This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable.

Finite-state descriptions for temporal semantics are outlined through which to distinguish soft inferences reflecting manners of conceptualization from more robust semantic entailments defined over models. Just what descriptions are built (before being interpreted model-theoretically) and how they are grounded in models of reality explain (upon examination) why some inferences are soft.