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A Note on Graded Modal Logic

Maarten De Rijke

Studia Logica 64 (2):271 - 283 (2000)

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Granular knowledge and rational approximation in general rough sets – I.A. Mani - 2024 - Journal of Applied Non-Classical Logics 34 (2-3):294-329.details Rough sets are used in numerous knowledge representation contexts and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalisations of graded and variable precision rough sets are investigated by the present author from the perspective of rationality of approximations (and the associated semantics of rationality in approximate reasoning). The studies are extended to ideal-based approximations (sometimes referred to as subsethood-based approximations). It is additionally shown that (...) Download Export citation Bookmark
Counting to Infinity: Graded Modal Logic with an Infinity Diamond.Ignacio Bellas Acosta & Yde Venema - 2024 - Review of Symbolic Logic 17 (1):1-35.details We extend the languages of both basic and graded modal logic with the infinity diamond, a modality that expresses the existence of infinitely many successors having a certain property. In both cases we define a natural notion of bisimilarity for the resulting formalisms, that we dub $\mathtt {ML}^{\infty }$ and $\mathtt {GML}^{\infty }$, respectively. We then characterise these logics as the bisimulation-invariant fragments of the naturally corresponding predicate logic, viz., the extension of first-order logic with the infinity quantifier. Furthermore, for (...) Download Export citation Bookmark
Arboreal categories and equi-resource homomorphism preservation theorems.Samson Abramsky & Luca Reggio - 2024 - Annals of Pure and Applied Logic 175 (6):103423.details Download Export citation Bookmark
Toward Model-Theoretic Modal Logics.M. A. Minghui - 2010 - Frontiers of Philosophy in China 5 (2):294-311.details Adding certain cardinality quantifiers into first-order language will give substantially more expressive languages. Thus, many mathematical concepts beyond first-order logic can be handled. Since basic modal logic can be seen as the bisimular invariant fragment of first-order logic on the level of models, it has no ability to handle modally these mathematical concepts beyond first-order logic. By adding modalities regarding the cardinalities of successor states, we can, in principle, investigate modal logics of all cardinalities. Thus ways of exploring model-theoretic logics (...) Download Export citation Bookmark
Toward model-theoretic modal logics.Minghui Ma - 2010 - Frontiers of Philosophy in China 5 (2):294-311.details Adding certain cardinality quantifiers into first-order language will give substantially more expressive languages. Thus, many mathematical concepts beyond first-order logic can be handled. Since basic modal logic can be seen as the bisimular invariant fragment of first-order logic on the level of models, it has no ability to handle modally these mathematical concepts beyond first-order logic. By adding modalities regarding the cardinalities of successor states, we can, in principle, investigate modal logics of all cardinalities. Thus ways of exploring model-theoretic logics (...) Download Export citation Bookmark

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