Shanahan, M. P.: Representing continuous change in the event calculus, Proceedings of the European Conference on Artificial Intelligence (ECAI-90), 1990.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....This method has not formally investigated even it seems reasonable. Continuous changes The full class RA can be treated, extending the original Sandewall s semantics for dealing with trajectories in the case of continuous time and feature values domains, in a similar way to that proposed by [Sha90] in the context of event calculus. In the main work [Pal97] we proposed an extension of FLP by means of trajectory action laws of the following form: S, T ]f : traj(tr) S, T ]act # ( S]f 1 = v 1 , S]f n = v n ) S, T ]f : traj( tr 1 , tr k ] together with a ....

M. Shanahan. Representing continuous change in the Event Calculus. In Proceedings of the 9th European Conference on Articial Intelligence, page 598, 1990.

....developed in [Sandewall, 1989] in which dynamic information is modelled by autonomous processes that run in parallel and that may eventually trigger further changes in the environment. This technique has been integrated, for example, into situation calculus [Reiter, 1996] event calculus [Shanahan, 1990] , or fluent calculus [Thielscher, 2001a] Implementing these approaches, the agent programming and planning languages ConGolog [Giacomo and Levesque, 2000] or FLUX [Martin, 2003] support the specification of concurrent processes and their effects. path info camera image path request position ....

M. Shanahan. Representing continuous change in the event calculus. In Proc. of the European Conf. on Artificial Intelligence (ECAI-90), pages 598--603, 1990.

....numbers. A prototype implementation of an integration of SLDNFA and CLP(R) a constraint solver for real number linear arithmetic, was presented in [3] Below, two simple applications involving real number entities are given. The rst example uses Shanahan s extension of EC for continuous change [49]. The example was presented in [3] and is a variant of one in [49] There is a barrel b and two water pipes p 1 ; p 2 , two taps tap 1 ; tap 2 connecting respectively p 1 to b and p 2 to b. Initially b is empty and both taps are closed. The problem is to nd a plan to ll b with a content of 100 ....

....CLP(R) a constraint solver for real number linear arithmetic, was presented in [3] Below, two simple applications involving real number entities are given. The rst example uses Shanahan s extension of EC for continuous change [49] The example was presented in [3] and is a variant of one in [49]. There is a barrel b and two water pipes p 1 ; p 2 , two taps tap 1 ; tap 2 connecting respectively p 1 to b and p 2 to b. Initially b is empty and both taps are closed. The problem is to nd a plan to ll b with a content of 100 liter. The de nition of holds contains one extra rule which ....

M. Shanahan. Representing continuous change in the event calculus. In Proc. of the European Conference on Arti cial Intelligence, page 598, 1990.

....level of water in a vessel achieves the vessel s rim, the level stops rising and the water spills over. In order to give a formal account of common sense knowledge we have to formalise such issues. In the present work we are going to describe the formalisation of continuous change as proposed in [36][44] 39] In order to formalise continuous change in Event Calculus we extend the calculus in the following ways: ffl consider a sort for reals; ffl represent time in the real line; ffl introduce the predicate T rajectory(f 1 ; t 1 ; f 2 ; d) which states that, if the fluent f 1 is initiated ....

M. Shanahan. Representing continuous change in the event calculus. In Proceedings ECAI-90, pages 598--603, 1990.

.... for a theory of cancelling and combined effects of actions similar to that in [4] It has already been pointed out [10] 12] 33] that a narrative based approach offers alternative ways to model non deterministic effects of actions, and is a natural setting in which to model continuous change [39] [43] 32] 41] Finally, we might extend the syntax and semantics of E to deal with incomplete information about the order and timing of action occurrences, perhaps building on the ideas in [10] and [12] and perhaps introducing temporal variables into the language in a manner similar to [5] and ....

Murray Shanahan, Representing Continuous Change in the Event Calculus, Proceedings ECAI'90, pages 598-603, 1990.

....(e.g. 40, 20, 21, 27, 54, 33, 9, 47] So much so, that some researchers identify the frame problem as characteristic of theories based on the situation calculus, instead of as a problem inherent to the formalization of dynamic systems. Unfortunately, as has been pointed out elsewhere (e.g. [16, 23, 55]) the original situation calculus is a limited language that has several shortcomings. Nevertheless, as Gelfond, Lifschitz and Rabinov argue [16] these limitations can be overcome. The objective of this thesis is twofold. On the one hand, we want to extend the expressiveness of the situation ....

....of Allen s theory of time [3] Galton uses the terminology state of motion and state of position for properties that correspond to our discrete fluents and continuous parameters respectively. Also, related ideas are explored by Shanahan in the framework of the event calculus in logic programming [55]. The majority of the problems that deal with properties that vary continuously with time are problems in the domain of physics. Since physics is concerned with building mathematical models for natural phenomena, we have to model actions or events that are considered natural. We use the term ....

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Shanahan, M. Representing continuous change in the event calculus. In Proceedings ECAI (1990).

....open intervals. If fluent MN was set to value : at time 1 and was set to a different value at time 2 (and no other settings for value : occurred in between) then the fluent MN has value : in the interval S 1 2 . This is the opposite convention to the event calculus [Shanahan, 1990] . We want this convention as robots have internal state so that it can affect what they will do; if a robot realises at time 2 that it should be doing something different, then it should change what it is doing immediately, and not wait. This notion of persistence is close to that of the event ....

....have internal state so that it can affect what they will do; if a robot realises at time 2 that it should be doing something different, then it should change what it is doing immediately, and not wait. This notion of persistence is close to that of the event calculus [Kowalski and Sergot, 1986; Shanahan, 1990] see Section 4.5) 1 This is to allow us to model transport delays (see Section 4.2) that are essential for the modelling of analogue systems. In general using this facility means that we have to maintain a history of T5UWV values and not just a state of T5UWV values. 2.3 Integration ....

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M. Shanahan. Representing continuous change in the event calculus. In Proc. ECAI-90, pages 598--603, 1990.

....event calculus and have extended it with abduction for the purpose of planning. 31] extended event calculus to deal with necessary preconditions of actions. 25] implemented a planning system based on this formalism. Other work has been done to extend event calculus with continuous actions [32] and time granularity [15] 26] Recently [10] applied abductive event calculus to solve a number of benchmark problems in temporal reasoning, such as the Murder Mystery, the Stolen Car problem, the Walking Turkey Shooting problem and the Russian Turkey Shooting problem. The latter problem ....

M. Shanahan. Representing continuous change in the event calculus. In Proc. of the European Conference on Artificial Intelligence, page 598, 1990. 29

....event calculus and have extended it with abduction for the purpose of planning. 21] extended event calculus to deal with necessary preconditions of actions. 17] implemented a planning system based on this formalism. Other work has been done to extend event calculus with continuous actions [22] and time granularity [11] 18] Recently [8] applied abductive event calculus to solve a number of benchmark problems in temporal reasoning, such as the Murder Mystery, the Stolen Car problem, the Walking Turkey Shooting problem and the Russian Turkey Shooting problem. The latter problem ....

M. Shanahan. Representing continuous change in the event calculus. In Proc. of the European Conference on Artificial Intelligence, page 598, 1990.

....actions as the only type of action that can be triggered. There is an important advantage of both the axiomatization presented here and Pinto s over approaches which depend on encapsulating the behaviour of at least one parameter inside an explicit T rajectory predicate (or similar) e.g. [14], 16] 15] This is that information about a parameter s behaviour, in the form of various mathematical constraints, may be distributed in a natural way throughout the domain dependent part of the theory. For example, in the water tanks scenario the mathematical knowledge of the domain is ....

Murray Shanahan, Representing Continuous Change in the Event Calculus, In Proceedings ECAI'90, pages 598-603, 1990.

....the situation calculus, the resulting sentences would be in the monadic situation calculus, and therefore would be less general than the logical theories to which our approach applies. There have been a few earlier papers on formalizing natural actions and continuous time. Shanahan s approach [30] is embedded in the event calculus (Kowalski and Sergot [11] Sandewall [27] relies on a temporal logic. Accordingly, these proposals are difficult to compare with ours, based as it is on the situation calculus. Below, we provide a comparison along one dimension: abductive planning, which seems ....

M.P. Shanahan. Representing continuous change in the event calculus. In Proceedings ECAI 90, pages 598--603, 1990.

.... the time line, rather than working along the series of intervals [0; 1 ] 1 ; 2 ] Again where time is interpreted only as the naturals, the theorem can be proved with respect to an expanded Event Calculus which includes trajectory mechanisms similar to those introduced by Shanahan [23], 24] 25] These mechanisms facilitate the description of the behaviours of parameters whose values can change between action occurrences according to mathematical functions of time. If we allow time to also be interpreted as the reals, things get more complicated. Investigations are ....

.... Investigations are currently underway to find syntactically or mathematically verifiable constraints on domain descriptions which guarantee plan consistency in the sense of Theorem 1, where the associated Event Calculus includes mechanisms for dealing with continuous change similar to those in [23], 24] or [13] 7 6 Discussion These notes were written partly as a response to the remarks by Reiter in [20] about abduction and planning in linear time formalisms. In particular, the splitting of the Happens predicate into the predicates Occurs and Perform (see axiom (EC7) is in order to ....

Murray Shanahan, Representing Continuous Change in the Event Calculus, In proceedings ECAI'90, pages 598-603, 1990.

....time. The solution is then to take this function of time to be the value of robotLoc. We call functional fluents whose values are continuous functions continuous fluents. The idea of continuous fluents is not new and has been investigated in various ways as in (Sandewall 1989; Galton 1990; Shanahan 1990; Miller 1996; Pinto 1997) Here we essentially follow Pinto (Pinto 1997) and only illustrate the basic principles by way of example. For our 1 dimensional robot, we introduce two kinds of functions of time, constant functions, denoted by 3 Throughout, free variables are assumed to be implicitly ....

Shanahan, M. 1990. Representing continuous change in the event calculus. In ECAI'90.

....continuous fluents, which are often called parameters, is not new. Sandewall (Sandewall 1989) proposed it when integrating the differential equations into logic, Galton (Galton 1990) investigated similar issues within a temporal logic, and Shanahan considers continuous change in the event calculus (Shanahan 1990). Finally, Miller and Pinto (Miller 1996; Pinto 1997) formulate continuous change in the situation calculus. Here we essentially follow Pinto, in a somewhat simplified form. We begin by introducing a new sort t function, whose elements are meant to be functions of time. We assume that there are ....

Shanahan, M. 1990. Representing continuous change in the event calculus. In ECAI'90.

....3] in fact [0]loaded = true is still missing from the problem domain) and unknown at 7; 2) the feature alive is now true in [0; 7] and false in [8; 1) while it should be unknown at 7. Some of these remaining problems can be solved via Shanahan s extension of EC to continuous change (see [Sha90] holds at(P; T ) happens( ET;Ev) ET T; initiates(Ev; Q) suceeds(Ev) not clipped(ET; Q; T ) trajectory(Q; ET;P;T ) where the predicate trajectory is like Sandewall s trajectory function T rajs (def. 2.1.17) In order to perform backward reasoning, it is possible to augment 2 The ....

M. Shanahan. Representing continuous change in the Event Calculus. In Proceedings of the 9th European Conference on Artificial Intelligence, page 598, 1990.

....and an implementation of a prototype was presented. This system integrates iff abduction and reasoning about linear equations and inequalities. Below, two simple applications involving real number entities are given. The first example uses Shanahan s extension of EC for continuous change [44]. The example was presented in [3] and is a variant of one in [44] There is a barrel b and two water pipes p 1 ; p 2 , two taps tap 1 ; tap 2 connecting respectively p 1 to b and p 2 to b. Initially b is empty and both taps are closed. The problem is to find a plan to fill b with a content of 100 ....

....system integrates iff abduction and reasoning about linear equations and inequalities. Below, two simple applications involving real number entities are given. The first example uses Shanahan s extension of EC for continuous change [44] The example was presented in [3] and is a variant of one in [44]. There is a barrel b and two water pipes p 1 ; p 2 , two taps tap 1 ; tap 2 connecting respectively p 1 to b and p 2 to b. Initially b is empty and both taps are closed. The problem is to find a plan to fill b with a content of 100 liter. The definition of holds contains one extra rule which ....

M. Shanahan. Representing continuous change in the event calculus. In Proc. of the European Conference on Artificial Intelligence, page 598, 1990.

....can be adapted in a natural way to deal with versioning of objects and schema evolution respectively. The literature on temporal reasoning and temporal databases is very extensive and we do not attempt a full survey here. For various extensions and applications of the event 3 calculus see, e.g. [11, 15, 20, 23, 24, 51, 54, 59, 62, 65]. Comparisons of the event calculus with situation calculus are provided in [53] and [45] For temporal databases, 43] provides a recent bibliography of work in this area together with pointers to previous bibliographies. The collection [69] gives an excellent overview of the main approaches and ....

....in the literature on temporal databases. The OEC can be extended to accommodate other kinds of time varying behaviour by incorporating various extensions that have been developed for the original, relational event calculus. In particular continuous change can be treated using the trajectories of [59]. We do not present the details here. The treatment can be imported from the relational versions without modification, and is actually slightly more convenient to formulate within the OEC, since it is continuous change of values of attributes that is of interest; it is difficult to imagine what ....

M.P. Shanahan. Representing continuous change in the event calculus. In Proceedings of ECAI-90, Stockholm, Sweden, 1990.

....actions as the only type of action that can be triggered. There is an importantadvantage of both the axiomatization presented here and Pinto s over approaches which depend on encapsulating the behaviour of at least one parameter inside an explicit T rajectory predicate (or similar) e.g. [11], 13] 12] This is that information about a parameter s behaviour, in the form of various mathematical constraints, may be distributed in a natural way throughout the domain dependent part of the theory.For example, in the water tanks scenario the mathematical knowledge of the domain is ....

Murray Shanahan, Representing Continuous Change in the Event Calculus, In Proceedings ECAI'90, pages 598-603, 1990.

....for which the event calculus was designed. In doing so, we shall appeal to an extension of the situation calculus, enriched with time and event occurrences. With this specification in hand, we shall be in a position to derive a logic program which is sound with respect to it. Murray Shanahan [16, 17] has extended the calculus of events in several interesting ways. However, he bases his research on an event calculus which loosely corresponds to the original calculus of events. In fact, Shanahan s event calculus avoids the problems we describe in this section by eliminating the notion of ....

Shanahan, M. Representing continuous change in the event calculus. In Proceedings ECAI (1990).

....While these actions are happening, they can affect fluents. For example, while the action fill is happening, the height of the water increases (see example 2. 16) This method will be proved later to be the same as the idea of a trajectory predicate in the continuous version of event calculus [Shanahan, 1990]. Also this approach is different from that of [Herrmann and Thielscher, 1996] in which actions are regarded as points between two processes. To include released fluents and non continuous fluents, the stratified persistence rule will be extended slightly. Released fluents will be included using ....

....sink is 0cm. At time point 10, the agent starts filling the kitchen sink with water at 2cm per 1 time unit. However, we cannot fill the water any more after the water reaches the top of the kitchen sink. The height of the kitchen sink is 30cm. We can express this example which was introduced in [Shanahan, 1990] by the following sentences, where fill is an action and height is a mathematical variable; given (value(height, 0) 0) start (fill, 10) value (height, H0 2 (T1 T0) at T1 if value(height, H0) at T0 while fill. end fill if value(height, 30) Note that in the last sentence, there is no ....

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M. Shanahan. Representing continuous change in the event calculus. In ECAI 90, pages 598--603, 1990.

....of other fluents that have. Domain constraints that attempt to constrain the relationship between inertial fluents can lead to inconsistency. 7 The issue of continuous change has been largely neglected in the design of formalisms for reasoning about action until recently [Sandewall, 1989] [Shanahan, 1990], Miller, 1996] Reiter, 1996] In the present formalism, following [Shanahan, 1990] continuous change is represented through the introduction of a new predicate and the addition of an extra axiom. The formula Trajectory(f1,t,f2,d) represents that, if the fluent f1 is initiated at time t, then ....

....between inertial fluents can lead to inconsistency. 7 The issue of continuous change has been largely neglected in the design of formalisms for reasoning about action until recently [Sandewall, 1989] Shanahan, 1990] Miller, 1996] Reiter, 1996] In the present formalism, following [Shanahan, 1990], continuous change is represented through the introduction of a new predicate and the addition of an extra axiom. The formula Trajectory(f1,t,f2,d) represents that, if the fluent f1 is initiated at time t, then after a period of time d the fluent f2 holds. We have the following axiom. ....

M.P.Shanahan, Representing Continuous Change in the Event Calculus, Proceedings ECAI 90, pp. 598--603.

.... ; Ringing ; t) A2) A disadvantage of rules such as (A1) is that it is difficult to express that the occurrence of the later action might be prevented by some intervening action (e.g. somebody might switch off the alarm during the night) A more flexible approach involves the use of trajectories [Shan 90] It is convenient to illustrate this technique here by introducing a new sort P of parameters into the language. Like fluents, parameters are time varying properties, but unlike (frame) fluents they have no associated default persistence. More precisely, parameters are names for ....

....range of formulations of the Event Calculus. The Event Calculus was originally formulated as a logic program in [KoSe 86] and many alternative and extended logic program formulations have subsequently been proposed, including [DeMi 92] DeVa 96] KaMi 97] KaMi 99] Kowa 92] SaKo 95] Shan 90] VaDe 94a] VaDe 94b] VaDe 95] and [VaDe 96] The Event Calculus has also been formulated in modal logic in [CeCh 95] CeCh 96] CeFr 97a] CeFr 97b] CeFr 98] and [ChMo 94] as an action description language in [KaMi 97] and [KaMi 98] and in an argumentation framework in [KaMi 99] ....

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M. P. Shanahan, Representing Continuous Change in the Event Calculus, Proceedings ECAI'90, pp. 598-603, 1990.

....and Cancelled, as in [Gelfond, et al. 1991] and [Lin Shoham, 1992] cater for concurrent actions that interfere with each other s effects. The Cancels predicate will be minimised via circumscription, along with Initiates, Terminates and Releases. The Trajectory predicate, first proposed in [Shanahan, 1990], is used to capture continuous change, as in the height of a falling ball or the level of liquid in a filling vessel, for example. Formula Meaning Cancels(a1,a2,b) The occurrence of a1 cancels the effect of a simultaneous occurrence of a2 on fluent b Cancelled(a,b,t1,t2) Some event occurs ....

M.P.Shanahan, Representing Continuous Change in the Event Calculus, Proceedings ECAI 90, pp. 598--603.

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Shanahan, M. P.: Representing continuous change in the event calculus, Proceedings of the European Conference on Artificial Intelligence (ECAI-90), 1990.

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Shanahan M., Representing continuous change in the Event Calculus, Proc. of the 9th European Conference on Arti cial Intelligence (ECAI), Stockholm, Sweden, John Wiley & Sons, 1990.

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