This paper provides a foundation for the polarity marking technique introduced by David Dowty [3] in connection with monotonicity reasoning in natural language and in linguistic analyses of negative polarity items based on categorial grammar. Dowty's work is an alternative to the better-known algorithmic approach first proposed by Johan van Benthem [11], and elaborated by Víctor Sánchez Valencia [10]. Dowty's system internalized the monotonicity/polarity markings by generating strings using a categorial grammar whose categories already contain the markings that the earlier (...) system would obtain by separate steps working on an already-derived string. Despite the linguistic advantages of the internalized system, no soundness proof has yet been given for it. This paper offers an account. The leading mathematical idea is to interpret categorial types as preorders (in order to talk about monotonicity in the first place), and then to add a primitive operation to the type hierarchy of taking the opposite of a preorder (in order to capture monotone decreasing functions). At the same time, the use of internalized categories also raises issues. Although these will not be addressed in full, the paper points out possible approaches to them. (shrink)

This paper presents the first use of a computational model of natural logic—a system of logical inference which operates over natural language—for textual inference. Most current approaches to the PAS- CAL RTE textual inference task achieve robustness by sacrificing semantic precision; while broadly effective, they are easily confounded by ubiquitous inferences involving monotonicity. At the other extreme, systems which rely on first-order logic and theorem proving are precise, but excessively brittle. This work aims at a middle way. Our system finds (...) a low-cost edit sequence which transforms the premise into the hypothesis; learns to classify entailment relations across atomic edits; and composes atomic entailments into a top-level entailment judgment. We provide the first reported results for any system on the FraCaS test suite. We also evaluate on RTE3 data, and show that hybridizing an existing RTE system with our natural logic system yields significant performance gains. (shrink)