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I.: A propositional typicality logic for extending rational consequence
 Trends in Belief Revision and Argumentation Dynamics, Studies in Logic – Logic and Cognitive Systems
, 2013
"... abstract. We introduce Propositional Typicality Logic (PTL), a logic for reasoning about typicality. We do so by enriching classical propositional logic with a typicality operator of which the intuition is to capture the most typical (or normal) situations in which a given formula holds. The semant ..."
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abstract. We introduce Propositional Typicality Logic (PTL), a logic for reasoning about typicality. We do so by enriching classical propositional logic with a typicality operator of which the intuition is to capture the most typical (or normal) situations in which a given formula holds. The semantics is in terms of ranked models as studied in KLMstyle preferential reasoning. This allows us to show that KLMstyle rational consequence relations can be embedded in our logic. Moreover we show that we can define consequence relations on the language of PTL itself, thereby moving beyond the propositional setting. Building on the existing link between propositional rational consequence and belief revision, we show that the same correspondence holds in the case of rational consequence and belief revision defined on the language of PTL. Finally we also investigate different notions of entailment for PTL and propose two appropriate candidates.
Bisimulation for singleagent plausibility models
"... Abstract. Epistemic plausibility models are Kripke models agents use to reason about the knowledge and beliefs of themselves and each other. Restricting ourselves to the singleagent case, we determine when such models are indistinguishable in the logical language containing conditional belief, i.e ..."
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Abstract. Epistemic plausibility models are Kripke models agents use to reason about the knowledge and beliefs of themselves and each other. Restricting ourselves to the singleagent case, we determine when such models are indistinguishable in the logical language containing conditional belief, i.e., we define a proper notion of bisimulation, and prove that bisimulation corresponds to logical equivalence on imagefinite models. We relate our results to other epistemic notions, such as safe belief and degrees of belief. Our results imply that there are only finitely many nonbisimilar singleagent epistemic plausibility models on a finite set of propositions. This gives decidability for singleagent epistemic plausibility planning. 1
Bisimulation for singleagent plausibility models
, 2013
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Belief Change with Uncertain Action Histories
"... We consider the iterated belief change that occurs following an alternating sequence of actions and observations. At each instant, an agent has beliefs about the actions that have occurred as well as beliefs about the resulting state of the world. We represent such problems by a sequence of ranking ..."
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We consider the iterated belief change that occurs following an alternating sequence of actions and observations. At each instant, an agent has beliefs about the actions that have occurred as well as beliefs about the resulting state of the world. We represent such problems by a sequence of ranking functions, so an agent assigns a quantitative plausibility value to every action and every state at each point in time. The resulting formalism is able to represent fallible belief, erroneous perception, exogenous actions, and failed actions. We illustrate that our framework is a generalization of several existing approaches to belief change, and it appropriately captures the nonelementary interaction between belief update and belief revision. 1.
Towards a Logic of Dilation
"... Abstract. We investigate the notion of dilation of a propositional theory based on neighbourhoods in a generalized approximation space. We take both a semantic and a syntactic approach in order to define a suitable notion of theory dilation in the context of approximate reasoning on the one hand, a ..."
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Abstract. We investigate the notion of dilation of a propositional theory based on neighbourhoods in a generalized approximation space. We take both a semantic and a syntactic approach in order to define a suitable notion of theory dilation in the context of approximate reasoning on the one hand, and a generalized notion of forgetting in propositional logic on the other hand. We place our work in the context of existing theories of approximation spaces and forgetting, and show that neighbourhoods obtained by combining collective and selective dilation provide a suitable semantic framework within which to reason computationally with uncertainty in a classical setting.