<p>We design a method for solving natural language one-dimensional ordering problems by tightly integrating and co-developing a semantic parser with a logical inference module that deduces conclusions from the constraints stated in the premises. The semantic parser builds on Heim and Kratzer’s syntax-based compositional semantics with lambda calculus and introduces abstract types, templated rules, and a dynamic component for interpreting entities. It maps natural language into first-order logical forms defined in an axiom system and domain language that we develop for one-dimensional ordering problems. These forms are evaluated by a logic-based inference module that we design and develop which enforces ordering constraints and determines whether candidate statements hold in all, some, or no possible worlds consistent with the premises, while addressing difficult constructs such as partial ordering and negation. The resulting system, the Formal Semantic Logic Inferer (FSLI), tightly integrates formal semantics with logic programming to provide a linguistically principled and logically sound framework for logical deduction problems stated in natural language. We demonstrate FSLI’s effectiveness on both synthetic and exam-style problems, achieving perfect performance in the controlled setting of the synthetic problems and high performance on the more linguistically and logically demanding exam-style ones.</p>