With the increasing empirical success of distributional models of compositional semantics, it is timely to consider the types of textual logic that such models are capable of capturing. In this paper, we address shortcomings in the ability of current models to capture logical operations such as negation. As a solution we propose a tripartite formulation for a continuous vector space representation of semantics and subsequently use this representation to develop a formal compositional notion of negation within such models.
The second class of approaches seeks to integrate boolean-like logical operations into distributional semantic models using existing mechanisms for representing and composing semantic vectors. postulate a mathematical framework generalising the syntax-semantic passage of Montague Grammar @cite_17 to other forms of syntactic and semantic representation. They show that the parses yielded by syntactic calculi satisfying certain structural constraints can be canonically mapped to vector combination operations in distributional semantic models. They illustrate their framework by demonstrating how the truth-value of sentences can be obtained from the combination of vector representations of words and multi-linear maps standing for logical predicates and relations. They furthermore give a matrix interpretation of negation as a swap' matrix which inverts the truth-value of vectorial sentence representations, and show how it can be embedded in sentence structure.
@cite_17
2156621282 2952300142 2110616675 1845242646
We present an approach to learning a model-theoretic semantics for natural language tied to Freebase. Crucially, our approach uses an open predicate vocabulary, enabling it to produce denotations for phrases such as "Republican front-runner from Texas" whose semantics cannot be represented using the Freebase schema. Our approach directly converts a sentence's syntactic CCG parse into a logical form containing predicates derived from the words in the sentence, assigning each word a consistent semantics across sentences. This logical form is evaluated against a learned probabilistic database that defines a distribution over denotations for each textual predicate. A training phase produces this probabilistic database using a corpus of entity-linked text and probabilistic matrix factorization with a novel ranking objective function. We evaluate our approach on a compositional question answering task where it outperforms several competitive baselines. We also compare our approach against manually annotated Freebase queries, finding that our open predicate vocabulary enables us to answer many questions that Freebase cannot. The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This paper seeks to bring this reconciliation one step further by showing how the mathematical constructs commonly used in compositional distributional models, such as tensors and matrices, can be used to simulate different aspects of predicate logic. This paper discusses how the canonical isomorphism between tensors and multilinear maps can be exploited to simulate a full-blown quantifier-free predicate calculus using tensors. It provides tensor interpretations of the set of logical connectives required to model propositional calculi. It suggests a variant of these tensor calculi capable of modelling quantifiers, using few non-linear operations. It finally discusses the relation between these variants, and how this relation should constitute the subject of future work. We present a syntactically enriched vector model that supports the computation of contextualized semantic representations in a quasi compositional fashion. It employs a systematic combination of first- and second-order context vectors. We apply our model to two different tasks and show that (i) it substantially outperforms previous work on a paraphrase ranking task, and (ii) achieves promising results on a wordsense similarity task; to our knowledge, it is the first time that an unsupervised method has been applied to this task. Formal and distributional semantic models offer complementary benefits in modeling meaning. The categorical compositional distributional model of meaning of (2010) (abbreviated to DisCoCat in the title) combines aspects of both to provide a general framework in which meanings of words, obtained distributionally, are composed using methods from the logical setting to form sentence meaning. Concrete consequences of this general abstract setting and applications to empirical data are under active study (, 2011; Grefenstette and Sadrzadeh, 2011). In this paper, we extend this study by examining transitive verbs, represented as matrices in a DisCoCat. We discuss three ways of constructing such matrices, and evaluate each method in a disambiguation task developed by Grefenstette and Sadrzadeh (2011).