Author:
Fahrenberg Uli,Johansen Christian,Struth Georg,Ziemiański Krzysztof
Abstract
AbstractWe show how modal quantales arise as convolution algebras $$Q^X$$
Q
X
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 $$Q^X$$
Q
X
. 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.
Funder
NTNU Norwegian University of Science and Technology
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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