Lifschitz, V., and Rabinov, A. Miracles in Formal Theories of Action. Artificial Intelligence 38 (1989), 225--237.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is the set of fluents that hold in that situation. Notice that the branching factor of the tree of situations rooted at S 0 equals the number of distinct actions that exist. In this section, we discuss a version of the situation calculus which has evolved through a sequence of refinements [29, 47, 41, 31]. The situation calculus is a sorted second order language with equality. We use the standard operators conjunction, disjunction, implication and equivalence ( oe and j respectively) and standard universal and existential quantifiers. Scoping is indicated by parentheses or by the dot notation ....

....n ; do( do(a 1 ; s) which we abbreviate as: do( a 1 ; a n ] s) Keep in mind that [a 1 ; a n ] is not a term in the language and that it can only appear as a first argument in a do function term. 2.1.2 Basic Axioms and Language. It has been pointed out (e.g. [29, 47]) that the sort of situations in the situation calculus can be formalized in much the same way as the sort of numbers is formalized in Peano s axioms in number theory. The formalization that we present here originates on Reiter s formalization that appears in [47] The basic axioms for situations ....

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Lifschitz, V., and Rabinov, A. Miracles in Formal Theories of Action. Artificial Intelligence 38 (1989), 225--237.

....for which S 0 is not equivalent to either McCain and Turner s or Baral and Gelfond s approach, and for which it gives better results than these approaches do. For the other existing causal approaches specifically, those of Morgenstern and Stein [25] Geffner [7] and Lifschitz, Haugh and Rabinov [11, 18] we give other, new examples of reasoning domains where our approach gives better results than they do. For two popular non causal approaches, we argue that they can be interpreted as implementing an approximation of I 0 . For one of them, namely Baker s approach [1, 4, 12] we actually prove ....

....values occur [10, 23] The YSP paper then showed that this method does not work well. One of the first proposed solutions [11, 17] to the YSP was to refine the original model selection criterion to select only the models with the least uncaused changes. Indeed, all existing causal approaches [7, 11, 17, 18, 19, 21, 25] implement some variation of this idea. In our own approach we will refine this idea by connecting causation to explanation: informally, if A causes B, then A also provides an explanation for B. But in domains subject to persistence, we may also say that if we have Ho(f; t) for some regular fluent ....

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V.L. Lifschitz and A. Rabinov. Miracles in formal theories of action. Artificial Intelligence, 38:225--237, 1989.

....4 In Chapter 3.5 we discuss in some detail their default theory for the Yale Shooting domain. approaches which employ variants of circumscription, autoepistemic logic, default logic and logic programming. Undoubtedly the greatest concentration of such work has been in circumscription [Hau87, Lif87a, LR89, Lif90, Bak91, GLR91, Lif91, LS91, CE92, LR94, KL95, Lin95, Gus96, Lin96]. There were also early published solutions to the Yale Shooting problem in autoepistemic logic [Gel88] default logic [Mor88] and logic programming [EK89, Eva89, AB90] A primary methodological weakness of much of the work cited above is the fact that it is motivated by, and validated for, only a ....

Vladimir Lifschitz and Arkady Rabinov. Miracles in formal theories of actions. Artificial Intelligence, 38(2):225--237, 1989.

....the afternoon . true, since what becomes true is some other situation, say Result(W aitkSteal; S) where we use W aitkSteal to mean that actions W ait and Steal happen at the same time. Our position here is different from those in existing approaches to temporal explanation championed by, e.g. [5, 6, 12, 42, 69]; they would conclude that some of the three W ait actions are abnormal. It is the abnormality of some of the three W ait actions that is consistent with the car being missing. But there are no satisfactory explanations for why one of the three W ait actions is abnormal. On the other hand, ....

Lifschitz, V. and Robinov, A., Miracles in formal theories of action, Artificial Intelligence, 38:2, 1989, 225--237

....discuss why we treat events as a kind of fluents and not as a separate sort. These issues will be treated in the longer version of [9] Loaded t Loaded t 1 Load t 1 t 1 t Alive Alive Shoot t 1 Figure 1: A Yale Shooting Causal Network least uncaused changes Indeed, all existing causal approaches [12, 13, 14, 15] implement some variation of this idea. But our own approach pushes it much further, making use of the intimate relation between causation and explanation: informally, if A causes B, then A also provides an explanation for B. But in domains subject to persistence, we may also say that if we have ....

....restricted versions of S 0 and the approaches of McCain and Turner [14] and Baral and Gelfond s L 3 [10] 6 . It becomes clear at first glance that Lin s recent approach [13] is almost identical to S 0 . For the causal approaches of Morgenstern and Stein [15] and Lifschitz, Haugh and Rabinov [12] we give examples [9] showing that they sometimes yield the wrong results. We take all this as evidence that S 0 works well for wide classes of causal theories. Our main theorem now states that for a wide class of reasoning domains we have that if S 0 works well for them, then I 0 does so too. In ....

V.L. Lifschitz and A. Rabinov. Miracles in formal theories of action. Artificial Intelligence, 38:225--237, 1989.

....but not explanation. New examples were then devised, with names such as the Stolen Car Problem [8] and the Stanford Murder Mystery [1] The responses again varied, including dismissals of some of the complaints, as well as new solutions to the YSP that allegedly avoided some of these problems ([19, 15, 2], etc. Each solution has attracted some measure of criticism. The lack of precise criteria against which to evaluate theories of action does not mean that the research has been worthless; quite the contrary. It is widely recognized that the frame problem is real and that its identification was ....

V. Lifschitz and A. Rabinov. Miracles in formal theories of action. Artificial Intelligence, 38:225--237, 1989.

.... first introduced by McCarthy and Hayes in [MH69] and is a specialisation of many sorted first order logic with equality (MFOL = Throughout the years several refinements and extensions have been made to cope with problems like temporal reasoning, concurrence, actions with duration inter alia [LR89, GLR91, Rei91]. Due to space limitations, we won t go into details about the formalism, but will only present the basic requirements. The version considered here was first proposed by Reiter in [Rei91] and subsequently extended in [Rei93, LR94, PR95] The set of sorts includes, among others, three sorts sit, ....

V. Lifschitz and A. Rabinov. Miracles in formal theories of action. Artificial Intelligence, 38:225--237, 1989.

....first order logic with equality (MFOL) It was first proposed in [8] as a formalism for specifying dynamic systems . Through the years several refinements and extensions have been proposed to allow SC to cope with problems like temporal reasoning, concurrency, actions with duration inter alia [6, 4, 13, 10, 11]. The main concepts of SC are situations, actions and fluents. A situation represents the state of the system that we are specifying. The system changes from one situation to another when an action is performed. The properties of the system are characterized by fluents, that may or may not hold ....

V. Lifschitz and A. Rabinov. Miracles in formal theories of action. Artificial Intelligence, 38:225--237, 1989.

....The paper presents the standard and alternative styles of representation first, then looks at the deductive approach, using both styles, and finally investigates the abductive approach. Most attempts to formalise temporal explanation have adopted the deductive approach [Morgenstern Stein, 1988] [Lifschitz Rabinov, 1989], Baker, 1989] Crawford Etherington, 1992] Suppose we have a formula T which captures the timeless laws of change in a given domain, and a formula H representing when certain time varying facts are true. According to the deductive approach, the explanation of an additional such fact F will ....

....situation s, and Holds(f,s) to represent that fluent f holds in situation s. If a fluent holds in a situation then it has the value true, and if it does not hold it has the value false. Several authors have attempted to deal with temporal explanation within the framework of the situation calculus [Lifschitz Rabinov, 1989], Baker, 1989] Crawford Etherington, 1992] But I will now argue that the style of representation they all use is problematic. To represent a particular domain using the situation calculus, we write two sets of sentences, one set describing which fluents change value as a result of performing ....

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V.Lifschitz and A.Rabinov, Miracles in Formal Theories of Action, Artificial Intelligence, vol 38 (1989), p 225.

....In the deductive approach, HoldsAt facts requiring explanation are conjoined with the domain, history and event calculus formulae, and explanations are expected to be among the logical consequences. This approach, using other formalisms, is common in the literature [Morgenstern Stein, 1988] [Lifschitz Rabinov, 1989], Baker, 1989] Baker, 1991] In the abductive approach, which is less common [Shanahan, 1989] Shanahan, 1993] explanations are Happens formulae which, when conjoined with the domain and history formulae and event calculus axioms, yield the facts to be explained as logical consequences. The ....

V.Lifschitz and A.Rabinov, Miracles in Formal Theories of Action, Artificial Intelligence, vol 38 (1989), pages 225-237.

....; also, we have made an informal comparison that makes clear that Lin s recent approach [ Lin, 1995; 1996 ] is largely identical to S 0 . For the other existing causal approaches specifically, those of Morgenstern and Stein [1988] Geffner [1990] and Lifschitz, Haugh and Rabinov [ Haugh, 1987; Lifschitz and Rabinov, 1989 ] we give examples of reasoning domains where our approach gives better results than they do. For some of the non causal approaches, we argue that they can be interpreted as implementing an approximation of I 0 . For one of the most well known of these, namely Baker s [ Baker, 1991; Crawford and ....

....as M 1 j Ho M 2 . Formally, M 1 j Ho M 2 iff for all g; t we have M 1 j= Ho(g; t) M 2 j= Ho(g; t) Loaded t Loaded t 1 Load t 1 t 1 t Alive Alive Shoot t 1 Figure 1: A Yale Shooting Causal Graph 3 Our Two Basic Ideas All existing causal approaches to formalizing persistence [ Haugh, 1987; Lifschitz and Rabinov, 1989; Morgenstern and Stein, 1988; Geffner, 1990; Lin, 1995; 1996; McCain and Turner, 1995 ] are based on variations of the same idea: prefer those models of a theory in which there is a cause for all changes of fluent values. We will refine this idea by connecting causation to explanation: ....

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V.L. Lifschitz and A. Rabinov. Miracles in formal theories of action. Artificial Intelligence, 38:225--237, 1989.

....been performed. Given that the Wait action has no known effects, what should the system conclude At a minimum, it should avoid collapsing in a contradiction, and with the right background knowledge, one would hope that the system could come up with a reasonable explanation. Lifschitz and Rabinov [16] handle this scenario by introducing miracles, or in other words, unexpected changes. Their solution is built on top of Lifschitz s causal minimization [14] in which nothing could change without a cause. In the new solution, nothing can change without a cause unless a miracle occurred; their new ....

Vladimir Lifschitz and Arkady Rabinov. Miracles in formal theories of action. Artificial Intelligence, 38:225--237, 1989.

....the gun to become unloaded, the minimization of causes will entail that the gun cannot become unloaded in the Yale Shooting Scenario. A solution similar to Lifschitz s was independently suggested by Haugh (1987) Moreover, researchers have suggested several modifications of Lifschitz s solution (Lifschitz and Rabinov, 1989; Baker, 1991) to correct some of the anomalies in Lifschitz s original solution. Much has been made of the anomalies, which we briefly discuss here, but as in the case of the Yale Shooting Problem in general, we believe that the emphasis on the anomalies has blinded most of the AI community to ....

Lifschitz, V. and Rabinov, A. (1989). Miracles in formal theories of action. AIJ Research Note.

....of A is generalized accordingly. The translation to logic programming presented here is extended to this concurrent A in the spirit of [13] The inconsistency of the Stolen Car domain (Example 4) illustrates the fact that A cannot be used for representing causal anomalies, or miracles [21]. We plan to address this issue in further work, too. Our preferred approach to causal anomalies is to view them as evidence of unknown events that occur concurrently with the given actions and contribute to the properties of the new situation. One other dialect of A is described in [19] It has ....

Vladimir Lifschitz and Arkady Rabinov. Miracles in formal theories of actions. Artificial Intelligence, 38(2):225--237, 1989.

....of A is generalized accordingly. The translation to logic programming presented here is extended to this concurrent A in the spirit of [13] The inconsistency of the Stolen Car domain (Example 4) illustrates the fact that A cannot be used for representing causal anomalies, or miracles [21]. We plan to address this issue in further work, too. Our preferred approach to causal anomalies is to view them as evidence of unknown events that occur concurrently with the given actions and contribute to the properties of the new situation. One other dialect of A is described in [19] It has ....

Vladimir Lifschitz and Arkady Rabinov. Miracles in formal theories of actions. Artificial Intelligence, 38(2):225--237, 1989.

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Lifschitz, Vladimir and Arkady Rabinov: "Miracles in Formal Theories of Action," AIJ Research Note, 1989

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