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18
Sensor Data Fusion for ContextAware Computing Using DempsterShafer Theory
, 2003
"... Towards having computers understand human users context information, this dissertation proposes a systematic contextsensing implementation methodology that can easily combine sensor outputs with subjective judgments. The feasibility of this idea is demonstrated via a meetingparticipants focusofa ..."
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Towards having computers understand human users context information, this dissertation proposes a systematic contextsensing implementation methodology that can easily combine sensor outputs with subjective judgments. The feasibility of this idea is demonstrated via a meetingparticipants focusofattention analysis case study with several simulated sensors using prerecorded experimental data and artificially generated sensor outputs distributed over a LAN network. The methodology advocates a topdown approach: (1) For a given application, a context information structure is defined
Shallow Models for NonIterative Modal Logics
"... Modal logics see a wide variety of applications in artificial intelligence, e.g. in reasoning about knowledge, belief, uncertainty, agency, defaults, and relevance. From the perspective of applications, the attractivity of modal logics stems from a combination of expressive power and comparatively l ..."
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Modal logics see a wide variety of applications in artificial intelligence, e.g. in reasoning about knowledge, belief, uncertainty, agency, defaults, and relevance. From the perspective of applications, the attractivity of modal logics stems from a combination of expressive power and comparatively low computational complexity. Compared to the classical treatment of modal logics with relational semantics, the use of modal logics in AI has two characteristic traits: Firstly, a large and growing variety of logics is used, adapted to the concrete situation at hand, and secondly, these logics are often nonnormal. Here, we present a shallow model construction that witnesses PSPACE bounds for a broad class of mostly nonnormal modal logics. Our approach is uniform and generic: we present general criteria that uniformly apply to and are easily checked in large numbers of examples. Thus, we not only reprove known complexity bounds for a wide variety of structurally different logics and obtain previously unknown PSPACEbounds, e.g. for Elgesem’s logic of agency, but also lay the foundations upon which the complexity of newly emerging logics can be determined.
Characterizing and Reasoning about Probabilistic and NonProbabilistic Expectation
, 2007
"... Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the underlying representation of uncertainty. We give sound and compl ..."
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Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the underlying representation of uncertainty. We give sound and complete axiomatizations for the logic in the case that the underlying representation is (a) probability, (b) sets of probability measures, (c) belief functions, and (d) possibility measures. We show that this logic is more expressive than the corresponding logic for reasoning about likelihood in the case of sets of probability measures, but equiexpressive in the case of probability, belief, and possibility. Finally, we show that satisfiability for these logics is NPcomplete, no harder than satisfiability for propositional logic.
USets as probabilistic sets
, 2003
"... Using topos theory I prove that reasoning about probabilities can be formalized with only one simple assumption: given two sets of measures A, B, if B A, then B is less imprecise than A. ..."
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Using topos theory I prove that reasoning about probabilities can be formalized with only one simple assumption: given two sets of measures A, B, if B A, then B is less imprecise than A.
A semantic PSPACE criterion for the next 700 rank 01 modal logics
"... Upper complexity bounds for modal logics are often a complex issue treated with a wide range of frequently adhoc techniques. As domainspecific modal logics (often nonnormal) abound in the literature and new ones appear at regular intervals, it is therefore desirable to develop a generic algorithmi ..."
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Upper complexity bounds for modal logics are often a complex issue treated with a wide range of frequently adhoc techniques. As domainspecific modal logics (often nonnormal) abound in the literature and new ones appear at regular intervals, it is therefore desirable to develop a generic algorithmic framework for deriving such bounds systematically. Here, we present a semanticsbased criterion for modal logics whose axioms do not nest modal operators to be decidable in PSPACE, typically a tight upper bound; the generality of our approach is based on a coalgebraic semantics. This result complements an earlier tableaubased method and extends the class of logics covered by generic techniques. In some cases, e.g. conditional logics, the semantic criterion is established very easily, and in others, notably various logics of quantitative uncertainty, it follows by dissecting offtheshelf results. Thus, our method allows establishing PSPACEcompleteness of a wide range of logics with only moderate effort.
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"... Reasoning with uncertainty and contextdependent languages A topos of presheaves can be seen as an extension of classical set theory, where sets vary over informational states, therefore it is a powerful and expressive mathematical framework. I introduce a suitable topos of presheaves where imprecis ..."
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Reasoning with uncertainty and contextdependent languages A topos of presheaves can be seen as an extension of classical set theory, where sets vary over informational states, therefore it is a powerful and expressive mathematical framework. I introduce a suitable topos of presheaves where imprecise probabilities and imprecise probabilistic reasoning can be represented. In this way we obtain a mathematical definition of impreciseprobabilistic sets. A valid and complete proof system, w.r.t. the intended semantics of imprecise probabilities, is described using the internal language of the topos. Key words: reasoning with uncertainty, topos theory, sheaf theory 1
A Categorical Approach to Data Fusion
"... Abstract Using suitable topoi of presheaves, a categorical definition of measure is given. When the general definition is specialized to particular categories made of sets of possibility, probability or imprecise probability measures, the internal language of the corresponding topos gives a valid a ..."
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Abstract Using suitable topoi of presheaves, a categorical definition of measure is given. When the general definition is specialized to particular categories made of sets of possibility, probability or imprecise probability measures, the internal language of the corresponding topos gives a valid and complete proof system for the corresponding semantics. An application of this method to data fusion in mobile robotics is presented.
A Probabilistic Logic Based on the Acceptability of Gambles ⋆
"... This article presents a probabilistic logic whose sentences can be interpreted as asserting the acceptability of gambles described in terms of an underlying logic. This probabilistic logic has a concrete syntax and a complete inference procedure, and it handles conditional as well as unconditional p ..."
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This article presents a probabilistic logic whose sentences can be interpreted as asserting the acceptability of gambles described in terms of an underlying logic. This probabilistic logic has a concrete syntax and a complete inference procedure, and it handles conditional as well as unconditional probabilities. It synthesizes Nilsson’s probabilistic logic and Frisch and Haddawy’s anytime inference procedure with Wilson and Moral’s logic of gambles. Two distinct semantics can be used for our probabilistic logic: (1) the measuretheoretic semantics used by the prior logics already mentioned and also by the more expressive logic of Fagin, Halpern, and Meggido and (2) a behavioral semantics. Under the measuretheoretic semantics, sentences of our probabilistic logic are interpreted as assertions about a probability distribution over interpretations of the underlying logic. Under the behavioral semantics, these sentences are interpreted only as asserting the acceptability of gambles, and this suggests different directions for generalization. Key words: