arXiv subjects

Damian Szmuc

Publications and source records attributed to Damian Szmuc.

2 recordsLinked to original sources

arXiv2026

Varieties of De Morgan bisemilattices

De Morgan bisemilattices are expansions of distributive bisemilattices by an involution satisfying De Morgan properties. They have attracted interest both as algebraic models of analytic containment logics, and as a case study for a certain generalisation of the Płonka sum construction (De Morgan- Płonka sums). In this paper, we provide a complete description of the lattice of subvarieties of the variety DMBL of De Morgan bisemilattices. For each subvariety in the lattice, we identify a finite set of finite generators, a characterisation of the De Morgan-Płonka representations of its members, and a syntactic description of its valid identities. In many cases, we also give an axiomatisation relative to DMBL.

math.LO↗

arXiv2023

On three-valued presentations of classical logic

Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations $st$, $ss$, $tt$, $ss\cap tt$, and $ts$, when the connectives are negation, conjunction, and disjunction. For $ts$ and $ss\cap tt$ the answer is trivial (no scheme works), and for $ss$ and $tt$ it is straightforward (they are the collapsible schemes, in which the middle value acts like one of the classical values). For $st$, the schemes in question are the Boolean normal schemes that are either monotonic or collapsible.

math.LO↗