Review of Symbolic Logic 10 (1):116-144 (2017)
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This paper explores a new language of neighbourhood structures where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. The resulting system of ‘instantial neighbourhood logic’ INL has a nontrivial mix of features from relational semantics and from neighbourhood semantics. We explore some basic model-theoretic behavior, including a matching notion of bisimulation, and give a complete axiom system for which we prove completeness by a new normal form technique. In addition, we relate INL to other modal logics by means of translations, and determine its precise SAT complexity. Finally, we discuss proof-theoretic fine-structure of INL in terms of semantic tableaux and some expressive fine-structure in terms of fragments, while discussing concrete illustrations of the instantial neighborhood language in topological spaces, in games with powers for players construed in a new way, as well as in dynamic logics of acquiring or deleting evidence. We conclude with some coalgebraic perspectives on what is achieved in this paper. Many of these final themes suggest follow-up work of independent interest.
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DOI | 10.1017/s1755020316000447 |
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References found in this work BETA
Dynamic Logics of Evidence-Based Beliefs.Johan van Benthem & Eric Pacuit - 2011 - Studia Logica 99 (1-3):61-92.
Dynamic Logics of Evidence-Based Beliefs.J. Benthem & E. Pacuit - 2011 - Studia Logica 99 (1-3):61-92.
Normal Monomodal Logics Can Simulate All Others.Marcus Kracht & Frank Wolter - 1999 - Journal of Symbolic Logic 64 (1):99-138.
View all 8 references / Add more references
Citations of this work BETA
A New Game Equivalence, its Logic and Algebra.Johan van Benthem, Nick Bezhanishvili & Sebastian Enqvist - 2019 - Journal of Philosophical Logic 48 (4):649-684.
A Propositional Dynamic Logic for Instantial Neighborhood Semantics.Johan van Benthem, Nick Bezhanishvili & Sebastian Enqvist - 2019 - Studia Logica 107 (4):719-751.
Weakly Aggregative Modal Logic: Characterization and Interpolation.Jixin Liu, Yanjing Wang & Yifeng Ding - 2019 - In Patrick Blackburn, Emiliano Lorini & Meiyun Guo (eds.), Logic, Rationality, and Interaction 7th International Workshop, LORI 2019, Chongqing, China, October 18–21, 2019, Proceedings. pp. 153-167.
Expressivity Results for Deontic Logics of Collective Agency.Allard Tamminga, Hein Duijf & Frederik Van De Putte - 2020 - Synthese 198 (9):8733-8753.
View all 9 citations / Add more citations
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