Son, T. C., and Baral, C. 2001. Formalizing sensing actions --- A transition function based approach. Artif. Intell. 125(1--2):19--91.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....along the line of Scherl and Levesque paper [25] Let us mention the work on the high level robot programming language GOLOG [11, 12] which is based on a theory of actions in the situation calculus. Other proposals have been developed by extending the action description language A [17] as in [23, 8], while in [27] a formal account of a robot s knowledge about the state of its environment has been developed in the context of the uent calculus. In this paper, we tackle the problem of reasoning about complex actions with incomplete knowledge in a modal action logic. The adoption of dynamic ....

....the agent, as we do, the only relevant characterization concerns the internal dynamics of the agent, which can be regarded as a result of executing actions on the mental state. As a consequence, we only keep the agent s representation of the world, while in other formalizations of sensing actions [25, 8], where the focus is on developing a theory of actions and knowledge rather than on modeling agent behaviors, both the mental state of the agent and the real state of the world are represented. In order to represent the mental state of an agent, we introduce an epistemic level in our logical ....

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C. Baral and T. C. Son. Formalizing Sensing Actions - A transition function based approach. Arti cial Intelligence, 125(1-2):19-91, January 2001.

.... a general account of the knowledge of robots must allow for distinguishing between the actual e#ects of actions and what a robot knows about these e#ects an aspect which is not covered by existing accounts of knowledge in action formalisms, such as [ Scherl and Levesque, 1993; Lobo et al. 1997; Son and Baral, 1998 ] The contribution of the present paper to the research on knowledge in cognitive robotics is manifold: 1. We extend the Fluent Calculus solution to the Frame Problem of [ Thielscher, 1999 ] that is, the concept of state update axioms, to representing and reasoning about the knowledge of a ....

....and reasoning about goal achievability that is possibly restricted due to limited knowledge of the e#ects of actions. This separating what a user knows from what a robot knows distinguishes our theory from other existing accounts of sensing action and knowledge, too, such as [ Lobo et al. 1997; Son and Baral, 1998 ] where also non sensing actions have identical e#ect on the external and internal states. Representing and reasoning about non knowledge has previously been realized in the context of the Situation Calculus [ Lakemeyer and Levesque, 1998; Lakemeyer and Levesque, 1999 ] Two approaches to ....

Tran Cao Son and Chitta Baral. Formalizing sensing actions---a transition function based approach, 1998. (Manuscript).

....leads sometimes to more economical and elegant formalization of knowledge representation problems. Since then, NATs have been used by a number of authors and are gaining popularity as a circumscriptive knowledge representation tool. For example, NATs have been used in reasoning about actions [25, 24, 31, 32, 48], for handling the qualification problem [39] formalizing narratives [3] expressing function value minimization [2] information filtering [1] describing action selection in planning [47] and in spatial reasoning [43] As another simple example for combining circumscriptions, imagine the task ....

T. C. Son and C. Baral. Formalizing sensing actions: A transition function based approach. Artificial Intelligence, 125(1-2):19--91, 2001.

....page 182) They in turn draw in Moore s work [Moore, 1979, Moore, 1985] on using possible world semantics to formally reason about knowledge and actions. Here we have adapted their definition in the context of transition based approaches to reason about actions ( Gelfond and Lifschitz, 1998, Son and Baral, 2001, Lobo et al. 1997] Example 35 (page 200) illustrates how definition A. 1 works. In particular, we will show how as the agent executes actions and makes observations, the set E captures the agent s knowledge about its actual location. A formal study of how the knowledge of the agent changes as ....

....observations, the set E captures the agent s knowledge about its actual location. A formal study of how the knowledge of the agent changes as it performs actions is outside the scope of this work. The reader is referred to [Moore, 1979, Moore, 1985, Scherl and Levesque, 1993, Bacchus et al. 1999, Son and Baral, 2001] for formal accounts of how to reason about actions and knowledge. We will use C to illustrate the concepts presented in this section. 197 We use the language C ( Giunchiglia and Lifschitz, 1998] to describe the effect of actions on the agent s location. The fluent loc (p, pa, dir) is used to ....

T.C. Son and C. Baral. Formalizing Sensing Actions: a transition function based approach. Artificial Intelligence, pages 19-91, 2001.

....182) They in turn draw in Moore s work [Moore, 1979, Moore, 1985] on using possible world semantics to formally reason about knowledge and actions. Here we have adapted their definition in the context of transition based approaches to reason about actions ( Gelfond and Lifschitz, 1998, Son and Baral, 2001, Lobo et al. 1997] Example 35 (page 200) illustrates how definition A.1 works. In particular, we will show how as the agent executes actions and makes observations, the set # captures the agent s knowledge about its actual location. A formal study of how the knowledge of the agent changes as ....

....observations, the set # captures the agent s knowledge about its actual location. A formal study of how the knowledge of the agent changes as it performs actions is outside the scope of this work. The reader is referred to [Moore, 1979, Moore, 1985, Scherl and Levesque, 1993, Bacchus et al. 1999, Son and Baral, 2001] for formal accounts of how to reason about actions and knowledge. We will use C to illustrate the concepts presented in this section. 197 We use the language C ( Giunchiglia and Lifschitz, 1998] to describe the effect of actions on the agent s location. The fluent loc(p,pa,dir) is used to ....

T.C. Son and C. Baral. Formalizing Sensing Actions: a transition function based approach. Artificial Intelligence, pages 19--91, 2001.

....line of Scherl and Levesque seminal paper[22] Let us mention the work on the high level robot programming language GOLOG [17, 19, 8, 9] which is based on a theory of actions in the situation calculus. Other proposals have been developed by extending the action description language A [13] as in [20, 4, 5]. In this paper we tackle the problem of reasoning about complex actions with incomplete knowledge in a modal action logic. The adoption of dynamic logic or a modal logic to formalize reasoning about actions and change is common to many proposals [7, 21, 6, 23, 14] and it allows very natural ....

....1 The fact that a state contains epistemic literals and not general epistemic formulas is clearly a limitation of the expressive power of the language, since no disjunctive belief formulas (as, for instance, B(a b) can belong to a state. This makes our language less expressive than those in [22, 5, 20]. However, this limitation is reasonable in a logic programming setting, and it has also been adopted in [5] in de ning approximations of the language AK which directly make use of a three valued interpretations. In our approach, this simplifying choice makes it feasible to describe action e ects ....

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C. Baral and T.C. Son. Formalizing Sensing Actions - a transition function based approach. Submitted for publication, 1998.

....Thus, this particular test is only guaranteed to provide knowledge about the existence of power at the electrical outlet under one test outcome. While researchers have extended theories of action to include the notion of sensing or knowledge producing actions (e.g. Scherl Levesque 1993; Baral Tran 1998; Golden Weld 1996; Funge 1998) and have characterized the effect of sensing actions on an agent s state of knowledge, and even how to plan (e.g. Stone 1998; Golden Weld 1996) and to project (e.g. De Giacomo Levesque 1999b) in certain cases, with sensing actions, they have not ....

Baral, C., and Tran, S. 1998. Formalizing sensing actions: a transition function based approach. In Proc. of AAAI 98 Fall Symposium on Cognitive Robotics.

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T. Son and C. Baral. Formalizing sensing actions: a transition function based approach. AI journal, 125(1-2):19--93, 2001.

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T.C. Son and C. Baral. Formalizing sensing actions - a transition function based approach. Artificial Intelligence, 125(1-2):19-- 91, January 2001.

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T. Son and C. Baral. Formalizing sensing actions: a transition function based approach. Artificial Intelligence, 125(1-2):19--93, 2001.

....the agent s belief about the world and the agent performs an action that is supposed to make # true in the resulting world, then the agent s belief about the resulting world can be described by #, where is the update operator of choice. Now let us consider reasoning about sensing actions [22,23], which in their pure form, when executed, do not change the world, but change the agent s knowledge about the world. Let sense f be a sensing action whose e#ect is that after it is executed the agent knows whether f is true or not. This can be expressed as Kf #Kf , where K is the modal operator ....

....of knowledge update, and their alternative characterizations are convenient when the use of the notion of knowledge update becomes an overkill. For example, the alternative characterization of sensing update below is a much simpler characterization that is used in reasoning about sensing actions [22,23]. 4.1 Gaining knowledge update We first introduce a notation that will be useful in our following discussions. Let W be a set of worlds and w W . By W , we denote the set # i# w # . Proposition 3 Given T and K# where # is objective and T #. Then M # = W # , w # ) is a ....

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T. Son and C. Baral. Formalizing sensing actions: a transition function based approach. Artificial Intelligence 125, 19-91, 2001.

....questions arise when one wants to remove this assumption: how to reason about the knowledge of agents and what is a plan in the presence of incomplete information. The first question led to the development of several approaches to reasoning about effects of sensing (or knowledge producing) actions [10, 15, 16, 22, 24, 27]. The second question led to the notions of conditional plans and conformant plans. The former contains sensing actions and conditionals such as the well known if then else construct and the latter is a sequence of actions which leads to the goal regardless of the value of the unknown fluents in ....

....of sensing actions and the class of conditional plans considered in this paper, which is large enough to cover conditional plans with bounded length and branching factor. We use the language AK and its 0 approximation as the language for representing and reasoning with sensing actions [24]. We adopt the 0 approximation of AK as the complexity of the planning problem with respect to this approximation (under limited sensing) is NP complete [1] which is lower than the complexity of the problem with respect to the AK semantics. This allows us to use different systems capable of ....

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T.C. Son and C. Baral. Formalizing sensing actions - a transition function based approach. Artificial Intelligence, 125(1-2):19--91, January 2001.

....world and the agent does an action that is supposed to make true in the resulting world, then the agent s belief about the resulting world can be described by OE Pi , where Pi is the update operator of choice. Now let us consider reasoning about sensing actions [Scherl and Levesque, 1993; Son and Baral, 2000] which in their pure form, when executed, do not change the world, but change the agent s knowledge about the world. Let sense f be a sensing action whose effect is that after it is executed the agent knows whether f is true or not. This can be expressed as Kf K:f , where K is the modal ....

....and their alternative characterization is handy when the use of the notion of knowledge update becomes an overkill. For example, the alternative characterization of sensing update below is a much simpler characterization that is used in reasoning about sensing actions [Scherl and Levesque, 1993; Son and Baral, 2000] We now introduce a notation that will be useful in our following discussions. Let W be a set of worlds and w 2 W . By W (w;OE) we denote the set fw 0 j w 0 2 W and w 0 j= OE iff w j= OEg. Proposition 2 Given T and KOE where OE is objective and T j= OE. Then M 0 = W 0 ; w 0 ) ....

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T. Son and C. Baral. Formalizing sensing actions: a transition function based approach. Artificial Intelligence, 125:19--92, 2000.

....for planning with incompleteness [EHW 92, KOG92, GB94, GEW96, GW96, PC96, SW98, WAS98, Rin99] we believe that the complexity results will shed additional light into these planners and also guide the development of future planners. Our complexity analysis will be based on an extension [BS98, BS00] of the action description language A proposed in 1991 by Gelfond and Lifschitz [GL93] The language A and its successors have made it easier to understand the fundamentals (such as inertia, ramification, qualification, concurrency, sensing, etc. involved in reasoning about actions and their ....

....logical statement with quantifiers, are more complex; none of our results and proofs apply verbatim to such problems. 1. 2 An extension of language A which describes sensing actions: brief reminder The formulation of the extension AK of A that allows sensing actions recalled here from [BS98, BS00] is based on earlier work of formalizing sensing actions in [Moo85, SL93] In the domain description D, in addition to value propositions and effect propositions, we may also have sensing propositions of the type a determines f i . To deal with incomplete information about the real world, we ....

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C. Baral and T. Son, Formalizing sensing actions: a transition function based approach, Artificial Intelligence, 2000 (to appear).

....for planning with incompleteness [EHW 92, KOG92, GB94, GEW96, GW96, PC96, SW98, WAS98, Rin99] we believe that the complexity results will shed additional light into these planners and also guide the development of future planners. Our complexity analysis will be based on an extension [BS98, BS00] of the action description language A proposed in 1991 by Gelfond and Lifschitz [GL93] The language A and its successors have made it easier to understand the fundamentals (such as inertia, ramification, qualification, concurrency, sensing, etc. involved in reasoning about actions and ....

....logical statement with quantifiers, are more complex; none of our results and proofs apply verbatim to such problems. 1. 2 An extension of language A which describes sensing actions: brief reminder The formulation of the extension AK of A that allows sensing actions recalled here from [BS98, BS00] is based on earlier work of formalizing sensing actions in [Moo85, SL93] In the domain description D, in addition to value propositions and effect propositions, we may also have sensing propositions of the type a determines f i . To deal with incomplete information about the real ....

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C. Baral and T. Son. Formalizing sensing actions: a transition function based approach. Technical report, Dept of Computer Science, University of Texas at El Paso, http://cs.utep.edu/chitta/chitta.html), 1998).

....proposition relates the rational entailment of D and entailment in (D) w.r.t. queries. Proposition 3 (Soundness and Completeness) Let D be a domain description and f be a fluent in D. Then, for any conditional plan c, D) j= knows after(f; c; s 0 ) iff D j= r AK f after c: Proof: In [BS98] 3 3 To keep the paper within reasonable size we have not included the proofs related to logic programs and some of the other proofs in this document. They are made available through the web. 18 2.5 State space analysis In this section we analyze the size of the state space, when reasoning ....

....D w.r.t. queries. Proposition 7 (Soundness and Completeness of 0 (D) w.r.t. j= 0 ) Let D be a domain description. Then, for every fluent name f and action a in D, 1. 0 (D) j= holds(f; res(a; s 0 ) iff D j= 0 f after a; 2. 0 (D) j= holds(f; res(a; s 0 ) iff D j= 0 :f after a. Proof. In [BS98] 2 We would like to point out that our attempt to compute 1 Approximation using logic programs was unsuccessful in the sense that we could only come up with a sound (but not complete) translation. We presented this translation in [BS97] 28 4 Related research 4.1 Relationship with Scherl ....

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C. Baral and T. Son. Formalizing sensing actions: a transition function based approach. Technical report, Dept of Computer Science, University of Texas at El Paso (http://cs.utep.edu/chitta/chitta.html), 1998.

....(K(s 0 ; S) oe (s 0 ) Relationship with Lobo et al. s semantics In (Lobo et al. 1997) AK , an extension of A has been introduced to allow reasoning about sensing actions. The syntax of AK and AS are almost identical. The differences between the two approaches are discussed in details in (Baral and Son, 1998). We prove that Proposition 4 Let D be a domain description, be a fluent formula in D, and c be a conditional plan in D. Then, D j= r AS after c iff D j= LTM after c where j= LTM denotes the entailment relationship defined by the semantics of (Lobo et al. 1997) Approximation ....

Baral, C. and Son T.C.: Formalizing sensing actions: a transition function based approach. Technical report, Dept of Computer Science, University of Texas at El Paso (http://cs.utep.edu/chitta/chitta.html), 1998.

....only changes the agent s knowledge about the world (without changing the world) while the later may change the world. Sensing actions were initially formalized by Moore in [Moore, 1985] and successor state axioms involving sensing actions were developed in [Scherl and Levesque, 1993] Recently in [Baral and Son, 1998] Baral and Son describe states and transitions that account for sensing actions. These three approaches use the possible world approach in their characterization. Recently Geffner and Bonet [Geffner and Bonet, 1998] describe how high level planning in presence of incomplete information can be ....

....by Kripkemodels, while in the second the agent reasons with the set of states with associated probabilities, it thinks it may be in. We expand on this in this paper. 2 Possible world based characterization of sensing actions: the language AK In this section we review the language AK from [Baral and Son, 1998], which allows reasoning about sensing actions. 2.1 Syntax of AK AK has two disjoint nonempty sets of symbols, called fluent names (F) and action names (A) A fluent literal is either a fluent name or a fluent name preceded by : For a fluent f , by :f we mean f , and by f we mean :f . 2.1.1 ....

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C. Baral and T.C. Son. Formalizing sensing actions: a transition function based approach. AAAI Fall Symposium, 1998, 13-20.

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Son, T. C., and Baral, C. 2001. Formalizing sensing actions --- A transition function based approach. Artif. Intell. 125(1--2):19--91.

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T. C. Son and C. Baral, `Formalizing sensing actions: A transition function based approach', Artif. Intell., 125(1--2), 19--91, (2001).

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BARAL, C., AND SON, T. C. Formalizing Sensing Actions - A transition function based approach. Artificial Intelligence 125, 1-2 (January 2001), 19--91.

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T. C. Son and C. Baral. Formalizing sensing actions: A transition function based approach. AIJ, 125, 2001.

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Tran Cao Son and Chitta Baral. Formalizing sensing actions a transition function based approach. Artificial Intelligence, 125(1--2):19--91, 2001.

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T. C. Son and C. Baral. Formalizing sensing actions - a transition function based approach. Artificial Intelligence, 125(1-2):19--91, 2001.

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T.C. Son, C. Baral, Formalizing sensing actions---A transition function based approach, Artificial Intelligence 125 (2001) 19--91.

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