Abstract:
This paper concerns residuated lattice-ordered idempotent commutative
monoids that are subdirect products of chains. An algebra of this
kind is a generalized Sugihara monoid (GSM) if it is generated by the lower
bounds of the monoid identity; it is a Sugihara monoid if it has a compatible
involution :. Our main theorem establishes a category equivalence
between GSMs and relative Stone algebras with a nucleus (i.e., a closure
operator preserving the lattice operations). An analogous result is obtained
for Sugihara monoids. Among other applications, it is shown that Sugihara
monoids are strongly amalgamable, and that the relevance logic RMt has
the projective Beth de nability property for deduction.
