A convergence law for continuous logic and continuous structures with finite domains

ArXi:2504.08923v2 Announce Type: replace-cross We consider continuous relational structures with finite domain $[n]:= \{1, \ldots, n\}$ and a many valued logic, $CLA$, with values in the unit interval and which uses continuous connectives and continuous aggregation functions. $CLA$ subsumes first-order logic on ``conventional'' finite structures. To each relation symbol $R$ and identity constraint $ic$ on a tuple the length of which matches the arity of $R$ we associate a continuous probability density function $\mu_R^{ic}: [0, 1] \to [0, \infty.