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## Nonmonotonic Reasoning, Preferential Models and Cumulative Logics (1990)

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Citations: | 614 - 14 self |

### Citations

8753 |
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
- Pearl
- 1988
(Show Context)
Citation Context ... Pearl and H. Geffner [34] have built upon E. Adams’ logics, our system P, and his motivation in an effort to provide a system for nonmonotonic reasoning. For a gentle introduction, see chapter 10 of =-=[33]-=-. The semantics proposed here are not probabilistic. Probabilistic semantics that are equivalent with a restricted family of models (ranked models) will be described elsewhere. The preferential models... |

1731 | An axiomatic basis for computer programming
- Hoare
- 1969
(Show Context)
Citation Context ...ogic. The next two rules express the influence of the underlying logic, defined by the universe U, on the notion of plausible consequence. Their role is similar to that of the rules of consequence of =-=[16]-=-. |= α ↔ β , α ∼ γ β ∼ γ (Left Logical Equivalence) (2) Left Logical Equivalence expresses the requirement that logically equivalent formulas have exactly the same consequences and corresponds to rule... |

1634 |
A logic for default reasoning
- Reiter
- 1980
(Show Context)
Citation Context .... Many researchers have proposed systems that perform such nonmonotonic inferences. The best known are probably: negation as failure [5], circumscription [29], the modal system of [30], default logic =-=[35]-=-, autoepistemic logic [31] and inheritance systems [45]. Each of those systems is worth studying by itself, but a general framework in which those many examples could be compared and classified is mis... |

1065 |
Negation as Failure
- CLARK
- 1978
(Show Context)
Citation Context ... systems will have to do the same kind of (nonmonotonic) inferences. Many researchers have proposed systems that perform such nonmonotonic inferences. The best known are probably: negation as failure =-=[5]-=-, circumscription [29], the modal system of [30], default logic [35], autoepistemic logic [31] and inheritance systems [45]. Each of those systems is worth studying by itself, but a general framework ... |

954 | Circumscription — a form of non-monotonic reasoning - McCarthy - 1980 |

338 | Circumscription
- Lifschitz
- 1994
(Show Context)
Citation Context ...o the limit assumption of Stalnaker [40] and Lewis [24], but it is defined in a more general context. Smoothness is the property called, contrary to mathematical usage, well-foundedness in [8] and in =-=[26]-=-. We shall now describe how a cumulative model defines a consequence relation. Definition 8 Suppose a cumulative model W = 〈S, l, ≺〉 is given. The consequence relation defined by W will be denoted by ... |

269 | What does a conditional knowledge base entail
- Lehmann
- 1989
(Show Context)
Citation Context ...c system of nonmonotonic reasoning. Important steps towards such a system, taken after obtaining the results reported here but before the final redaction of this paper, are reported in [19], [22] and =-=[20]-=-. At this point it could be useful to state the philosophy of this paper concerning the relative importance of proof-theory and semantics. We consider, in this paper, the axiomatic systems as the main... |

262 |
The Logic of Conditionals
- Adams
- 1975
(Show Context)
Citation Context ...ter concerns a extended language and it is not clear that a proof in the extended language may be translated in the restricted one. This very fragment had been considered by E. Adams in [2] (see also =-=[1]-=- for an earlier version and motivation). E. Adams’ purpose was to propose probabilistic semantics for indicative conditionals and not the study of nonmonotonic logics. Recently J. Pearl and H. Geffner... |

260 |
Nonmonotonic logic I
- McDermott, Doyle
- 1980
(Show Context)
Citation Context ...onotonic) inferences. Many researchers have proposed systems that perform such nonmonotonic inferences. The best known are probably: negation as failure [5], circumscription [29], the modal system of =-=[30]-=-, default logic [35], autoepistemic logic [31] and inheritance systems [45]. Each of those systems is worth studying by itself, but a general framework in which those many examples could be compared a... |

218 | Defeasible logic
- Nute
- 1994
(Show Context)
Citation Context ...subsection. This work stems from a very different motivation than the vast body of work concerned with conditional logic and its semantics, (see in particular [40],[24] and [23]) which is surveyed in =-=[32]-=-. Two main differences must be pointed at. The first difference is that conditional logic considers a binary intensional connective that can be embedded inside other connectives and even itself, where... |

202 |
Theoretical foundations for nonmonotonic reasoning in expert systems. In: K.R. Apt (Ed.) Logics and models of Concurrent Systems
- Gabbay
- 1985
(Show Context)
Citation Context ...notonic consequence relations, defined in the style of Gentzen [13]. Both proof-theoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in =-=[10]-=-, while the latter has been advocated by Y. Shoham in [38]. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interes... |

197 | Reasoning about Change - Shoham - 1988 |

192 |
The Mathematics of Inheritance Systems
- Touretzky
- 1986
(Show Context)
Citation Context ...uch nonmonotonic inferences. The best known are probably: negation as failure [5], circumscription [29], the modal system of [30], default logic [35], autoepistemic logic [31] and inheritance systems =-=[45]-=-. Each of those systems is worth studying by itself, but a general framework in which those many examples could be compared and classified is missing. We provide here a first attempt at such a general... |

128 |
General theory of cumulative inference
- Makinson
- 1989
(Show Context)
Citation Context ...mpactness come to mind, and the relation between Tarski’s infinitistic approach and Gentzen’s finitistic approach is much less clear. We develop here a finitistic approach in the style of Gentzen. In =-=[28]-=-, D. Makinson developed, 2in parallel with and independently from our effort, an infinitistic view of nonmonotonic consequence relations. Later efforts in this direction, by M. Freund and D. Lehmann ... |

106 | Simple consequence relations
- Avron
- 1991
(Show Context)
Citation Context ...] (see [44] for an English translation) and G. Gentzen [12] (see [13] for an English translation and related papers). For an up-to-date view on monotonic consequence relations, the reader may consult =-=[3]-=-. Tarski studied the consequences of arbitrary sets of formulas whereas Gentzen restricted himself to finite such sets. In the presence of compactness, the difference between the two approaches is sma... |

104 |
A Semantical Approach to Nonmonotonic Logics
- Shoham
- 1987
(Show Context)
Citation Context ...tzen [13]. Both proof-theoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in =-=[38]-=-. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been ... |

97 | Counterfactuals - Ginsberg - 1986 |

79 |
Possible-world semantics for autoepistemic logic
- Moore
- 1984
(Show Context)
Citation Context ...oposed systems that perform such nonmonotonic inferences. The best known are probably: negation as failure [5], circumscription [29], the modal system of [30], default logic [35], autoepistemic logic =-=[31]-=- and inheritance systems [45]. Each of those systems is worth studying by itself, but a general framework in which those many examples could be compared and classified is missing. We provide here a fi... |

73 | An approach to default reasoning based on a First-order conditional logic: Revised report
- Delgrande
- 1988
(Show Context)
Citation Context ...epistemic logic in [15]. One of the conclusions of this paper will be that none of the nonmonotonic systems defined so far in the literature, except those based on conditional logic described in [6], =-=[7]-=- and [34], may represent all nonmonotonic inference systems that may be defined by preferential models. The framework of preferential models, therefore, has an expressive power that cannot be captured... |

67 | Towards a theory of knowledge and ignorance: Preliminary report
- Halpern, Moses
- 1985
(Show Context)
Citation Context ...idea that nonmonotonic deduction should be modeled by some normality relation between worlds is very natural and may be traced back to J. McCarthy. It appears also in relation with epistemic logic in =-=[15]-=-. One of the conclusions of this paper will be that none of the nonmonotonic systems defined so far in the literature, except those based on conditional logic described in [6], [7] and [34], may repre... |

48 | Logics for conditionals - Veltman - 1985 |

47 |
Quick completeness proofs for some logics of conditionals
- Burgess
- 1981
(Show Context)
Citation Context ... of Rational Monotonicity (see equation (25)). One of the logical systems, P, studied in this paper turns out to be the flat (i.e. non-nested) fragment of a conditional logic studied by J. Burgess in =-=[4]-=- and by F. Veltman in [47]. Because of their richer language, the semantics proposed in those papers are more complex than ours: a ternary relation of accessibility between worlds is used in place of ... |

34 |
On the adequacy of predicate circumscription for closed-world reasoning
- Etherington, Mercer, et al.
- 1985
(Show Context)
Citation Context ...t is akin to the limit assumption of Stalnaker [40] and Lewis [24], but it is defined in a more general context. Smoothness is the property called, contrary to mathematical usage, well-foundedness in =-=[8]-=- and in [26]. We shall now describe how a cumulative model defines a consequence relation. Definition 8 Suppose a cumulative model W = 〈S, l, ≺〉 is given. The consequence relation defined by W will be... |

30 | Fundamentale Begriffe der Methodologie der deduktiven Wissesnchaften. Monatshefte für Mathematik und Physik - Tarski - 1930 |

20 | What's Wrong with Non-Monotonic Logic
- Israel
- 1980
(Show Context)
Citation Context ...on their consequence relations. This is a bold step to take since some of the nonmonotonic systems mentioned above were not meant to define a consequence relation, as was soon noticed by D. Israel in =-=[17]-=-. D. Gabbay asked the question: what are the minimal conditions a consequence relation should satisfy to represent a bona fide nonmonotonic logic? He proposed three: reflexivity (see equation 1 in sec... |

19 |
Intensional logics without iterative axioms
- Lewis
- 1975
(Show Context)
Citation Context ...nmonotonic consequence as a meta-notion, but allowing basic propositions on a rich language, we strike at the right language. It allows a new approach of questions about computational complexity (see =-=[25]-=- for some general decidability results), but this is left for future work. 2.2 Pragmatics We shall now briefly sketch why we think that the study of nonmonotonic consequence relations will be a benefi... |

17 |
Über einige fundamentale Begriffe der Metamathematik
- Tarski
- 1930
(Show Context)
Citation Context ...notonic reasoning may be found in [36]. 1.2 Nonmonotonic consequence relations The idea that the best framework to study the deduction process is that of consequence relations dates back to A. Tarski =-=[42]-=-, [41] and [43] (see [44] for an English translation) and G. Gentzen [12] (see [13] for an English translation and related papers). For an up-to-date view on monotonic consequence relations, the reade... |

16 |
The Collected Papers of Gerhard Gentzen, edited by
- Gentzen
- 1969
(Show Context)
Citation Context ...ould help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen =-=[13]-=-. Both proof-theoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in [38]. Fiv... |

15 |
Completeness and axiomatizability
- Scott
- 1974
(Show Context)
Citation Context ...t all such sets, though, seem to be worthy of that name and our use of the term for any such set is running against a fairly well-established terminology. The term conditional assertion is taken from =-=[37]-=- (p. 417). We hope that, by considering nonmonotonic consequence as a meta-notion, but allowing basic propositions on a rich language, we strike at the right language. It allows a new approach of ques... |

14 |
A first-order logic for prototypical properties
- Delgrande
- 1987
(Show Context)
Citation Context ...with epistemic logic in [15]. One of the conclusions of this paper will be that none of the nonmonotonic systems defined so far in the literature, except those based on conditional logic described in =-=[6]-=-, [7] and [34], may represent all nonmonotonic inference systems that may be defined by preferential models. The framework of preferential models, therefore, has an expressive power that cannot be cap... |

12 |
M models and cumulative logics
- Kraus, Lehmann, et al.
(Show Context)
Citation Context ...o study those systems and in particular settle questions of interderivability and find efficient decision procedures. Preliminary versions of the material contained in this paper appeared in [21] and =-=[18]-=-. 1.3 Conditional logic In this subsection, the relation between our work and conditional logic will be briefly surveyed. Since the link, we claim, is mainly at the level of the formal systems and not... |

9 |
Canonical extensions to the infinite case of finitary nonmonotonic inference operations
- Freund, Lehmann, et al.
- 1989
(Show Context)
Citation Context ..., D. Makinson developed, 2in parallel with and independently from our effort, an infinitistic view of nonmonotonic consequence relations. Later efforts in this direction, by M. Freund and D. Lehmann =-=[9]-=-, have benefited from the results presented here. D. Gabbay [10] was probably the first to suggest to focus the study of nonmonotonic logics on their consequence relations. This is a bold step to take... |

8 |
über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen
- Gentzen
- 1932
(Show Context)
Citation Context ...tions The idea that the best framework to study the deduction process is that of consequence relations dates back to A. Tarski [42], [41] and [43] (see [44] for an English translation) and G. Gentzen =-=[12]-=- (see [13] for an English translation and related papers). For an up-to-date view on monotonic consequence relations, the reader may consult [3]. Tarski studied the consequences of arbitrary sets of f... |

7 |
Completeness and decidability of three logics of counterfactual conditionals
- Lewis
- 1971
(Show Context)
Citation Context ...logic may easily skip this subsection. This work stems from a very different motivation than the vast body of work concerned with conditional logic and its semantics, (see in particular [40],[24] and =-=[23]-=-) which is surveyed in [32]. Two main differences must be pointed at. The first difference is that conditional logic considers a binary intensional connective that can be embedded inside other connect... |

7 | papers from 1923 to 1938 - Logic, Metamathematics - 1983 |

6 |
Rational logics and their models; A study in cumulative logics
- Lehmann, Magidor
- 1988
(Show Context)
Citation Context ...y specific system of nonmonotonic reasoning. Important steps towards such a system, taken after obtaining the results reported here but before the final redaction of this paper, are reported in [19], =-=[22]-=- and [20]. At this point it could be useful to state the philosophy of this paper concerning the relative importance of proof-theory and semantics. We consider, in this paper, the axiomatic systems as... |

5 | einige fundamentale Begriffe der Metamathematik, Compte Rendus de la Société des Sciences et des Lettres de Varsovie - 1930a, ¨Uber - 1983 |

4 | A Theory of Conditionals, volume 2 - Stalnaker - 1968 |

4 |
Grundzüge des Systemenkalküls, Erster Teil
- Tarski
- 1935
(Show Context)
Citation Context ...ng may be found in [36]. 1.2 Nonmonotonic consequence relations The idea that the best framework to study the deduction process is that of consequence relations dates back to A. Tarski [42], [41] and =-=[43]-=- (see [44] for an English translation) and G. Gentzen [12] (see [13] for an English translation and related papers). For an up-to-date view on monotonic consequence relations, the reader may consult [... |

4 | Foundations of Conditional Logic - Benthem - 1984 |

4 |
Papers from
- Logic, Metamathematics
- 1923
(Show Context)
Citation Context ...found in [36]. 1.2 Nonmonotonic consequence relations The idea that the best framework to study the deduction process is that of consequence relations dates back to A. Tarski [42], [41] and [43] (see =-=[44]-=- for an English translation) and G. Gentzen [12] (see [13] for an English translation and related papers). For an up-to-date view on monotonic consequence relations, the reader may consult [3]. Tarski... |

2 |
H.: Probabilistic semantics for a subset of default reasoning
- Pearl, Geffner
- 1988
(Show Context)
Citation Context ...c logic in [15]. One of the conclusions of this paper will be that none of the nonmonotonic systems defined so far in the literature, except those based on conditional logic described in [6], [7] and =-=[34]-=-, may represent all nonmonotonic inference systems that may be defined by preferential models. The framework of preferential models, therefore, has an expressive power that cannot be captured by negat... |

2 |
Nonmonotonic Reasoning, volume 2
- Reiter
- 1987
(Show Context)
Citation Context ...concentrating on properties that are or should be enjoyed by at least important families of nonmonotonic reasoning systems. An up-to-date survey of the field of nonmonotonic reasoning may be found in =-=[36]-=-. 1.2 Nonmonotonic consequence relations The idea that the best framework to study the deduction process is that of consequence relations dates back to A. Tarski [42], [41] and [43] (see [44] for an E... |

1 | die existenz unabhangiger axiomensysteme zu unendlichen satzsystemen - Uber - 1932 |

1 |
Non monotonic logics: Models and proofs
- Lehmann, Kraus
- 1988
(Show Context)
Citation Context ...al tool to study those systems and in particular settle questions of interderivability and find efficient decision procedures. Preliminary versions of the material contained in this paper appeared in =-=[21]-=- and [18]. 1.3 Conditional logic In this subsection, the relation between our work and conditional logic will be briefly surveyed. Since the link, we claim, is mainly at the level of the formal system... |

1 |
A Theory of Conditionals, volume 2 of American Philosophical Quarterly Monograph Series
- Stalnaker
- 1968
(Show Context)
Citation Context ...n conditional logic may easily skip this subsection. This work stems from a very different motivation than the vast body of work concerned with conditional logic and its semantics, (see in particular =-=[40]-=-,[24] and [23]) which is surveyed in [32]. Two main differences must be pointed at. The first difference is that conditional logic considers a binary intensional connective that can be embedded inside... |