This paper develops an inference system for natural language within the ‘Natural Logic’ paradigm as advocated by van Benthem, Sánchez and others. The system that we propose is based on the Lambek calculus and works directly on the Curry-Howard counterparts for syntactic representations of natural language, with no intermediate translation to logical formulae. The Lambek -based system we propose extends the system by Fyodorov et~al., which is based on the Ajdukiewicz/Bar-Hillel calculus Bar Hillel,. This enables the system to deal with (...) new kinds of inferences, involving relative clauses, non-constituent coordination, and meaning postulates that involve complex expressions. Basing the system on the Lambek calculus leads to problems with non-normalized proof terms, which are treated by using normalization axioms. (shrink)

Evidence is presented to show that the role of a generative grammar of a natural language is not merely to generate the grammatical sentences of that language, but also to relate them to their logical forms. The notion of logical form is to be made sense of in terms a natural logic, a logical for natural language, whose goals are to express all concepts capable of being expressed in natural language, to characterize all the valid inferences that can be made (...) in natural language, and to mesh with adequate linguistic descriptions of all natural languages. The latter requirement imposes empirical linguistic constraints on natural logic. A number of examples are discussed. (shrink)

This paper develops a version of Natural Logic – an inference system that works directly on natural language syntactic representations, with no intermediate translation to logical formulae. Following work by Sánchez, we develop a small fragment that computes semantic order relations between derivation trees in Categorial Grammar. The proposed system has the following new characteristics: It uses orderings between derivation trees as purely syntactic units, derivable by a formal calculus. The system is extended for conjunctive phenomena like coordination and relative (...) clauses. This allows a simple account of non-monotonic expressions that are reducible to conjunctions of monotonic ones. A decision procedure for provability is developed for a fragment of Natural Logic. (shrink)

This paper proposes a new architecture for textual inference in which finding a good alignment is separated from evaluating entailment. Current approaches to semantic inference in question answering and textual entailment have approximated the entailment problem as that of computing the best alignment of the hypothesis to the text, using a locally decomposable matching score. While this formulation is adequate for representing local (word-level) phenomena such as synonymy, it is incapable of representing global interactions, such as that between verb negation (...) and the addition/removal of qualifiers, which are often critical for determining entailment. We propose a pipelined approach where alignment is followed by a classification step, in which we extract features representing high-level characteristics of the entailment problem, and give the resulting feature vector to a statistical classifier trained on development data. (shrink)

separated from evaluating entailment. Current approaches to semantic inference in question answer-.

assumptions latent in a vanilla treebank grammar. Indeed, its performance of 86.36% (LP/LR F1) is..

We implement the extension of the logical consequence relation to a partial order ≤ on arbitary types built from e (entities) and t (Booleans) that was given in [1], and the definition of monotonicity preserving and monotonicity reversing functions in terms of ≤. Next, we present a new algorithm for polarity marking, and implement this for a particular fragment of syntax. Finally, we list the reseach agenda that these definitions and this algorithm suggest. The implementations use Haskell [8], and are (...) given in ‘literate programming’ style [9]. (shrink)