A Finite Row Semantics for First-Order Logic and Counterfactuals

This paper introduces a finite row-based semantics for a non-nested fragment of first-order predicate logic. Rows are assignments of signs to monadic predicates, including projections of polyadic relations, and configurations of rows represent admissible individuals. Quantified formulas constrain configurations, while ground atomic formulas impose relational constraints without assigning constants to fixed individuals. On this basis, we develop a non-metric account of counterfactual conditionals. Counterfactuals are evaluated relative to configurations and their revisions: compatible antecedents are handled by restriction, while incompatible antecedents are handled by preserving all constraints consistent with the antecedent. This yields distinct “would” and “might” conditionals and avoids collapse to material implication. The semantics is fully finite and decidable, reducing logical evaluation to operations on a fixed combinatorial structure. The framework provides a simple alternative to both classical model theory and possible-worlds approaches to counterfactuals.