## SLDNFA: an abductive procedure for normal abductive programs (1992)

Venue: | Proc. of the International Joint Conference and Symposium on Logic Programming |

Citations: | 64 - 15 self |

### BibTeX

@INPROCEEDINGS{Denecker92sldnfa:an,

author = {Marc Denecker and Danny De Schreye},

title = {SLDNFA: an abductive procedure for normal abductive programs},

booktitle = {Proc. of the International Joint Conference and Symposium on Logic Programming},

year = {1992},

pages = {686--700},

publisher = {MIT Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

A family of extensions of SLDNF-resolution for normal abductive programs is presented. The main difference between our approach and existing procedures is the treatment of non-ground abductive goals. A completion semantics is given and the soundness and completeness of the procedures has been proven. The research presented here, provides a simple framework of abductive procedures, in which a number of parameters can be set, in order to fit the abduction procedure to the application under consideration.

### Citations

1858 |
Foundations of Logic Programming
- Lloyd
- 1987
(Show Context)
Citation Context ...e solution after all, as announced earlier. Another issue is the relation to SLDNF. Although the denition of SLDNFA refutation is structured rather dierently than the denition of SLDNF refutation ([14=-=-=-]), for non-abductive programs, we have proved that the denitions of SLDNFA and SLDNF are equivalent: for programs without abducible predicates and for every SLDNFA refutation, it is possible to const... |

1424 |
A logic for default reasoning
- Reiter
- 1980
(Show Context)
Citation Context ...r time" [19]. Hanks and McDermott used the famous Yale turkey shooting problem (YTS) to show that well-known non-monotonic reasoning systems as McCarthy's circumscription [30], Reiter's default l=-=ogic [37]-=- and McDermott's non-monotonic logic [31] failed to represent the frame axiom correctly. Negation as failure was not considered in this study. Nevertheless, the frame axiom has a correct representatio... |

959 |
Negation as failure
- Clark
- 1978
(Show Context)
Citation Context ...NFA can be constructed. We have proved the following soundness result for the SLDNFA procedure with respect to completion semantics (see [5]). Below, comp(L+Sk();P + ) denotes the Clark completion ([3]) of the non-abductive program consisting of the clauses of P and . &(Q 0 ) denotes the open conjunction of literals of Q. Theorem 3.1 (soundness) If (,) is the result of an SLDNFA refutation for a... |

845 | The well-founded semantics for general logic programs
- Gelder, Ross, et al.
- 1991
(Show Context)
Citation Context ...nly sound wrt the 3-valued completion semantics but also wrt more fine-grained semantics for logic programs. In [10], we presented the justification semantics which extends the well-founded semantics =-=[42]-=- and the extended well-founded semantics for abductive logic programs [35]. In contrast to most current LP semantics, justification semantics is based on general interpretations instead of Herbrand in... |

816 |
Circumscriptionâ€”a form of non-monotonic reasoning
- McCarthy
- 1980
(Show Context)
Citation Context ...ndency of facts to endure over time" [19]. Hanks and McDermott used the famous Yale turkey shooting problem (YTS) to show that well-known non-monotonic reasoning systems as McCarthy's circumscrip=-=tion [30]-=-, Reiter's default logic [37] and McDermott's non-monotonic logic [31] failed to represent the frame axiom correctly. Negation as failure was not considered in this study. Nevertheless, the frame axio... |

381 | Bilattices and the semantics of logic programming
- Fitting
- 1991
(Show Context)
Citation Context ...ion. However, for most programs (i.e. stratied or locally stratied programs) this problem does not occur. A more radical solution for the problem would be to consider 3-valued completion semantics ([9]). SLDNFA is still correct wrt to these semantics and for each , P + is consistent. Another issue to be investigated is the soundness of SLDNFA wrt other moresne-grained semantics such as the Genera... |

370 |
A logical framework for default reasoning
- Poole, Goebel, et al.
- 1987
(Show Context)
Citation Context ...in order tost the abduction procedure to the application under consideration. 1 Introduction Negation as failure and abduction have been recognized as important forms of nonmonotonic reasoning ([13], =-=[18]-=-). We present a general procedure for logic programs which integrates both paradigms. This procedure resulted from research in the domain of temporal reasoning. Temporal reasoning is an excellent doma... |

333 | An efficient unification algorithm
- Martelli, Montanari
- 1982
(Show Context)
Citation Context ... a solved form of an equality set E iff E s is in solved form and E s is an mgu of E or, if no mgu exists, E s is f2g. To unify a set of terms including skolem constants, the unification algorithm of =-=[29]-=- must be slightly extended. The modified algorithm treats skolem constants as variables. Definition 3.5 The equality reduction is the process of transforming a set E of equalities to a set E s of equa... |

256 |
A temporal logic for reasoning about processes and plans. Cognitive science
- McDermott
- 1982
(Show Context)
Citation Context ...e famous Yale turkey shooting problem (YTS) to show that well-known non-monotonic reasoning systems as McCarthy's circumscription [30], Reiter's default logic [37] and McDermott's non-monotonic logic =-=[31]-=- failed to represent the frame axiom correctly. Negation as failure was not considered in this study. Nevertheless, the frame axiom has a correct representation in situation calculus or event calculus... |

234 |
Negation in Logic Programming
- Kunen
- 1987
(Show Context)
Citation Context ...proved treatment of non-ground abductive goals which has been incorporated in a procedure, called SLDNFA. We prove its sound- and completeness wrt an extension of the 3-valued completion semantics of =-=[24]-=- for abductive logic programs. Although the inspiration for the design of SLDNFA stems from temporal reasoning, we formulate it in full generality and it can be applied in any domain where abduction i... |

218 |
Unification revisited
- Lassez, Maher, et al.
- 1986
(Show Context)
Citation Context ...more conventional definitions. What conventionally is called a normal program corresponds in our terminology to a complete normal logic program. A substitution, its domain and range are defined as in =-=[25, 26]-=-. Substitutions are denoted by `; oe; ffi. The application of a substitution ` on a term t or a formula or set of these is defined as in [26], but is denoted by `(t) instead of t`. Composition of subs... |

203 | Abduction compared with negation as failure - Eshghi, Kowalski |

178 |
Making PROLOG More Expressive
- Lloyd, Topor
- 1984
(Show Context)
Citation Context ... abductive logic programs. Indeed, assume that we want to prove a formula F wrt an abductive program P (under completion semantic). Consider the general query / :F . By applying the transformation of =-=[27]-=-, this general query can be transformed into a normal query Q =/ L 1 ; : : : ; L n and a program P 0 . Moreover, it holds that P j= F iff P + P 0 j=/ L 1 ; : : : ; L n under 3valued completion semanti... |

172 |
Acyclic programs
- Apt, Bezem
- 1990
(Show Context)
Citation Context ...or testing nonmonotonic reasoning techniques because of the frame problem. The frame axiom has a correct representation in situation and event calculus with negation as failure, as was illustrated in =-=[1]-=- for the famous Yale Turkey Shooting problem. A major restriction of negation as failure is its incapacity of representing incomplete knowledge. The original event calculus only supports the predictio... |

168 | On the relationship between abduction and deduction
- Console, Dupre, et al.
- 1991
(Show Context)
Citation Context ...oresne-grained semantics such as the Generalised Stable Models ([12]). A completeness result on SLDNFA has been proven with respect to the completion semantics dened for abductive normal programs in [4]. The denition is an extension of the denition for non-abductive programs. Denition 3.5 Let P be a normal abductive program based on some language L. The completion of P wrt to L, is the theory con... |

141 |
Features and Fluents
- Sandewall
- 1994
(Show Context)
Citation Context ... solving wellknown temporal reasoning problems involving prediction and postdiction under uncertainty (e.g. Yale Turkey Shooting, Russian Turkey Shooting, Stanford Murder Mystery, stolen car problem (=-=[39]-=-)). The examples illustrate well the role of the two nonmonotonic paradigms in temporal reasoning: negation as failure for the frame problem and abduction for incomplete knowledge. Our experiences wit... |

140 | Prediction is deduction but explanation is abduction
- Shanahan
- 1989
(Show Context)
Citation Context ...te and the set of events. In planning, however, the set of events is the subject of the search, and thus, a priori unknown. A solution to this problem is to extend event calculus with abduction ([8], =-=[20]-=-). In planning problems for example, the predicates which describe the events, i.e. happens=1; act=2 andsare abducible. An abductive solution for a goal, describing the goal state, gives a description... |

139 |
Default reasoning, nonmonotonic logics, and the frame problem
- Hanks, McDermott
- 1986
(Show Context)
Citation Context ...asoning. Temporal reasoning is an excellent domain for testing non-monotonic reasoning techniques because of the frame problem: "the problem of representing the tendency of facts to endure over t=-=ime" [19]-=-. Hanks and McDermott used the famous Yale turkey shooting problem (YTS) to show that well-known non-monotonic reasoning systems as McCarthy's circumscription [30], Reiter's default logic [37] and McD... |

136 |
Database Updates Through Abduction
- Kakas, Mancarella
- 1990
(Show Context)
Citation Context ...ecuting the goalsp, the abductive atoms cannot become ground. A procedure for planning should be able to cope with such situations. This condition is not satised by the abductive procedure dened in [1=-=1]-=-. In the past, special abductive procedures for temporal reasoning with abductive event calculus have been presented ([8], [20], [16, 17]). However, as the three authors argue, the treatment of constr... |

113 |
Abductive planning with event calculus
- Eshghi
- 1988
(Show Context)
Citation Context ...l state and the set of events. In planning, however, the set of events is the subject of the search, and thus, a priori unknown. A solution to this problem is to extend event calculus with abduction (=-=[8]-=-, [20]). In planning problems for example, the predicates which describe the events, i.e. happens=1; act=2 andsare abducible. An abductive solution for a goal, describing the goal state, gives a descr... |

112 | SATCHMO: A theorem prover implemented in Prolog
- Manthey, Bry
- 1988
(Show Context)
Citation Context ... subject for future research is to compare with special purpose procedures (such as the one in [38]). In [9, 11], we have formalised a procedural duality between abduction and an extension of Satchmo =-=[28]-=- for model generation under FEQ with equality atoms in the head of the rules. Interestingly, the duality framework indicates a close relation between Eshghi's approach of abducing equality facts [13] ... |

109 |
Generalized stable models: a semantics for abduction
- Kakas, Mancarella
- 1990
(Show Context)
Citation Context ...rrect wrt to these semantics and for each , P + is consistent. Another issue to be investigated is the soundness of SLDNFA wrt other moresne-grained semantics such as the Generalised Stable Models ([12]). A completeness result on SLDNFA has been proven with respect to the completion semantics dened for abductive normal programs in [4]. The denition is an extension of the denition for non-abductiv... |

70 | Causes for events: their computation and applications - Cox, Pietrzykowski - 1992 |

64 |
Intensional updates: Abduction via deduction
- Bry
- 1990
(Show Context)
Citation Context ...very positive or negative fact in D which does not occur in D 0 , neither occurs in D 00 . 47 Despite this, SLDNFA can be used for database updating but using a meta-approach, an idea already used in =-=[2]-=- 7 . The idea is to describe the new database in function of the old one and a set of insert=1 and retract=1 facts. We sketch the approach. Below, a database consists of a set Db of ground facts of ba... |

62 | Temporal reasoning with abductive event calculus
- Denecker, Missiaen, et al.
- 1992
(Show Context)
Citation Context ... This predicate describes the set of events. As a consequence, the planner generates plans with a minimal number of events. Our prototype is implemented as a vanilla meta-program on top of Prolog. In =-=[12]-=- the power of the system is shown by applying it to planning with complex context dependent events and solving wellknown temporal reasoning problems involving prediction and postdiction under uncertai... |

62 |
A Theorem-Proving Approach to Database Integrity
- Sadri, Kowalski
- 1988
(Show Context)
Citation Context ...ning regime. Loop detection, intelligent control and intelligent backtracking could be of use to the system. An interesting feature of SLDNFA (and the planner) is the use of integrity constraints. In =-=[38]-=-, a method is described to transform any set of integrity constraints to a normal program and a goal. In an abductive program, we can simulate this procedure by adding for any integrity constraint IC,... |

48 |
Problems and promises of computational logic
- Kowalski
- 1990
(Show Context)
Citation Context ...et, in order to fit the abduction procedure to the application under consideration. 1 Introduction Negation as failure and abduction have been recognized as important forms of non-monotonic reasoning =-=[23]-=-, [4], [36]. They have been shown useful for fault diagnosis [4], natural language understanding [4], knowledge assimilation [20] and default reasoning [14], [36]. Here we present a technical contribu... |

35 |
Localized Abductive Planning with the Event Calculus
- Missiaen
- 1991
(Show Context)
Citation Context ...his condition is not satised by the abductive procedure dened in [11]. In the past, special abductive procedures for temporal reasoning with abductive event calculus have been presented ([8], [20], [1=-=6, 17]-=-). However, as the three authors argue, the treatment of constraints in [8] and the treatment of non-ground abductive failure goals in [20], [16, 17] can be very inecient. The abductive procedure SLDN... |

32 |
An Ecient Uni Algorithm
- Martelli, Montanari
- 1982
(Show Context)
Citation Context ...hen t is not a variable. The equality reduction is the process of transforming a set E of equalities to a set E s of equalities in solved form by a modied version of the MartelliMontanari algorithm ([=-=15-=-]). The modied algorithm consists of the same rewrite rules, except that skolems constants are treated as variables, and one additional rewrite rule, which replaces an atom of the form sk = X by the s... |

29 |
Updating knowledge bases II
- Guessoum, Lloyd
- 1991
(Show Context)
Citation Context ... on the other hand investigates the tree branch per branch and, using an iterative deepening regime, will ultimatelysnd all solutions insnite branches. Another related procedure has been presented in =-=[10]-=-. This belief revision procedure tries to construct an SLDNF-refutation for a given goal by adding facts to the program (as in SLDNFA) to succeed positive goals and by deleting clauses of the program ... |

29 |
A Completeness Theorem for SLDNF Resolution
- Cavedon, Lloyd
- 1989
(Show Context)
Citation Context ...al programs. Similarly as for SLDNF, completeness results for infinite SLDNFA-trees could probably be obtained by imposing conditions such as allowedness and strictness on the abductive programs (see =-=[3]-=-). This is subject to future research. The proof of the completeness theorems is also in the spirit of Clark's completeness proof for SLDNF. We show that with a finite SLDNFA-tree, a formula can be as... |

29 |
A Query Evaluation Method for Abductive Logic Programming
- Satoh, Iwayama
- 1992
(Show Context)
Citation Context ...ductive procedure for 2-valued completion semantics or generalised stable semantics, consistency checking is necessary. A sound abductive procedure has been developed for generalised stable semantics =-=[40]-=-. The procedure is an extension of the abductive procedure of [20] with special consistency checking techniques for dealing with predicates like p which are possibly looping over negation. In the abov... |

27 | Hypothetical Reasoning with Well Founded Semantics
- Pereira, Aparicio, et al.
- 1991
(Show Context)
Citation Context ...ined semantics for logic programs. In [10], we presented the justification semantics which extends the well-founded semantics [42] and the extended well-founded semantics for abductive logic programs =-=[35]-=-. In contrast to most current LP semantics, justification semantics is based on general interpretations instead of Herbrand interpretations. [10] shows how the abductive logic program formalism under ... |

25 |
Residue: A deductive approach to design synthesis
- Finger, Genesereth
- 1985
(Show Context)
Citation Context ...und) abducible facts and an answer substitution ` such that P + \Delta j= `(Q). For logic programs without negation as failure, the SLD-procedure can be extended easily to an abductive procedure [7], =-=[16]-=-. Combining abduction with negation as failure is less straightforward. SLDNFA is an extension of the well-known SLDNF procedure [26] for complete logic programs. The SLDNF procedure can be viewed as ... |

23 | Generalised stable models: a semantics for abduction - Kakas, Mancarella - 1990 |

16 |
Schreye. Justification semantics: a unifying framework for the semantics of logic programs
- Denecker, De
- 1993
(Show Context)
Citation Context ...tant property of 3-valued completion semantics is that any (abductive) logic program is consistent. This property is an extension of a result obtained in [24] and was proven for the abductive case in =-=[8, 10]-=-. It is formulated in the following theorem. Theorem 2.1 Let P be an (abductive) logic program based on L. Let I be any 2-valued interpretation of L n fp=n j p=n is a defined predicate of !L;P?g satis... |

13 |
On the duality of abduction and model generation
- Denecker, Schreye
- 1992
(Show Context)
Citation Context ... with non-ground abductive literals. Strong indications exist that the techniques incorporated in SLDNFA can solve the problem ofsoundering negation for positive goals but not for negative goals. In (=-=[6-=-]), we have formalised a procedural duality between abduction and model generation. A current limitation of the duality framework is its restriction to denite abductive programs. In future work we int... |

11 |
abductive planning for robot assembly
- Missiaen
(Show Context)
Citation Context ...ete term rewriting system. The normalisation of the terms can be integrated in the procedure of applying the variable substitution. This way the duality framework shows that the procedure of [41] and =-=[33, 32]-=- can be seen as an efficient implementation of the proposal in [13]. In [6], an abductive procedure is presented which, for a given hierarchical normal abductive program P and query /Q, derives an exp... |

10 |
Negation as failure as an approach to the hanks and mcdermott problem
- Evans
- 1989
(Show Context)
Citation Context ...A Compulog-II under contract 6810 y supported by the Belgian National Fund for Scientific Research 1 been shown that the YTS representation in these formalisms solves the problem correctly [1], [14], =-=[15]-=-. Negation as failure alone is not sufficient for representing many temporal reasoning problems. A major restriction is its inability of representing incomplete knowledge. The original event calculus ... |

8 | On the duality of abduction and model generation in a framework for model generation with equality
- Denecker, Schreye
- 1994
(Show Context)
Citation Context ...stance of the body of the rule is found and this fires the abduction of the head of the rule. A subject for future research is to compare with special purpose procedures (such as the one in [38]). In =-=[9, 11]-=-, we have formalised a procedural duality between abduction and an extension of Satchmo [28] for model generation under FEQ with equality atoms in the head of the rules. Interestingly, the duality fra... |

7 |
Introduction to Artifical Intelligence
- Charniak, McDermott
- 1989
(Show Context)
Citation Context ... order to fit the abduction procedure to the application under consideration. 1 Introduction Negation as failure and abduction have been recognized as important forms of non-monotonic reasoning [23], =-=[4]-=-, [36]. They have been shown useful for fault diagnosis [4], natural language understanding [4], knowledge assimilation [20] and default reasoning [14], [36]. Here we present a technical contribution ... |

5 |
Lode Missiaen, and Maurice Bruynooghe. Temporal reasoning with abductive event calculus
- Denecker
- 1992
(Show Context)
Citation Context ... for abductive event calculus by adding a module with a constraint solver for temporal reasoning. Our prototype is implemented as a vanilla meta-program on top of Prolog (about 240 lines of code). In =-=[7]-=- the power of the system is showed by applying it to planning with context dependent events and solving well-known temporal reasoning problems involving prediction and postdiction under uncertainty (e... |

4 |
Schreye. A family of abductive procedures for normal abductive programs, their soundness and completeness
- Denecker, De
- 1992
(Show Context)
Citation Context ...DNFA and its soundness and completeness. In section 4, we present variants of SLDNFA, which yield other completeness results. Finally, we end with a discussion. Due to space restrictions, we refer to =-=[5]-=- for all proofs. 2 Basic computation steps in SLDNFA The SLDNFA procedure is an abductive procedure for normal abductive programs. An abductive logic program is a normal logic program (with negation a... |

4 |
Introduction to Metamathematics, volume 1
- Kleene
- 1952
(Show Context)
Citation Context ...letion semantics for complete logic programs of [24] for abductive programs and the 2-valued completion semantics for abductive logic programs of [6] with 3-valued models. 3-valued logic goes back to =-=[22]-=-, in which a third truth-value undefined or u was introduced. A 3-valued interpretation maps functors on functions like a classical interpretation but maps predicates to 3-valued relations. A 3-valued... |

2 |
Logic programming in arti intelligence
- Kowalski
- 1991
(Show Context)
Citation Context ... set, in order tost the abduction procedure to the application under consideration. 1 Introduction Negation as failure and abduction have been recognized as important forms of nonmonotonic reasoning (=-=[13]-=-, [18]). We present a general procedure for logic programs which integrates both paradigms. This procedure resulted from research in the domain of temporal reasoning. Temporal reasoning is an excellen... |

2 |
Features and
- Sandewall
- 1991
(Show Context)
Citation Context ...solving well-known temporal reasoning problems involving prediction and postdiction under uncertainty (e.g. Yale Turkey Shooting, Russian Turkey Shooting, Stanford Murder Mystery, stolen car problem (=-=[19]-=-)). Our experiences have highlighted the need for an intelligent control strategy. Our implementation uses the straightforwardsdepthsrst, left to right control strategy. In many examples, the system e... |

1 |
A completeness theorem for sldnf resolution. Journal of logic programming
- Cavedon, Lloyd
- 1989
(Show Context)
Citation Context ...hierarchical programs. Similarly as for SLDNF, completeness results for innite SLDNFA-trees could be obtained by imposing conditions such as allowedness and strictness on the abductive programs (see [=-=2-=-]). This is subject to future research. 4 Extensions of the abductive procedure. The current SLDNFA procedure can be extended in dierent ways, in order to obtain even more solutions. As a result, the ... |