Institutional Semantics for Many-valued Logics(abstract)
We develop many-valued logic, including a generic abstract
model theory, over a fully abstract syntax.
We show that important many-valued logic model theories, such as
traditional first-order many-valued logic and fuzzy multi-algebras,
may be conservatively embedded into our abstract framework.
Our development is technically based upon the so-called theory
of institutions of Goguen and Burstall and may serve as a template for
defining at hand many-valued logic model theories over various
concrete syntaxes or, from another perspective, to combine
many-valued logic with other logical systems.
We also show that our generic many-valued logic abstract model
theory enjoys a couple of important institutional model theory
properties that support the development of deep model theory methods.
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