S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. Annals of Mathematics and Artificial Intelligence, special issue on Processing of Declarative Knowledge, 1994. (To appear).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....language for Cognitive Robotics in which are combined a variety of challenging aspects of complex environments. Furnishing the calculus with a new axiomatic foundation, we have first of all overcome an important limitation of [65] caused by relying on the notion of unification completeness [62, 22]: Defining inequality of state terms as non unifiability wrt. AC1 did not permit any domain specific equalities like O#ce(Alice) R402 since this leads to a contradiction given that, e.g. the state terms InRoom(O#ce(Alice) and InRoom(R402 ) are not AC1 unifiable. The new, conceptually even ....

Ste#en Holldobler and Michael Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14(1):99--133, 1995.

....= f #= # # [ z = z # z ## z # = z ## = #z a , z b , z c , z d ) z 1 = z a z b z 2 = z c z 3 = z a z c z 4 = z b z d ] Unlike the definition of EUNA in terms of unification completeness wrt. AC1, as used in earlier versions of the Fluent Calculus [ Holldobler and Thielscher, 1995; Thielscher, 1999 ] the new axioms allow to incorporate domain dependent assumptions of unique names [ Storr and Thielscher, 2000 ] For computing with state terms, two immediate consequences of these axioms are of importance, the following rules of cancellation and distribution. Proposition ....

Ste#en Holldobler and Michael Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14(1):99-- 133, 1995.

....a standard semantics. However, the equational logic approach to deductive planning of Holldobler and Schneeberger does [13] and, moreover, is provably equivalent to Bibel s approach and fragments of linear logic [9] Although in the meantime the original approach has been extended in various ways [14, 4], it always dealt with total order planning. In this paper we present a new approach which combines resource based reasoning and partial order least commitment planning in a constraint equational logic programming framework. In this purely declarative system the question whether a goal can be ....

....extend our constraint equational logic approach to model such multi contributor causal structures. On the other hand, the resource based equational logic approach does not only handle the frame problem naturally and elegantly, but it has already been extended to deal with objects and specificity [14], hierarchical planning problems [4] parallel actions [3] and with the ramification problem [30] All these extension handle total order planning problems only. We strongly believe that the technics developed within the equational logic approach can be extended to be applicable to partial order ....

S. Holldobler and M. Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14:99--133, 1995.

....for a certain class of planning problems [19] In particular, the approach developed in [26] is based on logic programming with an associated equational theory. Since its first formalization, this method has been extended into various directions, e.g. to handle objects [20] specificity [28], concurrent [3] as well as non deterministic actions [5, 45] and ramifications [46] Moreover, its relation to the high level specification languages A [16] and the Ego World Semantics [42] were clarified [45, 44] Although these results illustrate the expressiveness of the equational logic ....

....as it can factor out common structure at argument level (see [13, 12] for further details) As has already been mentioned in the introduction, the basic ELP approach has recently been extended into various ontological directions. Most of these extensions require a so called specificity criterion [28], which allows for more than one description of an action whose effect depends on the situation at hand. It has been shown that specificty necessarily involves a certain kind of nonmonotnicity. Hence, its integration into our equational logic program (3) requires negative literals in the body of ....

Steffen Holldobler and Michael Thielscher. Computing Change and Specificity with Equational Logic Programs. Annals of Mathematics and Artificial Intelligence, special issue on Processing of Declarative Knowledge, 1995.

..... As the shooting scenario already exemplifies there may be more than one description of a certain action applicable to a given state. Such potential conflicts can be avoided by defining a partial order on action descriptions and applying only the most specific action according to this ordering [13]. Formally, an action description hC 1 ; A; E 2 i is more specific than a description hC 2 ; A; E 2 i iff C 2 ae C 1 . The successor of a state Z wrt an action A is obtained by applying the most specific description of A to Z . Thus, in the shooting scenario the application of the shoot action to ....

....into (4) as follows. causes (S; S) causes (S; AjP ] G) action (C; A; E) C ffi V = AC1 S; non specific (A; C; S) causes (V ffi E; P; G) 6) Finally, as equations occur in the body of program clauses we have to add the axiom of reflexivity. X = AC1 X: 7) It has been shown in [13] that the completion of the equational theory AC1 and the logic program (2) 5) 6) 7) is a model for causes ( S ; a 1 ; an ] G ) iff the initial situation S can be transformed into the goal situation G by applying the actions a 1 ; an , n 0 . In particular, in each step ....

S. Holldobler and M. Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14:99-- 133, 1995.

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S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. Annals of Mathematics and Artificial Intelligence, special issue on Processing of Declarative Knowledge, 1994. (To appear).

No context found.

S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. Annals of Mathematics and Artificial Intelligence, 1995.

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S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. Annals of Mathematics and Artif. Intell., 1995.

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S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. Annals of Mathematics and Artificial Intelligence, special issue on Processing of Declarative Knowledge, 1994. (To appear).

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S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. Annals of Mathematics and Artificial Intelligence, special issue on Processing of Declarative Knowledge, 1994. (To appear.)

....might contain other resources aside from the required lemonade. 2. 3 The Postcondition Problem in Deductive Planning Apart from solving temporal projection (prediction) and planning problems, the ELP based approach is also suitable for a certain kind of postdiction problems, as has been argued in [15]. Postdiction means given a goal situation, what can be deduced about the initial situation, i.e. which resources are needed to obtain a specific goal. For example, suppose we want to buy a can of lemonade, what do we need to achieve this goal To answer this question, the query causes(I, P, ....

S. Holldobler and M. Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14(1):99-133, 1995.

....up from an identical collection of reified fluents. In addition, denials of equalities, such as in the second part of formula (12) need to be derivable. This requires an extension of the standard assumption of unique names for fluents to uniqueness of states, denoted by EUNA (see, e.g. [8, 14]) The assertion that some fluent f holds (resp. does not hold) in some situation s can now be formalized by #z. resp. #z. State(s) #z) This allows to reintroduce the Holds predicate, now, however, not as a primitive notion but as a derived concept: # #z. z (13) In this way, any ....

S. Holldobler and M. Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artif. Intell., 14(1):99--133, 1995.

....interpretations which interpret as multiset building operators, i.e. I is defined on these symbols as in Section 3. In addition, list expressions of the form [h t] are interpreted as usual. This is not a restriction as any other models for AC1 # can be mapped onto such a ( I , see [17]) Now, let (P # , AC1 # ) contain the definition of a set of action descriptions and let be a model for (P # , AC1 # ) Furthermore, let i and g be ground AC1 terms denoting the initial situation i I =S 0 and the goal situation g I =S n , respectively, and let a 1 , a n ....

....only if s and t are AC1 terms. In the following section we show that the application of SLDENF resolution to our equational logic program yields the intended results. General soundness and completeness results concerning SLDENF resolution, which extend the results of [28] can be found in [17]. 6 Soundness and Completeness of SLDENF Resolution In this section we assume that i and g are ground AC1 terms denoting an initial situation i I and a goal situation g I , respectively. Furthermore, p denotes a list of action names [a 1 , a n ] Note that SLDENF refutations are ....

[Article contains additional citation context not shown here]

S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. 1993 (submitted).

....in this paper these two restrictions are sufficient conditions to ensure that the entailment problem is decidable. We use here a new formulation of the fluent calculus discussed in detail in [20] which uses the axioms F mset instead of extended unique names assumptions requires in earlier papers [12, 18], because this formulation formalizes exactly the intuition of state terms being finite multisets of fluents. For notational convenience we abbreviate a term do(a n ; do( do(a 1 ; S 0 ) to a n : a 1 S 0 . 2.4 Binary Decision Diagrams The idea of BDDs is similar to decision ....

S. Holldobler and M. Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14:99--133, 1995.

....inference rule for the defined class of equational logic programs. In the sequel we will briefly define our notions of objects and specificity, and we will specify the equational logic programs needed to compute the application of methods. Remark A full version of the talk will be published in [9] and is available from the authors. ....

S. Holldobler and M. Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 1995. (to appear).

....axioms of equality. In order to reason about negated equalities, this theory is turned into a so called unification complete theory AC1 . AC1 is then built into the unification computation and SLDENF resolution can be used to determine whether a query follows from a normal logic program (see [4]) There is a straightforward mapping Delta from multisets of fluents to their corresponding term representations. Let M be a multiset of terms, then M = 1 if M = f ffi M 1 if M = ff g [M 1 : Actions are represented in the fluent calculus with the help of a frame assumptions. ....

S. Holldobler and M. Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14:99--133, 1995.

..... As the shooting scenario already exemplifies there may be more than one description of a certain action applicable to a given state. Such potential conflicts can be avoided by defining a partial order on action descriptions and applying only the most specific action according to this ordering [17]. Formally, an action description hC 1 ; A; E 2 i is more specific than a description hC 2 ; A; E 2 i iff C 2 ae C 1 . 1 Without loss of generality we may assume that the negation sign occurs only in front of atoms. Thus, we may build fluent formulas from fluent literals and the connectives , ....

....into (4) as follows. causes (S; S) causes (S; AjP ] G) action (C; A; E) C ffi V = AC1 S; non specific (A; C; S) causes (V ffi E; P; G) 6) 5 Finally, as equations occur in the body of program clauses we have to add the axiom of reflexivity. X = AC1 X: 7) It has been shown in [17] that the completion of the equational theory AC1 and the logic program (2) 5) 6) 7) is a model for causes ( S ; a 1 ; an ] G ) iff the initial situation S can be transformed into the goal situation G by applying the actions a 1 ; an , n 0 . In particular, in each step ....

S. Holldobler and M. Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14:99--133, 1995.

....these literals is the consumption of its antecedent; hence, we cannot deduce, say, Fe S under the modified interpretation of implications. In general, the notions of consuming and producing facts enable us to model and reason about dynamic environments, where facts are likely to be temporary [17, 18]. Given the resource oriented interpretation of implications, a corresponding modification of the basic concepts in the connection method, first presented in [2] is the following so called linearity restriction: Each literal must be engaged in at most one connection. In what follows, we ....

Holldobler, S., Thielscher, M.: Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14(1):99--133, 1995.

....Throughout this paper, we use a Prolog like syntax, i.e. constants and predicates are in lower cases whereas variables are denoted by upper case letters. Moreover, free variables are assumed to be universally quantified and, as usual, the term [h j t] denotes a list with head h and tail t . 8 In [12] the concurrent execution of actions is not taken into consideration; this extension is obviously necessary for encoding AC . 9 i.e. every situation unifiable with V ffi c1 ffi Delta Delta Delta ffi c l wrt. to the underlying equational theory (AC1) say, along with (open ) closed , ....

S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. Annals of Mathematics and Artificial Intelligence, special issue on Processing of Declarative Knowledge, 1994. (To appear).

....contain other resources aside from the required lemonade. 2. 3 The Postcondition Problem in Deductive Planning Apart from solving temporal projection (prediction) and planning problems, the ELP based approach is also suitable for a certain kind of postdiction problems, as has been argued in [15]. Postdiction means given a goal situation, what can be deduced about the initial situation, i.e. which resources are needed to obtain a specific goal. For example, suppose we want to buy a can of lemonade, what do we need to achieve this goal To answer this question, the query causes(I; P; ....

S. Holldobler and M. Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14(1):99-133, 1995.

....interpret ; and ffi as multiset building operators, i.e. Delta I is defined on these symbols as in Section 3. In addition, list expressions of the form [h j t] are interpreted as usual. This is not a restriction as any other models for AC1 can be mapped onto such a ( Delta I ; D) see [17]) Now, let (P ; AC1 ) contain the definition of a set of action descriptions A and let M = Delta I ; D) be a model for (P ; AC1 ) Furthermore, let i and g be ground AC1 terms denoting the initial situation i I =S 0 and the goal situation g I =S n , respectively, and let ....

....only if s and t are AC1 terms. In the following section we show that the application of SLDENF resolution to our equational logic program yields the intended results. General soundness and completeness results concerning SLDENF resolution, which extend the results of [28] can be found in [17]. 6 Soundness and Completeness of SLDENF Resolution In this section we assume that i and g are ground AC1 terms denoting an initial situation i I and a goal situation g I , respectively. Furthermore, p denotes a list of action names [a 1 ; a n ] Note that SLDENF refutations are ....

[Article contains additional citation context not shown here]

S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. 1993 (submitted).

....holds: 1. If s and t are not E unifiable then E j= 9X : s = t . 2. If s and t are E unifiable then for each complete set of E unifiers cUE (s; t) E j= 8X 0 s = t 2cU E (s;t) 9Y : eqn( 1 A (34) where Y denotes the variables which occur in eqn( but not in X . In [ Holldobler and Thielscher, 1995 ] we have proved the existence of such a unification complete theory AC1 for the equational theory AC1 used in FCNCC . Since we do not intend to compute with AC1 , we are only interested in the properties of this theory as given by Definition 11; its actual design is irrelevant for our ....

Steffen Holldobler and Michael Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14(1):99--133, 1995.

....; aliveg . Since the effects of an action may vary from situation to situation, one often needs more than just a single specification such as (1) In order to avoid unintended conflicts in case of multiple descriptions of one action, we employ the following partial order on action descriptions [ Holldobler and Thielscher, 1995 ] Definition 3 An action description hC 1 ; a 1 ; E 1 i is more specific than a description hC 2 ; a 2 ; E 2 i iff a 1 = a 2 and C 1 oe C 2 . If A is a set of action descriptions, S a situation and a an action name then a successor of S is obtained by applying the most specific (wrt A ) ....

.... a special unification procedure but also contains negative literals, an adequate computation mechanism is SLDENF resolution, i.e. SLD resolution augmented by theory unification and the negation as failure principle to handle negative subgoals [ Shepherdson, 1992; Thielscher, 1995 ] In [ Holldobler and Thielscher, 1995 ] the application of this calculus to our ELP has been proved adequate wrt the semantics given by Definitions 1 3. 4 2 We use a Prolog like syntax, i.e. constants and predicates are in lower cases whereas variables are denoted by upper case letters. As usual, the term [h j t] denotes a ....

S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. Annals of Mathematics and Artif. Intell., 1995.

....result Trans(f 1 ; 2 ; 3 g; s) fwater spillsg . In order to avoid this kind of counterintuitive behavior, we employ an additional criterion to suppress the application of some causal law as soon as, roughly spoken, more specific information is available (see also [ Baral and Gelfond, 1993; Holldobler and Thielscher, 1995 ] For instance, Law 3 in (2) should override 1 and 2 whenever it is applicable. Formally, we introduce the following partial ordering on causal laws: Definition 4 Let 1 ; 2 be two causal laws then 1 is called more specific than 2 , written 1 OE 2 , iff cond ( 1 ) oe cond ....

S. Holldobler and M. Thielscher. Computing Change and Specificity with Equational Logic Programs. Annals of Mathematics and Artificial Intelligence, 1995.

....in the discussion, Section 7. In the second part of the paper, Section 6, we integrate the concept of causal relationships into a particular action calculus which is based on reifying entire state descriptions and which employs the logic programming paradigm [ Holldobler and Schneeberger, 1990; Holldobler and Thielscher, 1995 ] While for sake of simplicity states are described via a set of propositional constants in the first part (see Section 2) the calculus itself employs more complex a notion of fluent, which comes along with fluent formulas involving quantifications. The extended calculus will be proved sound ....

....the ramification problem compared to others, the second part of the paper is devoted to the development of a suitable, concrete calculus. This calculus will be based on the logic programming paradigm. More precisely, we adapt and extend a method described in [ Holldobler and Schneeberger, 1990; Holldobler and Thielscher, 1995 ] which applies the concept of reification to entire states, i.e. each of which is formally represented as single term and, thus, is manipulable by means of program clauses. The adequate treatment of these terms requires a (domain independent) equational theory, which, essentially, formalizes ....

[Article contains additional citation context not shown here]

Steffen Holldobler and Michael Thielscher. Computing change and specificity with equational logic programs. Annals of Mathematics and Artificial Intelligence, 14(1):99--133, 1995.

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