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  1. Formal Learning Theory.Oliver Schulte - 2008 - Stanford Encyclopedia of Philosophy.
    Formal learning theory is the mathematical embodiment of a normative epistemology. It deals with the question of how an agent should use observations about her environment to arrive at correct and informative conclusions. Philosophers such as Putnam, Glymour and Kelly have developed learning theory as a normative framework for scientific reasoning and inductive inference.
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  • A ModalWalk Through Space.Marco Aiello & Johan van Benthem - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):319-363.
    We investigate the major mathematical theories of space from a modal standpoint: topology, affine geometry, metric geometry, and vector algebra. This allows us to see new fine-structure in spatial patterns which suggests analogies across these mathematical theories in terms of modal, temporal, and conditional logics. Throughout the modal walk through space, expressive power is analyzed in terms of language design, bisimulations, and correspondence phenomena. The result is both unification across the areas visited, and the uncovering of interesting new questions.
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  • A Quick Guided Tour to the Modal Logic S4.2.Aggeliki Chalki, Costas D. Koutras & Yorgos Zikos - 2018 - Logic Journal of the IGPL 26 (4):429-451.
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  • Advances in Modal Logic, Volume.Rajeev Gore - unknown
    We study a propositional bimodal logic consisting of two S4 modalities and [a], together with the interaction axiom scheme a ϕ → a ϕ. In the intended semantics, the plain..
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  • Topological Reasoning and the Logic of Knowledge.Andrew Dabrowski, Lawrence S. Moss & Rohit Parikh - 1996 - Annals of Pure and Applied Logic 78 (1-3):73-110.
    We present a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces , and we obtain complete axiomatizations for the sentences which hold in these interpretations. In addition, we axiomatize the validities of the smaller class of topological spaces in a system we call topologic . We also prove decidability for these two systems. Our results on topologic relate (...)
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  • A Hybrid Logic for Reasoning About Knowledge and Topology.Bernhard Heinemann - 2008 - Journal of Logic, Language and Information 17 (1):19-41.
    We extend Moss and Parikh’s bi-modal system for knowledge and effort by means of hybrid logic. In this way, some additional concepts from topology related to knowledge can be captured. We prove the soundness and completeness as well as the decidability of the extended system. Special emphasis will be placed on algebras.
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  • The Topology of Justification.Sergei Artemov & Elena Nogina - 2008 - Logic and Logical Philosophy 17 (1-2):59-71.
    Justification Logic is a family of epistemic logical systems obtained from modal logics of knowledge by adding a new type of formula t:F, which is read t is a justification for F. The principal epistemic modal logic S4 includes Tarski’s well-known topological interpretation, according to which the modality 2X is read the Interior of X in a topological space (the topological equivalent of the ‘knowable part of X’). In this paper, we extend Tarski’s topological interpretation from S4 to Justification Logic (...)
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  • 25th Workshop on Logic, Language, Information and Computation.Lawrence Moss, Maricarmen Martinez, Xavier Caicedo & Ruy de Queiroz - forthcoming - Logic Journal of the IGPL.
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  • A Topological Approach to Full Belief.Alexandru Baltag, Nick Bezhanishvili, Aybüke Özgün & Sonja Smets - 2019 - Journal of Philosophical Logic 48 (2):205-244.
    Stalnaker, 169–199 2006) introduced a combined epistemic-doxastic logic that can formally express a strong concept of belief, a concept of belief as ‘subjective certainty’. In this paper, we provide a topological semantics for belief, in particular, for Stalnaker’s notion of belief defined as ‘epistemic possibility of knowledge’, in terms of the closure of the interior operator on extremally disconnected spaces. This semantics extends the standard topological interpretation of knowledge with a new topological semantics for belief. We prove that the belief (...)
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  • Updating Knowledge Using Subsets.Konstantinos Georgatos - 2011 - Journal of Applied Non-Classical Logics 21 (3-4):427-441.
    Larry Moss and Rohit Parikh used subset semantics to characterize a family of logics for reasoning about knowledge. An important feature of their framework is that subsets always decrease based on the assumption that knowledge always increases. We drop this assumption and modify the semantics to account for logics of knowledge that handle arbitrary changes, that is, changes that do not necessarily result in knowledge increase, such as the update of our knowledge due to an action. We present a system (...)
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  • Announcement as Effort on Topological Spaces.Hans van Ditmarsch, Sophia Knight & Aybüke Özgün - forthcoming - Synthese:1-43.
    We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, with S5 knowledge modality, and demonstrate their completeness. We moreover consider the weaker axiomatizations of three logics with S4 type of knowledge and prove soundness and (...)
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  • A Grim Semantics For Logics of Belief.Christopher Steinsvold - 2008 - Journal of Philosophical Logic 37 (1):45-56.
    Patrick Grim has presented arguments supporting the intuition that any notion of a totality of truths is incoherent. We suggest a natural semantics for various logics of belief which reflect Grim’s intuition. The semantics is a topological semantics, and we suggest that the condition can be interpreted to reflect Grim’s intuition. Beyond this, we present a natural canonical topological model for K4 and KD4.
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  • Reverse Public Announcement Operators on Expanded Models.Ryuichi Sebastian Haney - 2018 - Journal of Logic, Language and Information 27 (3):205-224.
    Past public announcement operators have been defined in Hoshi and Yap :259–281, 2009) and Yap, to describe an agent’s knowledge before an announcement occurs. These operators rely on branching-time structures that do not mirror the traditional, relativization-based semantics of public announcement logic, and favor a historical reading of past announcements. In this paper, we introduce reverse public announcement operators that are interpreted on expanded models. Our model expansion adds accessibility links from an epistemic model \ to a filtrated submodel of (...)
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  • Dynamic Logics of Evidence-Based Beliefs.J. Benthem & E. Pacuit - 2011 - Studia Logica 99 (1-3):61-92.
    This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.
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  • Expressivity in Polygonal, Plane Mereotopology.Ian Pratt & Dominik Schoop - 2000 - Journal of Symbolic Logic 65 (2):822-838.
    In recent years, there has been renewed interest in the development of formal languages for describing mereological (part-whole) and topological relationships between objects in space. Typically, the non-logical primitives of these languages are properties and relations such as `x is connected' or `x is a part of y', and the entities over which their variables range are, accordingly, not points, but regions: spatial entities other than regions are admitted, if at all, only as logical constructs of regions. This paper considers (...)
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  • Dynamic Logics of Evidence-Based Beliefs.Johan van Benthem & Eric Pacuit - 2011 - Studia Logica 99 (1-3):61-92.
  • Using Hybrid Logic for Coping with Functions in Subset Spaces.Bernhard Heinemann - 2010 - Studia Logica 94 (1):23-45.
    We extend Moss and Parikh’s modal logic for subset spaces by adding, among other things, state-valued and set-valued functions. This is done with the aid of some basic concepts from hybrid logic. We prove the soundness and completeness of the derived logics with regard to the class of all correspondingly enriched subset spaces, and show that these logics are decidable.
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