Nathanael Chambers, Daniel Cer, Trond Grenager, David Hall, Chloe Kiddon Bill MacCartney, Marie-Catherine de Marneffe, Daniel Ramage Eric Yeh, Christopher D. Manning Computer Science Department Stanford University Stanford, CA 94305.

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)

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)

Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic (...) of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities. (shrink)

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.

We propose an approach to natural language inference based on a model of natural logic, which identifies valid inferences by their lexical and syntactic features, without full semantic interpretation. We greatly extend past work in natural logic, which has focused solely on semantic containment and monotonicity, to incorporate both semantic exclusion and implicativity. Our system decomposes an inference problem into a sequence of atomic edits linking premise to hypothesis; predicts a lexical entailment relation for each edit using a statistical classifier; (...) propagates these relations upward through a syntax tree according to semantic properties of intermediate nodes; and composes the resulting entailment relations across the edit sequence. We evaluate our system on the FraCaS test suite, and achieve a 27% reduction in error from previous work. We also show that hybridizing an existing RTE system with our natural logic system yields significant gains on the RTE3 test suite. (shrink)

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

The alignment problem—establishing links between corresponding phrases in two related sentences—is as important in natural language inference (NLI) as it is in machine translation (MT). But the tools and techniques of MT alignment do not readily transfer to NLI, where one cannot assume semantic equivalence, and for which large volumes of bitext are lacking. We present a new NLI aligner, the MANLI system, designed to address these challenges. It uses a phrase-based alignment representation, exploits external lexical resources, and capitalizes on (...) a new set of supervised training data. We compare the performance of MANLI to existing NLI and MT aligners on an NLI alignment task over the well-known Recognizing Textual Entailment data. We show that MANLI significantly outperforms existing aligners, achieving gains of 6.2% in F1 over a representative NLI aligner and 10.5% over GIZA++. (shrink)

We describe an approach to textual inference that improves alignments at both the typed dependency level and at a deeper semantic level. We present a machine learning approach to alignment scoring, a stochastic search procedure, and a new tool that finds deeper semantic alignments, allowing rapid development of semantic features over the aligned graphs. Further, we describe a complementary semantic component based on natural logic, which shows an added gain of 3.13% accuracy on the RTE3 test set.