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It is a landmark theorem of McKinsey and Tarski that if we interpret modal diamond as closure (and hence modal box as interior), then S4 is the logic of any dense-in-itself metrizable space. The McKinsey-Tarski Theorem relies heavily on a metric that gives rise to the topology. We give a new and ...
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For a topological space X, let L(X) be the modal logic of X where \Box is interpreted as interior (and hence \Diamond as closure) in X. It is known that the modal logics S4, S4.1, S4.2, S4.1.2, S4.Grz, S4.Grz_n, and their intersections arise as L(X) for some Stone space X. We give an example of a...
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In this paper we formalize an approach to knowledge that we call Interrogative Epistemology, in the spirit of Hintikka's "interrogative model" of knowledge. According to our approach, an agent's knowledge is shaped and limited by her interrogative agenda (as defined by her fundamental questions o...
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This paper studies the logical features of social group creation. We focus on the mechanisms which indicate when agents can form a team based on the correspondence in their set of features (behavior, opinions, etc.). Our basic approach uses a semi-metric on the set of agents, which is used to con...
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This paper is part of an on-going programme in which we provide a logical study of social network formations. In the proposed setting, agent a will consider agent b as part of her network if the number of features (properties) on which they differ is small enough, given the constraints on the siz...
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This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and we use argumentation theory to single out the relevant set...
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A lattice P is transferable for a class of lattices K if whenever P can be embedded into the ideal lattice I(L) of some L ∈ K, then P can be embedded into L. There is a rich theory of transferability for lattices. Here we introduce the analogous notion of MacNeille transferability, replacing the ...
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Computational social choice is concerned with the design and analysis of methods for collective decision making. It is a research area that is located at the interface of Computer Science and Economics. This volume reports on a number of recent research trends in computational social choice. It h...
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Brouwer’s ideas of construction, proof, and inquiry in mathematics are more widely applicable. On a well-known philosophical view, intuitionistic logic is a general account of meaning and reasoning for natural language and epistemology. In this brief discussion piece, I go one step further, and d...
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This paper is a light walk along interfaces between logic and probability, triggered by a chance encounter with Ed Brinksma. It is not a research paper, or a literature survey, but a pointer to issues. I discuss both direct combinations of logic and probability and structured ways in which logic ...
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We propose a new perspective on logics of computation by combining instantial neighborhood logic INL with bisimulation safe operations adapted from PDL and dynamic game logic. INL is a recently proposed modal logic, based on a richer extension of neighborhood semantics which permits both universa...