲˲˲˲˲which is based on the distinction betweenwhat is true and what has a cause.˲˲gE-RES implements the E action language,which is based on the event calculus.Formalisms and tools for automatedcommonsense reasoning are closely relatedto those for planning. The task inplanning is to take as input an initial stateand a goal state, and produce as outputa sequence of actions that bring aboutthe goal state starting from the initialstate. Most planners support the PDDLplanning domain definition language hthat is used in international planningcompetitions. PDDL treats many of thesame phenomena of action and changeas the event calculus such as contextsensitiveeffects and the commonsenselaw of inertia. i The main difference betweenplanners and logical common-A Unix ExampleHow does one actually go about using the Discrete Event CalculusReasoner? Suppose we wish to reason about the Unix system. Weenter the following text into a file called Unix.e:sort dirsort filenamefluent Cwd(dir)fluent In(filename, dir)event Mv(filename, filename)[filename1, filename2, dir, time]HoldsAt(Cwd(dir), time) & filename1!=filename2 ->Initiates(Mv(filename1, filename2), In(filename2, dir),time).[filename1, filename2, dir, time]HoldsAt(Cwd(dir), time) & filename1!=filename2 ->Terminates(Mv(filename1, filename2), In(filename1, dir),time).We define two sorts (or types): one for directories and onefor filenames. We define two fluents (or properties): one thatrepresents the current working directory and one that representsthat a filename is in a directory. We define an event that representsthat a mv command is issued. We then write two logical axioms.These axioms specify that, if one is in a directory and one issues thecommandmv filename1 filename2where filename1 is different from filename2, then filename2 willbe in the directory and filename1 will no longer be in the directory.The notation [filename1, filename2, dir, time] means “for allfilename1, filename2, dir, and time.” The notation -> means“implies.”Suppose we wish to solve the following projection problem. Initially,the current working directory is D and the only filename in directoryD is N1. We issue the command mv N1 N2. What is the result? Todetermine the answer, we enter the following problem into a file:load Unix.edir Dfilename N1, N2HoldsAt(Cwd(D), 0).[filename] HoldsAt(In(filename, D), 0) filename=N1.Happens(Mv(N1, N2), 0).completion HappensThe notation means “if and only if.” When we provide this fileas input to the Discrete Event Calculus Reasoner, it produces thefollowing output:1 model---model 1:0In(N1, D).Cwd(D).Happens(Mv(N1, N2), 0).1-In(N1, D).+In(N2, D).The result is that filename N1 is no longer in D and N2 is now in D.By default, the Discrete Event Calculus Reasoner shows only thedifferences from one timepoint to the next. A property that changesfrom true to false is indicated with a minus sign (“-”) and a propertythat changes from false to true is indicated with a plus sign (“+”).Suppose we wish to solve the following explanation problem.At timepoint 0, N1 is the only filename in directory D, whereasat timepoint 1, N2 is the only filename in directory D. Whathappened? We enter the following into a file:load Unix.edir Dfilename N1, N2[filename] HoldsAt(In(filename, D), 0) filename=N1.[filename] HoldsAt(In(filename, D), 1) filename=N2.range time 0 1When we run this through the Discrete Event Calculus Reasoner, itproduces the following:1 model---model 1:0In(N1, D).Cwd(D).Happens(Mv(N1, N2), 0).1-In(N1, D).+In(N2, D).The program determines that the command mv N1 N2 was issuedwhen the current working directory was D.range time 0 1116 communications of the acm | january 2009 | vol. 52 | no. 1

contributed articlessense reasoning tools is that plannersare highly optimized for planning andtypically support only planning, whereascommonsense reasoning tools supportplanning as well as other forms of reasoning,including projection, j postdiction(determining the initial state givena sequence of events and a final state),and model finding (filling in missingproperties and events given observedproperties and events).c http://www.cs.utexas.edu/users/mfkb/km.htmld http://www.fluxagent.org/e http://www.ida.liu.se/~jonkv/vital/f http://www.cs.utexas.edu/users/tag/cc/g http://www.ucl.ac.uk/~uczcrsm/LanguageE/h http://www.cs.yale.edu/homes/dvm/i Few PDDL tools implement continuous change andtriggered events. Exceptions are TM-LPSAT (http://cs1.cs.nyu.edu/~jiae/) and VAL (http://planning.cis.strath.ac.uk/VAL/).j Projection is performed by Drew McDermott’s PDDLsolution checker (ftp://ftp.cs.yale.edu/pub/mcdermott/software/pddl.tar.gz).Nonlogical MethodsA number of nonlogical methods forcommonsense reasoning have beendeveloped by artificial intelligence researchers.8 How do they compare withthe event calculus?When using the event calculus tosolve a problem in a domain, we typicallyassume that knowledge about thedomain has been previously entered.Analogical processing methods can beused to generate candidate inferencesin a novel domain by finding analogiesto familiar domains.The event calculus does not dealwith probabilities, although it does allowrepresentation of nondeterministiceffects of events. Methods based onprobability theory can be used to quantifyuncertainty about commonsenseknowledge, uncertainty about a givenscenario, and uncertainty about commonsenseinferences.Qualitative reasoning methods areparticularly strong at modeling and simulatingthe behavior of physical mechanismssuch as clocks, electrical circuits,pressure regulators, and water tanks.Natural-language-based methods 2have the advantage that commonsenseknowledge can be entered without havingto learn any special notation. Touse the event calculus one must have abasic familiarity with classical logic.The society of mind 5 allows multiplecommonsense reasoning methodsto be combined so that the best techniquescan be used to make progress ateach point in reasoning. The event calculuscan be one of these techniques.ConclusionThe automation of commonsense reasoningis coming to fruition. Futurechallenges include the developmentof useful commonsense knowledge forapplication areas and the efficient solutionof large commonsense reasoningproblems.The event calculus handles the importantproblems of commonsensereasoning, and is highly usable. It isbeing applied to business systems,natural language understanding, andvision. It will be interesting in the comingyears to explore its advantages forcreating more flexible and user-friendlysystems.References1. Cicekli, N. K. and Yildirim, Y. Formalizing workflowsusing the event calculus. M. T. Ibrahim, J. Küng,and N. Revell, Eds. Database and Expert SystemsApplications. Lecture Notes in Computer Science,Springer, Berlin, 2000, 222-231.2. Lieberman, H., Liu, H., Singh, P., and Barry, B. Beatingcommon sense into interactive applications. AIMagazine 25, 4 (2004), 63-76.3. McCarthy. J. Programs with common sense.Mechanisation of Thought Processes: Proceedings of aSymposium held at the National Physical Laboratoryon 24th, 25th, 26th and 27th November 1958. HerMajesty’s Stationery Office, London, 1959, 75-91.4. Miller, R. and Shanahan, M. Some alternativeformulations of the event calculus. A. C. Kakas and F.Sadri, Eds. Computational Logic: Logic Programmingand Beyond: Essays in Honour of Robert A. Kowalski,Part II, Lecture Notes in Computer Science, Springer,Berlin, 2002, 452-490.5. Minsky, M. The Emotion Machine: CommonsenseThinking, Artificial Intelligence, and the Future of theHuman Mind. Simon & Schuster, NY, 2006.6. Mueller, E. T. Event calculus reasoning throughsatisfiability. Journal of Logic and Computation 14, 5(2004), 703-730.7. Mueller, E. T. Understanding script-based stories usingcommonsense reasoning. Cognitive Systems Research5, 4 (2004), 307-340.8. Mueller, E. T. Commonsense Reasoning. MorganKaufmann, San Francisco, CA, 2006.9. Shanahan, M. Solving the Frame Problem. MIT Press,Cambridge, MA, 1997.10. Shanahan, M. Perception as abduction: Turning sensordata into meaningful representation. Cognitive Science29 (2005), 103-134.11. van Lambalgen, M. and Hamm, F. The ProperTreatment of Events. Blackwell, Malden, MA, 2005.12. Yolum, P. and Singh, M. P. Reasoning aboutcommitments in the event calculus: An approachfor specifying and executing protocols. Annals ofMathematics and Artificial Intelligence 42 1-3 (2004),227-253.Erik T. Mueller (etm@us.ibm.com) is a Research StaffMember at the IBM Thomas J. Watson Research Centerin Yorktown Heights, NY.© 2009 acm 0001-0782/09/0100 $5.00January 2009 | vol. 52 | no. 1 | communications of the acm 117