M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... (see Appendix A) Since E already allows for actions to occur 34 concurrently within a narrative, it seems likely that the language could also be extended to allow 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 ....

.... 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 [6] The utility and appeal of specialised declarative languages such as A and E lies in their simplicity. They are of sufficiently high level to allow various issues to be aired without immediately ....

Marc Denecker, Knowledge Representation and Reasoning in Incomplete Logic Programming, PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....Theory (CET) For all the acyclic logic programs [1] the predicate completion semantics coincide with other semantics such as the stable model semantics and the well founded model semantics. In the case of abductive logic programs, the semantical coincidence still holds, as shown by Denecker [4]. In the following translation, all the predicates will be selfexplanatory, where imm stands for immediate. Let D be a domain description in AC. The translation D is defined as follows: 1. Auxiliary predicates about subactions: Assume that we have standard rules for set related predicates ....

....F is abduced to be true (false, resp. initially, then it is true (false, resp. in the initial situation s 0 . The semantics of D is defined to be the union of the integrity constraints, the Clark Equality Theory, and the first order theory obtained by completing all the non abducible predicates [4]. The definition for abducible predicates initially true(F ) and initially false(F ) are left open. We will write COMP (D) to denote the semantics of of D. The following two results justify the above semantics definition. Proposition 4.1 D is an acyclic program with first order constraints in the ....

Denecker, M., Knowledge Representation and Reasoning in Incomplete Logic Programming, Department of Computer Science, K.U.Leuven, 1993

....of K RACi . 7.5.2 FC and the Abductive Logic Programming compared Theorem 7.5.1 The Abductive Logic Programming with integrity constraints (ALP) is correctly applicable to all chronicles in K IbsAd . Proof. ALP is correct and complete with respect to the A language, as proved by Denecker in [Den93, section 6.3] Per transitivity on the work of Thielscher (op. cit. ALP is correctly applicable to all problems in K IbsAd . 2 The Fluent Calculus, which actual range of applicability is K RACi , has a broader range of applicability than ALP (with respect to the Features and Fluents ....

Marc Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, University of Leuven, September 1993.

....use A for domain descriptions, the ideas of this paper still apply to other languages to describe the causeeffect relations. In Section 2 we present a new transformation from domain descriptions in A to abductive logic programs. The translation is different from all other translations in [GL 93, Den 93, Dung 93, BG 93, LP 96B] in that a real time dimension is incorporated so that one can represent and reason about narratives. In Section 3 we use the translation to represent temporal knowledge bases. The temporal facts, stamped with time points, will be represented by meta predicates. In this ....

....and thus CWA holds in such factories. Certainly there are domains where CWA does not hold. Open worlds are out of the scope of this paper. 2 From domain descriptions to logic programs There have been several translations of domain descriptions in A like languages into logic programs [GL 93, Den 93, Dung 93, BG 93, LP 96B] In these translations, the state transition is captured by a function of the form Result(A; S) which denotes the new situation resulting from doing A in S. These translations are appropriate for proving branching pace properties of domains of actions, but not suitable ....

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Denecker, M., Knowledge Representation and Reasoning in Incomplete Logic Programming, Ph.D. thesis, Department of Computer Science, K.U.Leuven, 1993

....(P 0 ; A; with empty integrity constraints, where P 0 is obtained from P and I. Lloyd and Topor [46] have developed a general technique which can transform a first order formula into logic programming rules. This transformation is extended, and its correctness is proved by Denecker [16]. In what follows we will often write integrity constraints in the above form, if possible. An abductive answer to a query Q in an abductive logic programming framework (P; A; I) is a set inclusion minimal subset R of instances of A such that COMP (P ; A) I [ R is consistent and COMP (P ; ....

....nice properties. For acyclic logic programs, the predicate completion semantics coincides with other semantics such as the stable model semantics [22] and the wellfounded model semantics [70] In the case of abductive logic programs, the semantical coincidence still holds, as shown by Denecker [16]. There have been many proposals, e.g. 15, 65] for abductive query evaluation procedures for abductive normal logic programs. The work reported in this paper has been experimented with the latest version of the REVISE system [13] an extended logic programming system for revising knowledge ....

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Denecker, M., Knowledge Representation and Reasoning in Incomplete Logic Programming, Ph.D. Thesis, Department of Computer Science, K.U.Leuven, 1993

....them can be extended for abductive logic programs. As is known, for acyclic programs 2 [5] their predicate completion models coincide with both the stable models and the well founded models. In the case of abductive logic programs, the semantical coincidence still holds, as shown by Denecker [10]. In this paper we will only use acyclic logic programs, and will define the semantics of logic programs as the predicate completion semantics. For abductive logic programs, we will complete all predicates except the abducible ones [8] Example 3.1 Consider an abductive logic programming ....

....agrees with its generalized stable model semantics [17] and generalized well founded model semantics [27] The above corollary means that the result of this paper can be experimented with any abductive logic programming system with one of the three major semantics. The detailed proof follows from [10]. 4.3 Soundness and Completeness In general it is very difficult to reason about actions in A . The purpose of the translation is to reduce the reasoning work in A to abductive querying in an abductive logic programming system. This section will show that reasoning in A is equivalent ....

M. Denecker. Knowledge representation and reasoning in incomplete logic programming. Ph.D. thesis, Department of Computer Science, K.U.Leuven, 1993.

....result(a; s) 2 Theta jsj 1 (noninertial(f; a; s) 2 Theta jsj 2 where jsj denotes the number of occurrences of result plus 1. Then it is straightforward to verify the above is a level mapping. We should point out that the above level mapping is a slight modification of that in [5, 6]. 2 Corollary 3.2 The completion semantics Comp( D) of D agrees with its generalized stable model semantics [8] and generalized well founded model semantics [17] Proof Since D is an acyclic logic program, According to [5] the completion semantics of any acyclic abductive logic program with ....

....out that the above level mapping is a slight modification of that in [5, 6] 2 Corollary 3. 2 The completion semantics Comp( D) of D agrees with its generalized stable model semantics [8] and generalized well founded model semantics [17] Proof Since D is an acyclic logic program, According to [5], the completion semantics of any acyclic abductive logic program with constraints coincides with its generalized stable model semantics [8] and generalized well founded model semantics [17] 2 The above corollary means that the result of this paper can be experimented with any abductive logic ....

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M. Denecker. Knowledge representation and reasoning in incomplete logic programming. Ph.D. thesis, Department of Computer Science, K.U.Leuven, 1993.

....agrees with its generalized stable model semantics [7] and generalized well founded model semantics [17] The above corollary means that the result of this paper can be experimented with any abductive logic programming system with one of the three major semantics. The detailed proof follows from [5]. 4 Soundness and Completeness In general it is very difficult to reason about actions in A . The purpose of the translation is to reduce the reasoning work in A to abductive querying in an abductive logic programming system. This section will show that reasoning in A is equivalent to ....

M. Denecker. Knowledge representation and reasoning in incomplete logic programming. Ph.D. thesis, Department of Computer Science, K.U.Leuven, 1993.

....1: Failed SLDNFA LO tree for :light off Given a theory T consisting of de nitions D and FOL axioms T and a query Q, SLDFNA LO generates a tuple ( S ; where is a set of de nitions for all open predicates except , S is a set of atoms describing a partial order and a substitution. In [7], the following correctness theorem is proven for SLDNFA LO. Theorem 5.1 It holds that D [ S [ T TO j= 8( Q) D [ S [ T TO j= T Moreover, let be any linearisation of S . Then it holds that: D [ f g j= 8( Q) D [ f g j= T D [ f g j= T TO 5.1 ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....fInit(A; St; l) Causes(A; St; l) j A A; St 2 St; l 2 b Fg, for which I D init is the least fixpoint of PID init . The rules Init(A; St; l) Causes(A; St; l) Ho(l; St) are the only rules for Init. Since the completion of the definition rules is entailed by the inductive definition semantics ([4]) the rules imply 8A; St; l : Init(A; St; l) Causes(A; St; l) Ho(l; St) and thereby capture the intended relation between strong and weak initiation. The mutual recursion in the definitions of Init and Causes indicates that strong initiations may provide causes for literals to become ....

....p in the head is the definition of p. An undefined predicate is a predicate without a definition: its meaning is not determined by the program. FOL formulae can be used to express information on undefined predicates. As semantics for open logic programs we adopt the justification semantics ([4]) formally an extension of well founded semantics which allows for undefined predicates. This semantics assigns, given any combination of values for the undefined predicates, unique truth values to the defined predicates by interpreting their clauses as an inductive definition. The resulting ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....would not make sense under this interpretation of u: abducible predicates have no definition and cannot be badly defined. Two theorems about 3 valued completion semantics are important in the context of this paper. The first is about the consistency of abductive logic programs. It was proven in [14, 10]. Theorem 2.1 Let P A be an abductive logic program based on Sigma. Let I be any Sigma abd interpretation where Sigma abd is obtained from Sigma by dropping all non abducible predicates except = Assume I j= FEQ( Sigma) Abd2(P A ) There exists a Sigma model M of P A such that M j ....

....abd = I. This proves the consistency of any abductive logic program, since any 2 valued Herbrand Sigma abd interpretation satisfies FEQ( Sigma) Abd2(P A ) A second theorem about the 3 valued completion semantics is that it is the weakest semantics known for abductive logic programming. In [14, 10], the following theorem is proven: Theorem 2.2 If M is a Sigma model of P A wrt (2 valued completion semantics [8] generalised stable semantics [32] generalised well founded semantics [49] justification semantics [14, 10] then M is a Sigma model of P A wrt 3 valued completion ....

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M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....predicate a entails that a is true. The problem is caused by the loop over negation of p. For programs which do not contain such loops, it can be shown that the undefined predicates can have any interpretation. In other semantics such as the 3 valued completion semantics for abductive programs [4], the justification semantics for abductive programs [7] and the generalised well founded semantics for abductive logic programs [28] even for programs with loops over negation, the interpretation of the undefined predicates can be any. Despite these problems with 2 valued completion semantics, ....

....Due to the fact that D is acyclic and in each clause of PD , the variables of the body occur in the head, all these semantics coincide in the (weak) sense that the set of all ground atoms implied by D under any of the semantics is identical. This extension of results of [1] is proven formally in [4]. Because of 8 these results, we can investigate the soundness and completeness of the transformation under the simplest semantics for open logic programs, the completion semantics of [3] The translation D of a domain description contains two defined predicates, Holds=2 and Noninertial=3. The ....

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M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....[7] Due to the fact that D is acyclic and in each clause of PD , the variables of the body occur in the head, all semantics coincide in the (weak) sense that the set of all ground atoms implied by D under any of the semantics is identical. This extension of results of [1] is proven formally in [4]. The soundness and completeness of is proven wrt the completion semantics of [3] Since an incomplete program does not contain clauses with undefined predicates in the head, the Clark completion [2] contains for each undefined predicate p=n the completed definition 8(p(x 1 ; x n ) ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

.... Delta = fe 1 e 2 g. 25 Given a theory T consisting of definitions D and FOL axioms T and a query Q, SLDFNA LO generates a tuple ( Delta; S ; where Delta is a set of definitions for all open predicates except , S is a set of atoms describing a partial order and a substitution. In [7], the following correctness theorem is proven for SLDNFA LO. Theorem 5.1 It holds that ffl D [ Delta [ S [ T TO j= 8( Q) ffl D [ Delta [ S [ T TO j= T Moreover, let Delta be a linearisation of S . Then it holds that: ffl D [ Delta [ f Delta g j= 8( Q) ffl D [ Delta [ f Delta ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....fact. Finally, SLDNFA has a special negative unification procedure for handling the case where skolem constants occur in negative goals. We will not go into detail on this procedure. We just mention that it produces expressions of the form sk 6= term as constraints on the generated solutions. In [ Denecker, 1993 ] the SLDNFA procedure is formalized and it is proven to be sound w.r.t. completion semantics: comp(P Delta) j= q. As a completeness result it is proven that if the computation terminates, then SLDNFA generates at least all minimal solutions. 4.2 A simple inductive procedure We design a ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....[47] we have developed Open Event Calculus, an OLP FOL theory describing time, action and state. The resulting theory has a rich ontology. We have used it to express a variety of temporal phenomena, such as point or interval based time [69] ramifications, concurrency and simultaneous events [26], qualitative and quantitative continuous processes [68] etc. By the use of OLP FOL as underlying language, all the above phenomena can be combined with diverse forms of uncertainty on the temporal information, such as uncertainty on the occurrence of actions, on the order in time of certain ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....on these, section 3 gives a semantics for the logic. Section 4 gives a number of well chosen examples which clarify the role of OLP FOL for knowledge representation. The paper closes with a discussion of related work and a conclusion. The proofs of the theorems are omitted and can be found in [4] and [6] 2 Preliminaries. An alphabet Sigma, terms, atoms, literals and formulae based on Sigma are defined as usual. As usual, a free variable in a formula is not bound by a quantifier; a closed or ground formula does not contain free variables. Substitutions and variable assignments are ....

....would not make sense under this interpretation of u: open predicates have no definition and cannot be badly defined 1 . For the purposes of this paper, one interesting advantage of using the 3 valued completion semantics is that it is the weakest semantics known for the (O)LP formalism. In [4], the following theorem is proven: Theorem 3.2 If M is a model of P D wrt (2 valued completion semantics [2] 3] generalised stable semantics [14] generalised well founded semantics [22] justification semantics [5] then M is a model of P D wrt 3 valued completion semantics. As a ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

.... is clearly a useful computational paradigm, it was not recognized earlier that the formalism of abductive logic programs with first order logic constraints provides the same declarative expressivity for representing incomplete information as full first order logic (FOL) This was shown in [5], where it was exploited to provide an implementation of the A language of [10] in the Situation Calculus formulated as an abductive logic program. In this paper we demonstrate how a temporal database with incomplete information can be formalized in the Abductive Event Calculus and how a suitable ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....eliminate problems occuring because of bidirectional persistence of properties (forward as well as backward in time) Extensions were introduced to improve the expressive power in several ways. One of the most important of these was the introduction of abduction, for example in [ 8 ] 15 ] and [ 5 ] , which made it possible to use the Event Calculus for planning and for diagnosis ( 7 ] as well as for temporal projection. In the original Event Calculus, as in most other versions, all change is supposed to be discrete. Recently there have been proposals ( 19 ] 16 ] to incorporate ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....completion semantics of open logic programs. This semantics entails the negation as finite failure principle. It is weaker than other semantics that we know that satisfy this principle, in the sense that a model of such another semantics is also a model of the 3 valued completion semantics. In [3], this was formally proven for all aforementioned semantics. As a consequence, the 3 valued completion semantics induces the weakest entailment relation j= if a program entails F according to the 3 valued completion semantics then also wrt to the other semantics. In intuitive terms: the ....

....be avoided then the only queries that can be sensibly answered are those which do no rely on facts being u in some models. If this rule is obeyed, then the semantics of the well defined part of a logic program is the same as under 2 valued semantics and reasoning by cases can be applied safely. In [3], we proved that 3 valued completion semantics is weaker than other well known semantics. The theorem states the following: Theorem 2.1 If M is a model of P wrt (2 valued completion semantics) generalised stable semantics) generalised well founded semantics) justification semantics) then M is ....

[Article contains additional citation context not shown here]

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....predicate a entails that a is true. The problem is caused by the loop over negation of p. For programs which do not contain such loops, it can be shown that the abductive predicates can have any interpretation. In other semantics such as the 3 valued completion semantics for abductive programs [4], the justification semantics for abductive programs [7] and the generalised well founded semantics for abductive logic programs [27] even for programs with loops over negation, the interpretation of the undefined predicates can be any. Despite these problems with 2 valued completion semantics, ....

....Due to the fact that D is acyclic and in each clause of PD , the variables of the body occur in the head, all these semantics coincide in the (weak) sense that the set of all ground atoms implied by D under any of the semantics is identical. This extension of results of [1] is proven formally in [4]. Because of these results, we can investigate the soundness and completeness of the transformation under the simplest semantics for open logic programs, the completion semantics of [3] The translation D of a domain description contains two defined predicates, Holds=2 and Noninertial=3. The ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

....Calculus. The axiom represents that the situations that can be reached from the initial situation by executing a finite sequence of actions are the only situations that exist. Under a stronger semantics for open logic programs than Console completion, for example under justification semantics ([5]) a similar axiom 1 is implied by the following clauses defining situations: situation(s 0 ) situation(result(A; S) situation(S) action(A) assuming a domain dependent type predicate action=1 for actions. As Console completion semantics is more commonly used and provides an immediate ....

M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

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M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

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M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

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M. Denecker. Knowledge Representation and Reasoning in Incomplete Logic Programming. PhD thesis, Department of Computer Science, K.U.Leuven, 1993.

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