Graded Equality in a Finite Row Semantics for First-Order Logic

We introduce a notion of similarity in a finite row-based semantics for a restricted fragment of first-order predicate logic. Rows encode complete patterns of predicate satisfaction, including projections of polyadic predicates, and weighted configurations assign non-negative weights to rows. Similarity is defined as indiscernibility across rows of positive weight, while degrees of similarity are obtained by measuring the proportion of rows on which two constants agree with respect to all projection predicates. The resulting notion is reflexive and symmetric but not transitive, and is best understood as a measure of structural similarity. Absolute identity is recovered as the limiting case of maximal similarity. The framework is finite and decidable, and provides a simple structural account of graded identity.