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System Z: a natural ordering of defaults with tractable applications to default reasoning
, 1990
"... Recent progress towards unifying the probabilistic and preferential models semantics for nonmonotonic reasoning has led to a remarkable observation: Any consistent system of default rules imposes an unambiguous and natural ordering on these rules which, to emphasize its simple and basic character, ..."
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Cited by 165 (0 self)
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Recent progress towards unifying the probabilistic and preferential models semantics for nonmonotonic reasoning has led to a remarkable observation: Any consistent system of default rules imposes an unambiguous and natural ordering on these rules which, to emphasize its simple and basic character, we term "Zordering. " This ordering can be used with various levels of refinement, to prioritize conflicting arguments, to rank the degree of abnormality of states of the world, and to define plausible consequence relationships. This paper defines the Zordering, briefly mentions its semantical origins, and iUustrates two simple entailment relationships induced by the ordering. Two extensions are then described, maximumentropy and conditional entailment, which trade in computational simplicity for semantic refinements. 1. Description We begin with a set of rules R = {r: %. ~ 6,} where % and [~r are propositional formulas over a finite alphabet of literals, ando denotes a new connective to be given default interpretations later on. A truth valuation of the fiterals in the language will be called a model. A model M is said to verify a rule ot ~ ifM ~ot ^ [3(i.e., o~and ~ are both true in M), and to falsify ot ~ ~ifM ~A ~ 13. Given a set R of such rules, we first define the relation of toleration.
Answer Set Programming and Plan Generation
 ARTIFICIAL INTELLIGENCE
, 2002
"... The idea of answer set programming is to represent a given computational problem by a logic program whose answer sets correspond to solutions, and then use an answer set solver, such as smodels or dlv, to find an answer set for this program. Applications of this method to planning are related to the ..."
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Cited by 136 (5 self)
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The idea of answer set programming is to represent a given computational problem by a logic program whose answer sets correspond to solutions, and then use an answer set solver, such as smodels or dlv, to find an answer set for this program. Applications of this method to planning are related to the line of research on the frame problem that started with the invention of formal nonmonotonic reasoning in 1980.
Answer Sets in General Nonmonotonic Reasoning (Preliminary Report)
, 1992
"... Languages of declarative logic programming differ from other modal nonmonotonic formalisms by lack of syntactic uniformity. For instance, negation as failure can be used in the body of a rule, but not in the head; in disjunctive programs, disjunction is used in the head of a rule, but not in the bod ..."
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Cited by 102 (9 self)
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Languages of declarative logic programming differ from other modal nonmonotonic formalisms by lack of syntactic uniformity. For instance, negation as failure can be used in the body of a rule, but not in the head; in disjunctive programs, disjunction is used in the head of a rule, but not in the body; in extended programs, negation as failure can be used on top of classical negation, but not the other way around. We argue that this lack of uniformity should not be viewed as a distinguishing feature of logic programming in general. As a starting point, we take a translation from the language of disjunctive programs with negation as failure and classical negation into MBNFthe logic of minimal belief and negation as failure. A class of theories based on this logic is defined, theories with protected literals, which is syntactically uniform and contains the translations of all programs. We show that theories with protected literals have a semantics similar to the answer set semantics us...
Minimal Belief and Negation as Failure
 Artificial Intelligence
, 1994
"... Fangzhen Lin and Yoav Shoham defined a propositional nonmonotonic logic which uses two independent modal operators. One of them represents minimal knowledge, the other is related to the ideas of justification (as understood in default logic) and of negation as failure. We describe a simplified versi ..."
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Cited by 72 (5 self)
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Fangzhen Lin and Yoav Shoham defined a propositional nonmonotonic logic which uses two independent modal operators. One of them represents minimal knowledge, the other is related to the ideas of justification (as understood in default logic) and of negation as failure. We describe a simplified version of that system, show how quantifiers can be included in it, and study its relation to circumscription and default logic, to logic programming, and to the theory of epistemic queries developed by Hector Levesque and Ray Reiter. 1 Introduction Lin and Shoham [16] defined a propositional nonmonotonic logic which uses two independent modal operators. One of them represents minimal knowledge, 1 the other is related to the ideas of justification (as understood in default logic) and of negation as failure. In this paper, we consider a special case of that system, in which Kripke structures of a particularly simple kind are used, and show how quantifiers can be included in it. This extension i...
Restricted Monotonicity
 In Proc. AAAI93
, 1993
"... A knowledge representation problem can be sometimes viewed as an element of a family of problems, with parameters corresponding to possible assumptions about the domain under consideration. When additional assumptions are made, the class of domains that are being described becomes smaller, so that t ..."
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Cited by 26 (4 self)
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A knowledge representation problem can be sometimes viewed as an element of a family of problems, with parameters corresponding to possible assumptions about the domain under consideration. When additional assumptions are made, the class of domains that are being described becomes smaller, so that the class of conclusions that are true in all the domains becomes larger. As a result, a satisfactory solution to a parametric knowledge representation problem on the basis of some nonmonotonic formalism can be expected to have a certain formal property, that we call restricted monotonicity. We argue that it is important to recognize parametric knowledge representation problems and to verify restricted monotonicity for their proposed solutions. Introduction This paper is about the methodology of representing knowledge in nonmonotonic formalisms. A knowledge representation problem can be sometimes viewed as an element of a family of problems, with parameters corresponding to possible assumpt...
Causal reconstruction
 Massachusetts Institute of Technology, AI Lab, memo
, 1993
"... Causal reconstruction is the task of reading a written causal description of a physical behavior, forming an internal model of the described activity, and demonstrating comprehension through question answering. This task is difficult because written descriptions often do not specify exactly how ..."
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Cited by 16 (0 self)
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Causal reconstruction is the task of reading a written causal description of a physical behavior, forming an internal model of the described activity, and demonstrating comprehension through question answering. This task is difficult because written descriptions often do not specify exactly how referenced events fit together. This article (1) characterizes the causal reconstruction problem, (2) presents a representation called transition space, which portrays events in terms of "transitions," or collections of changes expressible in everydaylanguage, and (3) describes a program called PATHFINDER, which uses the transition space representation to perform causal reconstruction on simplified English descriptions of physical activity.PATHFINDER works byidentifying partial matches between the representations of events and using these matches to form causal chains, fill causal gaps, and merge overlapping accounts of activity. By applying transformations to events prior to matching, PATHFINDER is also able to handle a range of discontinuities arising from a writer's use of analogy or abstraction.
Systematic Comparison of Approaches to Ramification Using Restricted Minimization of Change
, 1995
"... Most approaches to the ramification problem are based on the principle of minimization of change. It turns out, however, that this principle can not be applied uniformly, and many modern approaches use a classification of the fluents whereby change is only minimized in some of the fluents. The prese ..."
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Cited by 13 (5 self)
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Most approaches to the ramification problem are based on the principle of minimization of change. It turns out, however, that this principle can not be applied uniformly, and many modern approaches use a classification of the fluents whereby change is only minimized in some of the fluents. The present article reviews these approaches and their underlying motivations. It also presents a unified formal framework whereby it is possible to compare, between different approaches, the set of selected models in each of them as well as their range of correct applicability. Finally it discusses the applicability of the KatsunoMendelzon postulates for these approaches.
Knowledge Representation and Classical Logic
, 2007
"... Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspe ..."
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Cited by 11 (4 self)
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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspective of knowledge representation, their formal languages were not sufficiently expressive. On the other hand, most logicians were not concerned about the possibility of automated reasoning; from the perspective of knowledge representation, they were often too generous in the choice of syntactic constructs. In spite of these differences, classical mathematical logic has exerted significant influence on knowledge representation research, and it is appropriate to begin this handbook with a discussion of the relationship between these fields. The language of classical logic that is most widely used in the theory of knowledge representation is the language of firstorder (predicate) formulas. These are the formulas that John McCarthy proposed to use for representing declarative knowledge in his advice taker paper [176], and Alan Robinson proposed to prove automatically using resolution [236]. Propositional logic is, of course, the most important subset of firstorder logic; recent