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35
Propositional Independence: FormulaVariable Independence and Forgetting
 Journal of Artificial Intelligence Research
, 2003
"... Independence { the study of what is relevant to a given problem of reasoning { has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, ..."
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Cited by 89 (13 self)
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Independence { the study of what is relevant to a given problem of reasoning { has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, while the syntactic form of independence is computationally easy to check, there are cases in which things that intuitively are not relevant are not recognized as such. We also consider the problem of forgetting, i.e., distilling from a knowledge base only the part that is relevant to the set of queries constructed from a subset of the alphabet. While such process is computationally hard, it allows for a simpli  cation of subsequent reasoning, and can thus be viewed as a form of compilation: once the relevant part of a knowledge base has been extracted, all reasoning tasks to be performed can be simpli ed.
Operators and Laws for Combining Preference Relations
, 2002
"... The paper is a theoretical study of a generalization of the lexicographic rule for combining ordering relations. We define the concept of priority operator: a priority operator maps a family of relations to a single relation which represents their lexicographic combination according to a certain pri ..."
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Cited by 40 (0 self)
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The paper is a theoretical study of a generalization of the lexicographic rule for combining ordering relations. We define the concept of priority operator: a priority operator maps a family of relations to a single relation which represents their lexicographic combination according to a certain priority on the family of relations. We present four kinds of results. We show
Sharing Actions and Attributes in Modal Action Logic
 Theoretical Aspects of Computer Software
, 1991
"... Distributed systems may be specified in Structured Modal Action Logic by decomposing them into agents which interact by sharing attributes (memory) as well as actions. In the formalism we describe, specification texts denote theories, and theories denote the set of semantic structures which satisfy ..."
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Cited by 37 (5 self)
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Distributed systems may be specified in Structured Modal Action Logic by decomposing them into agents which interact by sharing attributes (memory) as well as actions. In the formalism we describe, specification texts denote theories, and theories denote the set of semantic structures which satisfy them. The semantic structures are Kripke models, as is usual for modal logic. The "possible worlds" in a Kripke model are the states of the agent, and there is a separate relation on the set of states for each action term. Agents potentially share actions as well as attributes in a way controlled by locality annotations in the specification texts. These become locality axioms in the logical theories the texts denote. These locality axioms provide a refined way of circumscribing the effects of actions. Safety and liveness conditions are expressed (implicitly) by deontic axioms, which impose obligations and deny permissions on actions. We show that "deontic defaults" exist so that the specifi...
Semantics of Inheritance in Logical Object Specifications
 Deductive and ObjectOriented Databases, 2nd Int. Conf. (DOOD'91), 411430, LNCS 566
, 1991
"... Our goal is to integrate the paradigms of objectoriented structuring and of rulebased specifications for databases. In this paper, we consider hierarchical specifications of objects and object types with attributes defined by logical rules, and we explain their local (single object) semantics as w ..."
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Cited by 34 (17 self)
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Our goal is to integrate the paradigms of objectoriented structuring and of rulebased specifications for databases. In this paper, we consider hierarchical specifications of objects and object types with attributes defined by logical rules, and we explain their local (single object) semantics as well as their composite (object society) semantics. In order to allow inheritance with exceptions (overriding) even for rules, the defining formulas are interpreted like defaults of di#erent priorities corresponding to levels in the object type hierarchy. Here, minimal model semantics known from default reasoning in artificial intelligence or from database completions can be utilized, but must be modified to respect objectoriented issues, in particular locality. We prove that intended models exist for object and composite specifications under natural conditions, even if general clauses are used as defaults. 1 Introduction Much has already been said about the relative merits of the objector...
Representing Defaults as Sentences with Reduced Priority
 Proc. Third International Conference on Principles of Knowledge Representation and Reasoning (KR'92
, 1992
"... We distinguish between two ways of thinking about defaults. The first way, in which defaults augment known premises by `strengthening' the underlying logic, is the traditional approach taken by most existing formalisms. In the second way, defaults are represented in the set of premises, but obt ..."
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Cited by 32 (6 self)
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We distinguish between two ways of thinking about defaults. The first way, in which defaults augment known premises by `strengthening' the underlying logic, is the traditional approach taken by most existing formalisms. In the second way, defaults are represented in the set of premises, but obtain their default status by having a reduced priority relative to the known premises. In this paper we: 1. Compare and contrast the approaches. We argue that the second approach makes for simpler representation of defaults and their interactions. 2. Describe a syntax and semantics for the second, less wellknown approach; we introduce the notion of ordered theory presentation (OTP) to represent theories with defaults. 3. Show how ordered theory presentations can represent familiar examples of interacting defaults in an intuitively clear and simple way; we give the Tweety example and the Yale Shooting example. We also show that the OTP framework is particularly well suited to inheritance examples....
A Framework for Iterated Revision
, 2000
"... We consider in this work the problem of iterated belief revision. We propose a family of belief revision operators called revision with memory operators and we give a logical (both syntactical and semantical) characterization of these operators. They obey what we call the principle of strong primacy ..."
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Cited by 24 (6 self)
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We consider in this work the problem of iterated belief revision. We propose a family of belief revision operators called revision with memory operators and we give a logical (both syntactical and semantical) characterization of these operators. They obey what we call the principle of strong primacy of update : when one revises his beliefs by a new evidence, then all possible worlds that satisfy this new evidence become more reliable than those that do not. We show that those operators have a satisfying behaviour concerning the iteration of the revision process. Then we provide four particular operators of this family.
BottomUp Query Evaluation with Partially Ordered Defaults
 Deductive and ObjectOriented Databases, Third Int. Conf., (DOOD'93), number 760 in LNCS
, 1993
"... . We propose a queryevaluation algorithm for database specifications consisting of overridable rules (defaults) and nonoverridable rules (axioms). Both kinds of rules may contain disjunctions. Preferences among the defaults are given by a partial order which corresponds to a subclass relationship ..."
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Cited by 19 (12 self)
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. We propose a queryevaluation algorithm for database specifications consisting of overridable rules (defaults) and nonoverridable rules (axioms). Both kinds of rules may contain disjunctions. Preferences among the defaults are given by a partial order which corresponds to a subclass relationship allowing multiple inheritance. We use a bottomup theorem proving procedure. It is applied to the set of (disjunctively) assumed default instances which essentially can again be computed by bottomup evaluation. Our approach has two main advantages: First, it gives a simple foundation for bottomup evaluation in the presence of defaults; this can be taken as a basis for different optimizations. Second, in contrast to other deduction algorithms, it is able to handle partially ordered defaults with a skeptical / minimal model semantics. 1 Introduction Our goal is to extend deductive databases [14, 10, 20] by overridable rules in order to increase the reusability of such specifications. This cl...
Generalized BottomUp Query Evaluation
 Advances in Database Technology  EDBT'92, 3rd Int. Conf., number 580 in LNCS
, 1992
"... Our goal is to generalize the well known bottomup, setoriented query evaluation for deductive databases in two aspects: First, we consider arbitrary clauses as rules in the database, not only Horn clauses or clauses with stratified negation. This allows to represent disjunctive information, in the ..."
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Cited by 17 (11 self)
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Our goal is to generalize the well known bottomup, setoriented query evaluation for deductive databases in two aspects: First, we consider arbitrary clauses as rules in the database, not only Horn clauses or clauses with stratified negation. This allows to represent disjunctive information, in the database as well as in answers to queries. We utilize NF 2 relations for modelling sets of disjunctive facts and operations of the corresponding relational algebra for computing consequences and answers. Thus our algorithm should be of practical importance for applying database techniques in generalized deductions. Second, we parameterize the implicit database completion which underlies query evaluation. The classical rule for Horn clause databases, which only assumes the negation of facts not implied by the database, is not applicable to disjunctive databases. Moreover, the choice of completion often depends on the intended application. Therefore we allow the specification of arbitrary clauses as defaults, and we extend our algorithm to consider such general defaults. 1
Defaults in Specifications
 in [RE93
, 1993
"... A formalism is motivated and described for representing defaults in specifications. The formalism is called Ordered Theory Presentations. The ability to represent defaults narrows the gap between a customer 's initial requirements and a formal specification, and supports reuse on both a small ..."
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Cited by 16 (2 self)
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A formalism is motivated and described for representing defaults in specifications. The formalism is called Ordered Theory Presentations. The ability to represent defaults narrows the gap between a customer 's initial requirements and a formal specification, and supports reuse on both a small and a large scale. We illustrate the issues throughout with reference to the lift example. We also consider the application of the formalism to specification revision. 1 Introduction Imagine specifying a lift system. There is a lift, with n buttons and n indicator lights inside, and there are doors. The buttons inside the lift are for requesting where the lift goes, and the indicator lights register such requests. There are floors, each with two buttons and indicator lights (one for requesting to go up and one for down). The indicator lights switch on in response to button pressings and off when the lift arrives at a floor; and the lift goes from floor to floor depending on the state of the ligh...
Deduction with Supernormal Defaults
, 1991
"... In this paper we consider supernormal defaults [Poo88] with a strict partial order defining their priorities [Bre91]. We investigate their relation to minimal or preferential entailment and show that the semantics given in [Bre91] has to be modified in order to be equivalent to a preferential model ..."
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Cited by 14 (8 self)
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In this paper we consider supernormal defaults [Poo88] with a strict partial order defining their priorities [Bre91]. We investigate their relation to minimal or preferential entailment and show that the semantics given in [Bre91] has to be modified in order to be equivalent to a preferential model approach. Concering the multiple extension problem, we introduce the careful view as an alternative to the credulous and skeptical one, which is needed to handle the generalized closed world assumption [Min82] within this framework. Given this "declaritive semantics" of such default theories, we will present a deduction algorithm for query answering. Compared to other approaches, the algorithm is quite efficient and general. Especially, it is able to generate disjunctive answers, to support the credulous, skeptical and careful view; and to cut fruitless search paths early. In order to check the applicability of defaults as soon as possible, we introduce the notion of a partial extension. 1 I...