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We provide a general framework to study modal logics of multiverses and survey the results on the modal logic of forcing, the modal logic of grounds, and the modal logic of inner models. We also provide new results on the modal logic of symmetric extensions.
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We investigate the issues of inductive problem-solving and learning by doxastic agents. We provide topological characterizations of solvability and learnability, and we use them to prove that AGM-style belief revision is ``universal", i.e., that every solvable problem is solvable by AGM condition...
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We establish the dichotomy property of Jerabek (2009) for stable canonical multi-conclusion rules of Bezhanishvili et al. (2014) for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics.
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The modal logic S4.3 defines the class of hereditarily extremally disconnected spaces (HED-spaces). We construct a countable HED-subspace X of the Gleason cover of the real closed unit interval [0; 1] such that S4.3 is the logic of X.
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Canonical formulas are a powerful tool for studying intuitionistic and modal logics. Actually, they provide a uniform and semantic way to axiomatise all extensions of intuitionistic logic and all modal logics above K4. Although the method originally hinged on the relational semantics of those log...
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This paper explores a new language of neighborhood structures where existential information can be given about what kind of worlds occur in a neighborhood of a current world. The resulting system of `instantial neighborhood logic' INL has a non-trivial mix of features from relational semantics an...
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Stalnaker introduced a combined epistemic-doxastic logic that can formally express a strong concept of belief, a concept which captures the `epistemic possibility of knowledge'. In this paper we first provide the most general extensional semantics for this concept of `strong belief', which valida...
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Free choice permission to Q may be modelled as an inverse universal modality saying that all Q-worlds are deontically accessible (or `acceptable'). We axiomatize the modal validities of the resulting somewhat unusual deontic logic, where permission is no longer the usual negation dual of obligati...
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Classical logic can be given a semantics based on models consisting of partial information stages, much like those for intuitionistic logic. In this way, a completeness proof becomes much more perspicuous. It suffices to use a unique Henkin model of consistent sets without any need for non-constr...
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We introduce a new weakly analytic subformula property (the bounded proof property) of hypersequent calculi for intermediate logics. We define one-step Heyting algebras and establish semantic criteria characterizing the bounded proof property in terms of these algebraic structures. Finally, using...
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We take a logical approach to threshold models, used to study the diffusion of opinions, new technologies, infections, or behaviors in social networks. Threshold models consist of a network graph of agents connected by a social relationship and a threshold value which regulates the diffusion proc...