The Experts below are selected from a list of 192 Experts worldwide ranked by ideXlab platform
Brian Logan - One of the best experts on this subject based on the ideXlab platform.
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Preference-based belief revision for rule-based agents
Synthese, 2008Co-Authors: Natasha Alechina, Mark Jago, Brian LoganAbstract:Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a Contraction Operation for rule-based reasoners, which we call McAllester Contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for Contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester Contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our Contraction Operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester Contraction can be used to define a revision Operation which is also polynomial time, and prove a representation theorem for the revision Operation.
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DALT - Resource-Bounded belief revision and Contraction
Lecture Notes in Computer Science, 2006Co-Authors: Natasha Alechina, Mark Jago, Brian LoganAbstract:Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, Gardenfors and Makinson (AGM) [1] describes postulates which rational belief revision and Contraction Operations should satisfy. The AGM postulates are usually taken as characterising idealised rational reasoners, and the corresponding belief change Operations are considered unsuitable for implementable agents due to their high computational cost [2]. The main result of this paper is to show that an efficient (linear time) belief Contraction Operation nevertheless satisfies all but one of the AGM postulates for Contraction. This Contraction Operation is defined for an implementable rule-based agent which can be seen as a reasoner in a very weak logic; although the agent's beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of Contraction for our agent.
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Resource-Bounded Belief Revision and Contraction
Lecture Notes in Computer Science, 2006Co-Authors: Natasha Alechina, Mark Jago, Brian LoganAbstract:Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, Gardenfors and Makinson (AGM) [1] describes postulates which rational belief revision and Contraction Operations should satisfy. The AGM postulates are usually taken as characterising idealised rational reasoners, and the corresponding belief change Operations are considered unsuitable for implementable agents due to their high computational cost [2]. The main result of this paper is to show that an efficient (linear time) belief Contraction Operation nevertheless satisfies all but one of the AGM postulates for Contraction. This Contraction Operation is defined for an implementable rule-based agent which can be seen as a reasoner in a very weak logic; although the agent's beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of Contraction for our agent.
Natasha Alechina - One of the best experts on this subject based on the ideXlab platform.
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Preference-based belief revision for rule-based agents
Synthese, 2008Co-Authors: Natasha Alechina, Mark Jago, Brian LoganAbstract:Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a Contraction Operation for rule-based reasoners, which we call McAllester Contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for Contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester Contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our Contraction Operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester Contraction can be used to define a revision Operation which is also polynomial time, and prove a representation theorem for the revision Operation.
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DALT - Resource-Bounded belief revision and Contraction
Lecture Notes in Computer Science, 2006Co-Authors: Natasha Alechina, Mark Jago, Brian LoganAbstract:Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, Gardenfors and Makinson (AGM) [1] describes postulates which rational belief revision and Contraction Operations should satisfy. The AGM postulates are usually taken as characterising idealised rational reasoners, and the corresponding belief change Operations are considered unsuitable for implementable agents due to their high computational cost [2]. The main result of this paper is to show that an efficient (linear time) belief Contraction Operation nevertheless satisfies all but one of the AGM postulates for Contraction. This Contraction Operation is defined for an implementable rule-based agent which can be seen as a reasoner in a very weak logic; although the agent's beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of Contraction for our agent.
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Resource-Bounded Belief Revision and Contraction
Lecture Notes in Computer Science, 2006Co-Authors: Natasha Alechina, Mark Jago, Brian LoganAbstract:Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, Gardenfors and Makinson (AGM) [1] describes postulates which rational belief revision and Contraction Operations should satisfy. The AGM postulates are usually taken as characterising idealised rational reasoners, and the corresponding belief change Operations are considered unsuitable for implementable agents due to their high computational cost [2]. The main result of this paper is to show that an efficient (linear time) belief Contraction Operation nevertheless satisfies all but one of the AGM postulates for Contraction. This Contraction Operation is defined for an implementable rule-based agent which can be seen as a reasoner in a very weak logic; although the agent's beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of Contraction for our agent.
Kinzang Chhogyal - One of the best experts on this subject based on the ideXlab platform.
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probabilistic belief Contraction considerations on epistemic entrenchment probability mixtures and kl divergence
Australasian Joint Conference on Artificial Intelligence, 2015Co-Authors: Abhaya C. Nayak, Kinzang Chhogyal, Abdul SattarAbstract:Probabilistic belief Contraction is an Operation that takes a probability distribution P representing a belief state along with an input sentence a representing some information to be removed from this belief state, and outputs a new probability distribution \(P^-_a\). The contracted belief state \(P^-_a\) can be represented as a mixture of two states: the original belief state P, and the resultant state \(P^*_{\lnot a}\) of revising P by \(\lnot a\). Crucial to this mixture is the mixing factor \(\epsilon \) which determines the proportion of P and \(P^*_{\lnot a}\) that are used in this process in a uniform manner. Ideas from information theory such as the principle of minimum cross-entropy have previously been used to motivate the choice of the probabilistic Contraction Operation. Central to this principle is the Kullback-Leibler (KL) divergence. In an earlier work we had shown that the KL divergence of \(P^-_a\) from P is fully determined by a function whose only argument is the mixing factor \(\epsilon \). In this paper we provide a way of interpreting \(\epsilon \) in terms of a belief ranking mechanism such as epistemic entrenchment that is in consonance with this result. We also provide a much needed justification for why the mixing factor \(\epsilon \) must be used in a uniform fashion by showing that the minimal divergence of \(P^-_{a}\) from P is achieved only when uniformity is respected.
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Australasian Conference on Artificial Intelligence - Probabilistic Belief Contraction: Considerations on Epistemic Entrenchment, Probability Mixtures and KL Divergence
AI 2015: Advances in Artificial Intelligence, 2015Co-Authors: Kinzang Chhogyal, Abhaya C. Nayak, Abdul SattarAbstract:Probabilistic belief Contraction is an Operation that takes a probability distribution P representing a belief state along with an input sentence a representing some information to be removed from this belief state, and outputs a new probability distribution \(P^-_a\). The contracted belief state \(P^-_a\) can be represented as a mixture of two states: the original belief state P, and the resultant state \(P^*_{\lnot a}\) of revising P by \(\lnot a\). Crucial to this mixture is the mixing factor \(\epsilon \) which determines the proportion of P and \(P^*_{\lnot a}\) that are used in this process in a uniform manner. Ideas from information theory such as the principle of minimum cross-entropy have previously been used to motivate the choice of the probabilistic Contraction Operation. Central to this principle is the Kullback-Leibler (KL) divergence. In an earlier work we had shown that the KL divergence of \(P^-_a\) from P is fully determined by a function whose only argument is the mixing factor \(\epsilon \). In this paper we provide a way of interpreting \(\epsilon \) in terms of a belief ranking mechanism such as epistemic entrenchment that is in consonance with this result. We also provide a much needed justification for why the mixing factor \(\epsilon \) must be used in a uniform fashion by showing that the minimal divergence of \(P^-_{a}\) from P is achieved only when uniformity is respected.
Brian D.o. Anderson - One of the best experts on this subject based on the ideXlab platform.
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Closing ranks in rigid multi‐agent formations using edge Contraction
International Journal of Robust and Nonlinear Control, 2010Co-Authors: Baris Fidan, Julien M. Hendrickx, Brian D.o. AndersonAbstract:This paper proposes a systematic approach to solve the closing rank problem for a rigid multi-agent formation, viz. restoring rigidity after loss of an agent. The approach is based on a particular graph Operation, the edge Contraction Operation. It is proven that when an agent is lost in an arbitrary two-dimensional rigid formation, rigidity can always be restored by transferring all links to which this agent was incident on to one of its neighbors, though not in general any arbitrary one of them. From a graph theoretical point of view, this corresponds to Contraction of a certain edge incident to the vertex representing the agent being lost. It is established, for any two-dimensional rigid formation (graph), that there exists at least two such edges that can be contracted to solve the closing ranks problem. Later, it is demonstrated that any potential decentralized algorithm to check if an arbitrary edge is contractible would need to use information on vertices and edges that can be at arbitrarily large distance from the edge considered; and a set of rigid graph theoretical results are established for several general settings, which can be used in selection of the edge to contract in these settings in order to solve the corresponding closing ranks problems. Partial results are also obtained for three- dimensional formations, and it is shown that the two-dimensional results do not generalize as such to higher dimension.
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Edge Contraction based maintenance of rigidity in multi-agent formations during agent loss
2009 17th Mediterranean Conference on Control and Automation, 2009Co-Authors: Baris Fidan, Julien M. Hendrickx, Brian D.o. AndersonAbstract:This paper proposes a systematic approach to the problem of restoring rigidity after loss of an agent, for two-dimensional rigid multi-agent formations based on a particular graph Operation, the edge Contraction Operation. A rigidity maintenance method is proposed, for the cases where an agent is lost in an arbitrary two-dimensional rigid formation, to restore rigidity by transferring all links to which this agent was incident on to one of its neighbors. From a graph theoretical point of view, this corresponds to Contraction of a certain edge incident to the vertex representing the agent being lost.
Mark Jago - One of the best experts on this subject based on the ideXlab platform.
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Preference-based belief revision for rule-based agents
Synthese, 2008Co-Authors: Natasha Alechina, Mark Jago, Brian LoganAbstract:Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a Contraction Operation for rule-based reasoners, which we call McAllester Contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for Contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester Contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our Contraction Operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester Contraction can be used to define a revision Operation which is also polynomial time, and prove a representation theorem for the revision Operation.
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DALT - Resource-Bounded belief revision and Contraction
Lecture Notes in Computer Science, 2006Co-Authors: Natasha Alechina, Mark Jago, Brian LoganAbstract:Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, Gardenfors and Makinson (AGM) [1] describes postulates which rational belief revision and Contraction Operations should satisfy. The AGM postulates are usually taken as characterising idealised rational reasoners, and the corresponding belief change Operations are considered unsuitable for implementable agents due to their high computational cost [2]. The main result of this paper is to show that an efficient (linear time) belief Contraction Operation nevertheless satisfies all but one of the AGM postulates for Contraction. This Contraction Operation is defined for an implementable rule-based agent which can be seen as a reasoner in a very weak logic; although the agent's beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of Contraction for our agent.
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Resource-Bounded Belief Revision and Contraction
Lecture Notes in Computer Science, 2006Co-Authors: Natasha Alechina, Mark Jago, Brian LoganAbstract:Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, Gardenfors and Makinson (AGM) [1] describes postulates which rational belief revision and Contraction Operations should satisfy. The AGM postulates are usually taken as characterising idealised rational reasoners, and the corresponding belief change Operations are considered unsuitable for implementable agents due to their high computational cost [2]. The main result of this paper is to show that an efficient (linear time) belief Contraction Operation nevertheless satisfies all but one of the AGM postulates for Contraction. This Contraction Operation is defined for an implementable rule-based agent which can be seen as a reasoner in a very weak logic; although the agent's beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of Contraction for our agent.