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- W4322007845 abstract "Abstract We show how modal quantales arise as convolution algebras $$Q^X$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>Q</mml:mi> <mml:mi>X</mml:mi> </mml:msup> </mml:math> of functions from catoids X , multisemigroups equipped with source and target maps, into modal quantales value or weight quantales Q . In the tradition of boolean algebras with operators we study modal correspondences between algebraic laws in X , Q and $$Q^X$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>Q</mml:mi> <mml:mi>X</mml:mi> </mml:msup> </mml:math> . The catoids introduced generalise Schweizer and Sklar’s function systems and single-set categories to structures isomorphic to algebras of ternary relations, as they are used for boolean algebras with operators and substructural logics. Our correspondence results support a generic construction of weighted modal quantales from catoids. This construction is illustrated by many examples. We also relate our results to reasoning with stochastic matrices or probabilistic predicate transformers." @default.
- W4322007845 created "2023-02-26" @default.
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- W4322007845 date "2023-02-25" @default.
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- W4322007845 title "Catoids and modal convolution algebras" @default.
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- W4322007845 doi "https://doi.org/10.1007/s00012-023-00805-9" @default.
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