M. Thielscher. AC1-Unifikation in der linearen logischen Programmierung. Diplomarbeit, Technische Hochschule Darmstadt, Fachbereich Informatik, 1992. (in preparation). 15  Home/Search   Document Not in Database   Summary   Related Articles   Check

....clause (T) are AC1 unifiable and the SLDE refutation of (4.8) generates the empty plan [ Since each most general AC1 unifier for (4. 8) and (T) is of the form fP 7 [ V 7 ; ffi g 1 ffi : ffi gn ; W 7 ; ffi i 0 jg = fj i 1 ; i m jg Gamma fj g 1 ; gn jg (see [36]) we conclude that fj g 1 ; g n jg fj i 1 ; i m jg . Hence, if fj i 1 ; i m jg = then the linear proof 1 1 satisfies the claim and generates the empty plan [ and, otherwise, the linear i 1 i 1 i 2 i 2 i 1 ; i 2 i i 2 . i 1 ; i m Gamma1 ....

....generating plan [a 2 ; a j ] Each most general AC1 unifier oe for the atoms in (4.9) and the conclusion of (4. 10) is of the form [ fP 7 [ a 1 (Y ) P 1 ] W 1 7 ; ffi g 1 ffi : ffi gn ; V 1 7 ; ffi i where is a grounding substitution containing only bindings for Y (see [36]) and fj i 0 jg = fj i 1 ; i m jg Gamma fj c 1 (Y ) c l (Y ) jg : 4.12) With this unifier (4.11) becomes :plan( e 1 (Y ) ffi : ffi e k (Y ) ffi i 0 ; P 1 ; g 1 ffi : ffi g n ) 4.13) By the induction hypotheses applied to the SLDE refutation of (4.13) we ....

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M. Thielscher. AC1-Unifikation in der linearen logischen Programmierung. Diplomarbeit, Intellektik, Informatik, TH Darmstadt, 1992.

....like the qualification or the ramification problem. We need efficient and fast implementations. As far as the equational logic approach is concerned this essentially requires to study AC1 matching and AC1 unification in the restricted way as needed for deductive planning. First steps are taken in [32], where it is shown that these problems are decidable and finitary and where minimal and complete matching and unification algorithms are given. These algorithms are implemented in Prolog. They are quite fast but have not yet been built into the abstract machine underlying Prolog. Even with an ....

M. Thielscher. AC1-Unifikation in der linearen logischen Programmierung. Master's thesis, Intellektik, Informatik, TH Darmstadt, 1992.

....step connecting st(P 0 ) Since we ensure that no other open subgoals are included in Delta 1 cannot influence the derivation of any other goal. 2 A problem of the form whether there exists a substitution such that M 1 M 2 for two multisets M 1 and M 2 holds has been studied in detail in [Thi92] There, efficient algorithms are given. Example 5.1 Reconsider example 3.1. Suppose Bert has a dollar note and one quarter and that in order to use the vending machine he needs two quarters. To use the vending machine he has to change his dollar into four quarters using a changing machine. The ....

Michael Thielscher. AC1-Unifikation in der linearen logischen Programmierung. Diplomarbeit, Technische Hochschule Darmstadt, September 1992. 25

....generates the empty plan [ Since each most general AC1 unifier for (4. 8) and (T) is of the form fP 7 [ V 7 ; ffi g 1 ffi : ffi gn ; W 7 ; ffi i 0 1 ffi : ffi i 0 m 0 g; where fj i 0 1 ; i 0 m 0 jg = fj i 1 ; i m jg Gamma fj g 1 ; gn jg (see [36]) we conclude that fj g 1 ; g n jg fj i 1 ; i m jg . Hence, if fj i 1 ; i m jg = then the linear proof 1 1 satisfies the claim and generates the empty plan [ and, otherwise, the linear proof i 1 i 1 i 2 i 2 i 1 ; i 2 i 1 Omega i 2 Omega r . i 1 ....

....; a j ] Each most general AC1 unifier oe for the atoms in (4.9) and the conclusion of (4. 10) is of the form [ fP 7 [ a 1 (Y ) P 1 ] W 1 7 ; ffi g 1 ffi : ffi gn ; V 1 7 ; ffi i 0 1 ffi : ffi i 0 m 0 g; where is a grounding substitution containing only bindings for Y (see [36]) and fj i 0 1 ; i 0 m 0 jg = fj i 1 ; i m jg Gamma fj c 1 (Y ) c l (Y ) jg : 4.12) Linear Deductive Planning 23 With this unifier (4.11) becomes :plan( e 1 (Y ) ffi : ffi e k (Y ) ffi i 0 1 ffi : ffi i 0 m 0 ; P 1 ; g 1 ffi : ffi g n ) ....

[Article contains additional citation context not shown here]

M. Thielscher. AC1-Unifikation in der linearen logischen Programmierung. Diplomarbeit, Intellektik, Informatik, TH Darmstadt, 1992.

....turned out to be very e#cient, as they consider the characteristics of the AC1 terms occurring in all applications of our equational logic programming approach to actions and change. The details of the algorithms as well as a proof of their correctness, completeness, and minimality can be found in [30]. 6 On Disjunction So far we dealt only with conjunctions of fluents and we have shown how such conjunctions can be used for modelling planning problems, objects, and database updates. In certain domains, however, disjunctions arise naturally. Thus, we are faced with the problem of extending our ....

M. Thielscher. AC1-Unifikation in der linearen logischen Programmierung. Diplomarbeit, Technische Hochschule Darmstadt, Fachbereich Informatik, 1992. (in preparation). 15

...., e I i . As our programs contain an equational theory we intend to build this theory into the unification computation. In particular, we are interested in the AC1 unification of two AC1 terms, which is decidable, finitary, and for which a complete and minimal unification algorithm is known [13, 29]. The programs are carefully specified such that the need for AC1 unification is localized within calls to subgoals of the form s = AC1 t or s AC1 t , whereas all other subgoals can be solved by applying the usual unification procedure. Following the ideas of [28] SLDENF resolution is like ....

....the usual unification procedure. Following the ideas of [28] SLDENF resolution is like SLDNF resolution [6] if the selected literal is not of the form s = AC1 t or s AC1 t . If the selected literal is of the form s = AC1 t and s and t are AC1 terms, then the AC1 unification algorithm in [13, 29] is called, which either returns a minimal complete set of AC1 unifiers for s and t if both terms are AC1 unifiable, or returns a failure message otherwise. In the former case, the literal s = AC1 t is removed from the goal and one of the AC1 unifiers is applied to the remaining literals ....

M. Thielscher. AC1-Unifikation in der linearen logischen Programmierung. Diplomarbeit, Intellektik, TH Darmstadt, 1992.

....I i i 2 A . As our programs contain an equational theory we intend to build this theory into the unification computation. In particular, we are interested in the AC1 unification of two AC1 terms, which is decidable, finitary, and for which a complete and minimal unification algorithm is known [13, 29]. The programs are carefully specified such that the need for AC1 unification is localized within calls to subgoals of the form s = AC1 t or s 6= AC1 t , whereas all other subgoals can be solved by applying the usual unification procedure. Following the ideas of [28] SLDENF resolution is like ....

....the usual unification procedure. Following the ideas of [28] SLDENF resolution is like SLDNF resolution [6] if the selected literal is not of the form s = AC1 t or s 6= AC1 t . If the selected literal is of the form s = AC1 t and s and t are AC1 terms, then the AC1 unification algorithm in [13, 29] is called, which either returns a minimal complete set of AC1 unifiers for s and t if both terms are AC1 unifiable, or returns a failure message otherwise. In the former case, the literal s = AC1 t is removed from the goal and one of the AC1 unifiers is applied to the remaining literals ....

M. Thielscher. AC1-Unifikation in der linearen logischen Programmierung. Diplomarbeit, Intellektik, TH Darmstadt, 1992.

....out to be very efficient, as they consider the characteristics of the AC1 terms occurring in all applications of our equational logic programming approach to actions and change. The details of the algorithms as well as a proof of their correctness, completeness, and minimality can be found in [28]. 6 On Disjunction So far we dealt only with conjunctions of fluents and we have shown how such conjunctions can be used for modelling planning problems, objects, and database updates. In certain domains, however, disjunctions arise naturally. Thus, we are faced with the problem of extending our ....

M. Thielscher. AC1-Unifikation in der linearen logischen Programmierung. Master's thesis, Intellektik, Informatik, TH Darmstadt, 1992.

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