arXiv subjects

Wilmari Morton

Publications and source records attributed to Wilmari Morton.

3 recordsLinked to original sources

arXiv2026

Representability for distributive quasi relation algebras via nested sums

We extend the work of Galatos (2004) on nested sums, originally called generalised ordinal sums, of residuated lattices. We show that the nested sum of an odd quasi relation algebra (qRA) satisfying certain conditions and an arbitrary qRA is again a qRA. In a recent paper by Craig and Robinson (2025) the notion of representability for distributive quasi relation algebras (DqRAs) was developed. For certain pairs of representable DqRAs, we prove that their nested sum is again representable. An important consequence of this result is that finite Sugihara chains are finitely representable.

math.LO↗

arXiv2026

Contractions of quasi relation algebras and applications to representability

Quasi relation algebras (qRAs) were first described by Galatos and Jipsen in 2013. They are generalisations of relation algebras and can also be viewed as certain residuated lattice expansions. We identify positive symmetric idempotent elements in qRAs and show that they can be used to construct new qRAs, so-called contractions of the original algebra. We then show that the contraction of a distributive qRA will be representable when the original algebra is representable. Further, we identify a class of distributive qRAs that are not finitely representable.

cs.LO↗

arXiv2025

Correspondence Theory for Many-valued Modal Logic

The aim of the present paper is to generalise Sahlqvist correspondence theory to the many-valued modal semantics defined by Fitting, assuming a perfect Heyting algebra as truth value space. We present the standard translations between many-valued modal languages and suitably defined first-order and second-order correspondence languages and prove their correctness. We introduce a notion of many-valued modal frame correspondence with a truth value parameter. Exploring the consequences of this definition, we define many-valued analogues of the syntactically specified classes of Sahlqvist and inductive formulas. We adapt the ALBA algorithm to effectively compute many-valued parameterized local frame correspondents for all many-valued Sahlqvist and inductive formulas. Lastly we prove that the many-valued frame correspondent (parameterized with any non-zero truth value) of every classical Sahlqvist formula is syntactically identical to its standard crisp frame correspondent.

math.LO↗