## An Overview of Nonmonotonic Reasoning and Logic Programming (1993)

Venue: | Journal of Logic Programming, Special Issue |

Citations: | 26 - 2 self |

### BibTeX

@ARTICLE{Minker93anoverview,

author = {Jack Minker},

title = {An Overview of Nonmonotonic Reasoning and Logic Programming},

journal = {Journal of Logic Programming, Special Issue},

year = {1993},

volume = {17},

pages = {95--126}

}

### Years of Citing Articles

### OpenURL

### Abstract

The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the pre-history of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic programming. The overview includes the major results developed including complexity results that are known about the various theories. I then provide a summary which includes an assessment of the field and what must be done to further research in nonmonotonic reasoning and logic programming. 1 Introduction Classical logic has played a major role in computer science. It has been an important tool both for the development of architecture and of software. Logicians have contended that reasoning, as performed by humans, is also amenable to analysis using classical logic. However, workers in the field of artificial 1 This paper is an updated version of an invited Banquet Address, First Interna...

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Citation Context ...las, where n is the number of formulas in the theory, it will be computationally complex. Various nonmonotonic formalisms based on conditional entailment have been developed by Geffner [Gef89], Pearl =-=[Pea88]-=-, Delgrande [Del88] and by Ginsberg [Gin86]. Conditional entailment bears some similarity to circumscription in that they both induce preferences between models. The original ideas on conditional enta... |

1857 |
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Citation Context ... concentrate on the formalizations of nonmonotonic reasoning and their relationships to logic programming. See [Rei87] for an earlier survey of the field. Books on the foundation of logic programming =-=[Llo87]-=- and on the foundations of disjunctive logic programming [LMR92] provide theoretical background on the semantics of logic programming including rules of 6 negation. The collected works of John McCarth... |

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Citation Context ...en supported models of normal programs and expansions of autoepistemic theories. Gelfond [Gel87] shows that general logic programs can be translated into autoepistemic theories. Gelfond and Lifschitz =-=[GL88]-=- show that stable model semantics is also equivalent to the translation of logic programs into autoepistemic theories as proposed by Gelfond. Lifschitz [Lif89a] shows that autoepistemic logic, stable ... |

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Citation Context ...as perhaps the first individual to discuss the need for the automation of commonsense reasoning, before any theory existed on the subject. Initial formalizations were propounded by McCarthy and Hayes =-=[MH69]-=-, who discussed philosophical problems from the standpoint of AI and introduced the frame problem, and by Sandewall [San85] who attempted to find a solution to the frame problem, discussed in terms of... |

1428 |
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Citation Context ...he first approach extends the logic system in different ways. This is characterized in papers by McCarthy [McC80] who formalized his theory of circumscription, 5 introduced earlier [McC77]; by Reiter =-=[Rei80a]-=- who introduced his theory of default reasoning; and by McDermott and Doyle [MD80] who used modal logic to handle nonmonotonicity. The second approach views logic as an object, and extends the reasoni... |

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Citation Context ...nonmonotonic reasoning as we know it today started approximately in 1975/1976, with papers published in the 1977-1979 time period. Two important papers, one by Reiter [Rei78a], and the other by Clark =-=[Cla78] appeared -=-in the book "Logic and Data Bases," edited by Gallaire and Minker [GM78]. Reiter set forth the rule of negation called the closed world assumption, (CWA). The CWA states that in Horn logic t... |

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Citation Context ...iffers from the conventional approaches. They base their method on using linear programming-based automated inference as introduced by Jeroslow [Jer88] instead of using the Robinson resolution method =-=[Rob65]-=-. They concentrate their development on compilers which move as much of the deduction to compile-time as possible. They compare, implement, and experiment with linear constraints corresponding to seve... |

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(Show Context)
Citation Context ...ive defaults. Gelfond et al. [GLPT91] show that one cannot simulate a ddt with a standard default theory. They note that ddt is a generalization of the semantics for disjunctive databases proposed by =-=[GL91]-=-. Baral and Subrahmanian [BS92] show that even though all default theories do not necessarily have extensions, Reiter's operator always has fixed-points over the power lattice. Such fixed-points indic... |

817 |
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(Show Context)
Citation Context ... to nonmonotonic reasoning can be characterized broadly as falling in two different classes. The first approach extends the logic system in different ways. This is characterized in papers by McCarthy =-=[McC80]-=- who formalized his theory of circumscription, 5 introduced earlier [McC77]; by Reiter [Rei80a] who introduced his theory of default reasoning; and by McDermott and Doyle [MD80] who used modal logic t... |

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Citation Context ... property iff whenever a formula is provable from a theory P , it is provable from any set P 0 such that P ` P 0 . The term "nonmonotonic reasoning" is probably attributable to Minsky's &quo=-=t;Frame Paper" [Mins74]-=-. Minsky informally addresses the notion of a frame (which does not relate to the frame problem) and states, A frame is a data-structure for representing a stereotype situation, like being in a certai... |

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Citation Context ... atoms, it does not work for non-ground atoms. Chan's constructive negation solves this problem. In the case of Horn theories there is a single model, given by the unique minimal model of the program =-=[EK76]-=-. Theories then exist for stratified normal programs and normal programs in general. In the area of stratified programs, there is a single meaning that can be ascribed to a program, as developed by Ap... |

622 |
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(Show Context)
Citation Context ...n are, I believe, the first formalizations of nonmonotonic reasoning. McCarthy first introduced his theory of circumscription in 1977 [McC77], and Doyle developed his truth maintenance system in 1979 =-=[Doy79]-=-. Reiter gave preliminary material on default reasoning in 1978 [Rei78b]. Nonmonotonic reasoning obtained its impetus in 1980 with the publication of an issue of the Artificial Intelligence Journal, d... |

612 |
Towards a theory of declarative knowledge
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(Show Context)
Citation Context ...f protected circumscription. Gelfond, Przymusinska and Przymusinski [GPP89] relate a propositional form of circumscription to stratified theories. (See Chandra and Harel [CH82], Apt, Blair and Walker =-=[ABW88]-=-, and Van Gelder [VG88] for work on stratified theories.) Minker, Lobo and Rajasekar [MLR91] complement the work by Gelfond, Przymusinska and Przymusinski [GPP89] by developing a procedure to compute ... |

542 | Nonmonotonic reasoning, preferential models and cumulative logics
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(Show Context)
Citation Context ...f a program according to their properties. He suggests that the selection of a method be based upon general properties of nonmonotonic inference operations in the spirit of Kraus, Lehmann and Megidor =-=[KLM90]-=-. He suggests that the decision as to the semantics to be used be based on general principles, two of which he calls cumulativity and rationality. He has compared different semantics according to thes... |

538 | Abductive logic programming
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(Show Context)
Citation Context ...planations for observations in a given theory. There have been two major approaches to abduction: one based on logic as defined by Selman and Levesque [SL90] and described in Kakas, Kowalski and Toni =-=[KKT92]-=-, and the other based on set-covering methods as given in the book by Peng and Reggia [PR90]. We discuss only the logic-based approach. The formal definition of abductive reasoning is that given a set... |

448 |
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- 1986
(Show Context)
Citation Context ...y constraints. They show that abductive logic programming is related to the justification-based truth maintenance system of Doyle [Doy79] and the assumption-based truth maintenance system of de Kleer =-=[DeK86]-=-. 23 For a summary of complexity results on abductive reasoning see the excellent survey by Cadoli and Schaerf [CS92]. A formal definition of abductive logic programming is given by Kakas and Mancarel... |

440 |
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- 1985
(Show Context)
Citation Context ...ator M into first-order logic. If p is a sentence in first-order logic, then Mp denotes the sentence in modal logic whose intended meaning is "p is consistent with what is known," or "m=-=aybe p." Moore [Moo85a] developed autoepist-=-emic logic (AEL), which is an improvement of the work by McDermott and Doyle. Instead of using a "possibly" modal operator, he uses a "necessarily" modal operator L. Intuitively, L... |

381 | A Kripke-Kleene Semantics for Logic Programs - Fitting - 1985 |

336 |
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(Show Context)
Citation Context ...G89]. They compute the stable models of a deductive database by first computing the well-founded semantics and then use a branch-and-bound strategy to compute the stable models. Gelfond and Lifschitz =-=[GL90]-=- expand the class of logic programs to include logical negation (:), in addition to negation-as-failure. They base their semantics on stable models. They argue that some facts of commonsense reasoning... |

322 | Computing Circumscription
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- 1985
(Show Context)
Citation Context ...icate from true to false at one point. This is referred to as pointwise circumscription. Lifschitz then defines prioritized circumscription which provides for priorities between predicates. Lifschitz =-=[Lif85]-=- describes the concept of parallel circumscription and also treats prioritized circumscription. Grosof [Gro91] has generalized prioritized circumscription to a partial order of priorities. Lifschitz [... |

318 |
A generalization of Bayesian inference
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(Show Context)
Citation Context ... to the well-founded 17 semantics. Their work provides a means to generalize autoepistemic reasoning and applies to work in abductive reasoning. Ng and Subrahmanian [NS91] investigate Dempster-Shafer =-=[Dem68]-=- probabilistic logic programs and develop a declarative semantics for this class. They transform each such program into a new program whose clauses may contain nonmonotonic negations in their bodies a... |

299 | and Johan de Kleer. Foundations of assumption-based truth maintence systems: preliminary report - Reiter - 1987 |

292 | A useful four-valued logic - Belnap - 1977 |

288 |
A theory of conditionals
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Citation Context ... [Gin86]. Conditional entailment bears some similarity to circumscription in that they both induce preferences between models. The original ideas on conditional entailment were set forth by Stalnaker =-=[Sta68]-=- and Lewis [Lew73]. For a detailed description of the role of conditionals in artificial intelligence, see Horty and Thomason [HT92]. 3.3 Default Reasoning Default reasoning, developed by Reiter [Rei8... |

267 |
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- Reiter
- 1977
(Show Context)
Citation Context ...he formalization of the field of nonmonotonic reasoning as we know it today started approximately in 1975/1976, with papers published in the 1977-1979 time period. Two important papers, one by Reiter =-=[Rei78a], and the -=-other by Clark [Cla78] appeared in the book "Logic and Data Bases," edited by Gallaire and Minker [GM78]. Reiter set forth the rule of negation called the closed world assumption, (CWA). The... |

254 |
On the declarative semantics of deductive databases and logic programs
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- 1988
(Show Context)
Citation Context ...the case of stratified disjunctive databases. Fern'andez and Minker [FM91b] develop a fixpoint operator for stratified disjunctive deductive databases that captures the perfect models of Przymusinski =-=[Prz88]-=-, and is able to compute prioritized circumscription. Przymusinski [Prz89] has developed an algorithm to compute circumscription in a wide class of circumscriptive theories. Ginsburg has implemented a... |

244 | Structure and complexity of relational queries
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- 1982
(Show Context)
Citation Context ...8] have extended the concept of protected circumscription. Gelfond, Przymusinska and Przymusinski [GPP89] relate a propositional form of circumscription to stratified theories. (See Chandra and Harel =-=[CH82]-=-, Apt, Blair and Walker [ABW88], and Van Gelder [VG88] for work on stratified theories.) Minker, Lobo and Rajasekar [MLR91] complement the work by Gelfond, Przymusinska and Przymusinski [GPP89] by dev... |

235 | What does a conditional knowledge base entail
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(Show Context)
Citation Context ...alent to contraposition. They are able to clarify some points about circumscription and show, for example, that the relations defined by circumscription do not satisfy, in general, contraposition. In =-=[LM92]-=- they study, in inference systems, the following question: given a knowledge base KB what are the assertions that are entailed by KB? They argue that any reasonable nonmonotonic inference procedure sh... |

223 |
Non-monotonic logic I
- McDermott, Doyle
- 1980
(Show Context)
Citation Context ...in papers by McCarthy [McC80] who formalized his theory of circumscription, 5 introduced earlier [McC77]; by Reiter [Rei80a] who introduced his theory of default reasoning; and by McDermott and Doyle =-=[MD80]-=- who used modal logic to handle nonmonotonicity. The second approach views logic as an object, and extends the reasoning system with meta-devices. This is explored by Weyrauch [Wey80] and Winograd [Wi... |

220 |
T.: OLDT Resolution with Tabulation
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(Show Context)
Citation Context ...mantics. Chen and Warren [CW92] developed a goaloriented method, XOLDTNF resolution, of computing the well-founded semantics. The inference system extends OLDT resolution developed by Tamaki and Sato =-=[TS86]-=- in that the truth value of an answer to a query may be undefined, due to the three-valued nature of the well-founded semantics. They avoid negative loops in the computation by negative contexts. The ... |

220 |
Unfounded sets and well-founded semantics for general logic programs
- Gelder, Ross, et al.
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(Show Context)
Citation Context ...stratified, there are several competing theories: the theory of stable models developed by Gelfond and Lifschitz [GL88]; the theory of well-founded semantics developed by Van Gelder, Ross and Schlipf =-=[VRS88]-=-, and elaborated upon by Przymusinski [Prz89a]; the theory of generalized well-founded semantics by Baral, Lobo and Minker [BLM90c] and the theory of stable classes developed by Baral and Subrahmanian... |

203 | Abduction Compared with Negation by Failure - Eshghi, Kowalski - 1989 |

191 |
Autoepistemic logic
- Marek, TruszczyĆski
- 1991
(Show Context)
Citation Context ...poses several different semantics, all based on the idea that having beliefs about an individual amounts to having a belief 14 using a certain type of name for the individual. Marek and Truszczy'nski =-=[MT91]-=- systematically study properties of AEL. A major issue in AEL is to define semantics for programs with negation. Gelfond [Gel87] observed that the logic program p / q; not r can be expressed in autoep... |

187 | Foundations of disjunctive logic programming
- Lobo, Minker, et al.
- 1992
(Show Context)
Citation Context ... their relationships to logic programming. See [Rei87] for an earlier survey of the field. Books on the foundation of logic programming [Llo87] and on the foundations of disjunctive logic programming =-=[LMR92]-=- provide theoretical background on the semantics of logic programming including rules of 6 negation. The collected works of John McCarthy [McC91] should be read as it is fundamental to an understandin... |

187 |
All I Know: A study in autoepistemic logic
- Levesque
- 1990
(Show Context)
Citation Context ...c and Kripke's approach to modal logic 12 [Kri71]. As observed by Shvarts [Shv90], AEL is one of the nonmonotonic logics that can be obtained from the approach of McDermott and Doyle [MD82]. Levesque =-=[Lev90]-=- generalizes Moore's notion of a stable expansion [Moo85a] to the full first-order case. He provides a semantic account of stable expansions in terms of a second modal operator O, where O(w) is read a... |

178 |
Complexity results for nonmonotonic logics
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- 1992
(Show Context)
Citation Context ...s and to modal logic S 5 . They further show that skeptical reasoning with sets closed under default theories is closely related with provability in S 5 . They provide complexity results. See Gottlob =-=[Got91]-=- and Niemela [Nie92] for complexity results involving expansions of default theories and autoepistemic expansions. In view of the relationships between the alternative theories, the tractability resul... |

178 |
Semantical Considerations on Modal Logic
- Kripke
- 1963
(Show Context)
Citation Context ... modalities, as p is possible if-and-only-if :p is not necessary. Hence, Mp is equivalent to :L :p. Ginsberg shows the relationship between autoepistemic logic and Kripke's approach to modal logic 12 =-=[Kri71]-=-. As observed by Shvarts [Shv90], AEL is one of the nonmonotonic logics that can be obtained from the approach of McDermott and Doyle [MD82]. Levesque [Lev90] generalizes Moore's notion of a stable ex... |

174 | The Mathematics of Inheritance Systems - Touretzky - 1986 |

159 | Stable semantics for disjunctive programs
- Przymusinski
- 1991
(Show Context)
Citation Context ...iversity of proposed semantics for extended logic programs. By adjusting their parameters they can specify several semantics using two kinds of negation: stationary [Prz90], extended stable semantics =-=[Prz91b]-=- and well-founded semantics [VRS88]. Minker and Ruiz [MR93] develop general techniques for dealing with extended disjunctive logic programs and extend the model, fixpoint and proof theories of an arbi... |

149 |
Foundations of a functional approach to knowledge representation
- Levesque
- 1984
(Show Context)
Citation Context ...assumption [Min82] as the basis for the negative introspection operator and demonstrates how other forms of AEL may be achieved. Lifschitz [Lif91] brings together work by Reiter [Rei90], and Levesque =-=[Lev84]-=- who discuss query evaluation in databases that are treated as first-order formulas that also contain an epistemic modal operator, and work in epistemic formulas used in knowledge representation for e... |

148 |
A System for Representing and Using Real-World Knowledge
- Fahlman
- 1977
(Show Context)
Citation Context ...ics. They also define well-founded semantics of default theories [BS91] as a particular extension class. Etherington and Reiter [ER83] use default logic to formalize NETL-like inheritance hierarchies =-=[Fah79]-=-. They provide the first attempt at a semantics for such hierarchies; a provably correct inference algorithm for acyclic networks; a guarantee that the acyclic network has extensions; and a provably c... |

148 | On the relation between default and autoepistemic logic - Konolige |

145 | Epistemological problems of artificial intelligence
- McCarthy
- 1977
(Show Context)
Citation Context ...he iff theory that can be assumed true. These two rules of negation are, I believe, the first formalizations of nonmonotonic reasoning. McCarthy first introduced his theory of circumscription in 1977 =-=[McC77]-=-, and Doyle developed his truth maintenance system in 1979 [Doy79]. Reiter gave preliminary material on default reasoning in 1978 [Rei78b]. Nonmonotonic reasoning obtained its impetus in 1980 with the... |

142 | Nonmonotonic Reasoning: Logical Foundations of Commonsense - Brewka - 1991 |

139 | Knowledge representation and reasoning
- Brachman, Levesque
- 2004
(Show Context)
Citation Context ... of the relationships among them, and in finding computational bounds on the various methods. Unfortunately, most of the bounds show that nonmonotonic reasoning is not tractable. As noted by Levesque =-=[Lev86], "..-=-.it remains to be seen how the computational promise of nonmonotonic reasoning can be correctly realized." That there are alternative theories is not, I believe, an impediment, since some of the ... |

136 |
Database Updates Through Abduction
- Kakas, Mancarella
- 1990
(Show Context)
Citation Context ...3 For a summary of complexity results on abductive reasoning see the excellent survey by Cadoli and Schaerf [CS92]. A formal definition of abductive logic programming is given by Kakas and Mancarella =-=[KM90]-=- to be a triple fP; 0; Ig, where P is a normal logic program, 0 is a set of abducible predicates, and I is a set of integrity constraints. A generalized stable model of fP; 0; Ig is defined as the sta... |

135 |
On indefinite databases and the closed world assumption
- Minker
- 1982
(Show Context)
Citation Context ... which the negative introspection operator used is Reiter's CWA. He then extends autoepistemic logic to generalized autoepistemic logic (GAEL), which uses Minker's generalized closed world assumption =-=[Min82]-=- as the basis for the negative introspection operator and demonstrates how other forms of AEL may be achieved. Lifschitz [Lif91] brings together work by Reiter [Rei90], and Levesque [Lev84] who discus... |

135 | The well-founded semantics coincides with the threevalued stable semantics
- Przymusinski
- 1990
(Show Context)
Citation Context ...ies: the theory of stable models developed by Gelfond and Lifschitz [GL88]; the theory of well-founded semantics developed by Van Gelder, Ross and Schlipf [VRS88], and elaborated upon by Przymusinski =-=[Prz89a]-=-; the theory of generalized well-founded semantics by Baral, Lobo and Minker [BLM90c] and the theory of stable classes developed by Baral and Subrahmanian [BS92]. As shown by Baral and Subrahmanian [B... |

130 |
Constructive negation based on the complete database
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- 1988
(Show Context)
Citation Context ...ic Programs In the case of normal logic programs, theories of negation for Horn theories have been developed: the closed world assumption (CWA) [Rei78a], Clark's completion theory [Cla78], and Chan's =-=[Cha88]-=- 16 constructive negation. Whereas Clark, using SLDNF can find answers to negated ground atoms, it does not work for non-ground atoms. Chan's constructive negation solves this problem. In the case of ... |

129 |
Negation as failure using tight derivations for general logic programs
- Gelder
- 1988
(Show Context)
Citation Context ...ion. Gelfond, Przymusinska and Przymusinski [GPP89] relate a propositional form of circumscription to stratified theories. (See Chandra and Harel [CH82], Apt, Blair and Walker [ABW88], and Van Gelder =-=[VG88]-=- for work on stratified theories.) Minker, Lobo and Rajasekar [MLR91] complement the work by Gelfond, Przymusinska and Przymusinski [GPP89] by developing a procedure to compute circumscription in disj... |