This paper is a brief history of natural logic at the interface of logic, linguistics, and nowadays also other disciplines. It merely summarizes some facts that deserve to be common knowledge.

The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether reductio (...) ad absurdum is needed. Thus our main goal is to derive results on the existence (or nonexistence) of syllogistic proof systems for relational fragments. We also determine the computational complexity of all our fragments. (shrink)

We propose a model of natural language inference which identifies valid inferences by their lexical and syntactic features, without full semantic interpretation. We extend past work in natural logic, which has focused on semantic containment and monotonicity, by incorporating both semantic exclusion and implicativity. Our model decomposes an inference problem into a sequence of atomic edits linking premise to hypothesis; predicts a lexical semantic relation for each edit; propagates these relations upward through a semantic composition tree according to properties of (...) intermediate nodes; and joins the resulting semantic relations across the edit sequence. A computational implementation of the model achieves 70% accuracy and 89% precision on the FraCaS test suite. Moreover, including this model as a component in an existing system yields significant performance gains on the Recognizing Textual Entailment challenge. (shrink)

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)