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18
The algebra of multiagent dynamic belief revision
 Electronic Notes in Theoretical Computer Science
, 2006
"... We refine our algebraic axiomatization in [8, 9] of epistemic actions and epistemic update (notions defined in [5, 6] using a relational, Kripkestyle semantics), to incorporate a mechanism for dynamic belief revision in a multiagent setting. Our approach has a number of novel features, when compar ..."
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Cited by 8 (4 self)
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We refine our algebraic axiomatization in [8, 9] of epistemic actions and epistemic update (notions defined in [5, 6] using a relational, Kripkestyle semantics), to incorporate a mechanism for dynamic belief revision in a multiagent setting. Our approach has a number of novel features, when compared with traditional belief revision systems such as AGM [2]. Firstly: while traditional belief revision was
Positive logic with adjoint modalities: Proof theory, semantics and reasoning about information. Review of Symbolic Logic (to appear
, 2010
"... We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T ..."
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Cited by 5 (3 self)
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We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4 and S5, such logics are useful, as shown in previous work by Baltag, Coecke and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For such a logic we present an algebraic semantics, using lattices with agentindexed families of adjoint pairs of operators, and a cutfree sequent calculus. The calculus exploits operators on sequents, in the style of “nested ” or “treesequent ” calculi; cutadmissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario.
High Level Quantum Structures in Linguistics and Multi Agent Systems
"... We present two applications to AI of recently introduced high level quantum structures. These structures are the categorical quantum logic of (Abramsky & Coecke 2004) and the quantale quantum logic of (Coecke, Moore, & Stubbe 2001). Firstly, we show how the diagrammatic toolkit of categoric ..."
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Cited by 2 (2 self)
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We present two applications to AI of recently introduced high level quantum structures. These structures are the categorical quantum logic of (Abramsky & Coecke 2004) and the quantale quantum logic of (Coecke, Moore, & Stubbe 2001). Firstly, we show how the diagrammatic toolkit of categorical quantum logic, when restricted to its pregroup fragment (Lambek 1999; 2001), simplifies analysis of sentence structure of different languages. Moreover, the quantitative values that arise in these diagrams signify different degrees of complexity of sentences, which turn out to vary for different languages. Secondly, we show how expanding the quantale quantum logic with epistemic modalities provides a powerful system to reason about information update in multiagent systems. Finally, we indicate how the above two applications to nonquantum domains can themselves be ‘requantized’, providing applications to quantum informatics of distributed systems.
Reasoning about Dynamic Epistemic Logic
"... We present an algebra and sequent calculus to reason about dynamic epistemic logic, a logic for information update in multiagent systems. We contribute to it by equipping it with a logical account of resources, a semiautomatic way of reasoning through the algebra and sequent calculus, and finally ..."
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Cited by 2 (0 self)
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We present an algebra and sequent calculus to reason about dynamic epistemic logic, a logic for information update in multiagent systems. We contribute to it by equipping it with a logical account of resources, a semiautomatic way of reasoning through the algebra and sequent calculus, and finally by generalizing it to nonboolean settings. Dynamic Epistemic Logic (DEL) is a PDLstyle logic [14] to reason about epistemic actions and updates in a multiagent system. It focuses in particular on epistemic programs, i.e. programs that update the information state of agents, and it has applications to modelling and reasoning about informationflow and information exchange between agents. This is a major problem in several fields such as secure communication where one has to deal with the privacy and authentication of communication protocols, software reliability for concurrent programs, Artificial Intelligence where agents are to be provided with reliable tools to reason about their environment and each other’s knowledge, and ecommerce where agents need to have knowledge acquisition strategies over complex networks. The standard approach to information flow in a multiagent system has been presented in [8] but it does not present a formal description of epistemic programs and their updates. The first attempts to
On the complexity of Dynamic Epistemic Logic
, 2012
"... Although Dynamic Epistemic Logic (DEL) is an influential logical framework for representing and reasoning about information change, little is known about the computational complexity of its associated decision problems. In fact, we only know that for public announcement logic, a fragment of DEL, th ..."
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Although Dynamic Epistemic Logic (DEL) is an influential logical framework for representing and reasoning about information change, little is known about the computational complexity of its associated decision problems. In fact, we only know that for public announcement logic, a fragment of DEL, the satisfiability problem and the modelchecking problem are respectively PSPACEcomplete and in P. We contribute to fill this gap by proving that for the DEL language with event models, the modelchecking problem is, surprisingly, PSPACEcomplete. Also, we prove that the satisfiability problem is NEXPTIMEcomplete. In doing so, we provide a sound and complete tableau method deciding the satisfiability problem.
Coalgebraic epistemic update without change of model
, 2007
"... We present a coalgebraic semantics for reasoning about information update in multiagent systems. The novelty is that we have one structure for both states and actions and thus our models do not involve the ”changeofmodel” phenomena that arise when using Kripke models. However, we prove that the u ..."
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We present a coalgebraic semantics for reasoning about information update in multiagent systems. The novelty is that we have one structure for both states and actions and thus our models do not involve the ”changeofmodel” phenomena that arise when using Kripke models. However, we prove that the usual models can be constructed from ours by categorical adjunction. The generality and abstraction of our coalgebraic model turns out to be extremely useful in proving preservation properties of update. In particular, we prove that positive knowledge is preserved and acquired as a result of epistemic update. We also prove common and nested knowledge properties of epistemic updates induced by specific epistemic actions such as public and private announcements, lying, and in particular unsafe actions of security protocols. Our model directly gives rise to a coalgebraic logic with both dynamic and epistemic modalities. We prove a soundness and completeness result for this logic, and illustrate the applicability of the logic by deriving knowledge properties of a simple security protocol.
A RunsandSystems Semantics for Logics of Announcements ∗
"... Logics of announcements are logics of knowledge to reason about agents that communicate by broadcasting interpreted messages. These logics are typically given a semantics in terms of updatable Kripke structures, which tend to be abstract. We revisit the semantics of logics of announcements and devel ..."
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Logics of announcements are logics of knowledge to reason about agents that communicate by broadcasting interpreted messages. These logics are typically given a semantics in terms of updatable Kripke structures, which tend to be abstract. We revisit the semantics of logics of announcements and develop a concrete semantics using runs and systems. The advantage is that we can devise models that capture scenarios without having to express properties of those scenarios within the logic itself. In this concrete setting, we study honesty as well as belief in the presence of announcements that are not broadcast to all agents in a system. 1
Learning in a changing world, an algebraic approach
"... We develop an algebraic modal logic that combines epistemic and dynamic modalities with a view to modelling information acquisition (learning) by automated agents in a changing world. Unlike most treatments of dynamic epistemic logic, we have transitions that “change the state ” of the underlying s ..."
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We develop an algebraic modal logic that combines epistemic and dynamic modalities with a view to modelling information acquisition (learning) by automated agents in a changing world. Unlike most treatments of dynamic epistemic logic, we have transitions that “change the state ” of the underlying system and not just the state of knowledge of the agents. The key novel feature that emerges is the need to have a way of “inverting transitions” and distinguishing between transitions that “really happen” and transitions that are possible. Our approach is algebraic, rather than being based on a Kripkestyle semantics. The semantics are given in terms of quantales. We study a class of quantales with the appropriate inverse operations and prove properties of the setting. We illustrate the ideas with toy robotnavigation problems. These illustrate how an agent learns information by taking actions.
4. Cut elimination argument 5. Consequences (completeness, decidability)
, 2007
"... 6. Conclusion and future plans ..."
High Level Quantum Structures in Linguistics and Multi Agent Systems
"... We present two applications to AI of recently introduced high level quantum structures. These structures are the categorical quantum logic of (Abramsky & Coecke 2004) and the quantale quantum logic of (Coecke, Moore, & Stubbe 2001). Firstly, we show how the diagrammatic toolkit of categoric ..."
Abstract
 Add to MetaCart
We present two applications to AI of recently introduced high level quantum structures. These structures are the categorical quantum logic of (Abramsky & Coecke 2004) and the quantale quantum logic of (Coecke, Moore, & Stubbe 2001). Firstly, we show how the diagrammatic toolkit of categorical quantum logic, when restricted to its pregroup fragment (Lambek 1999; 2001), simplifies analysis of sentence structure of different languages. Moreover, the quantitative values that arise in these diagrams signify different degrees of complexity of sentences, which turn out to vary for different languages. Secondly, we show how expanding the quantale quantum logic with epistemic modalities provides a powerful system to reason about information update in multiagent systems. Finally, we indicate how the above two applications to nonquantum domains can themselves be ‘requantized’, providing applications to quantum informatics of distributed systems.