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This paper connects a vector-based composition model to a formal semantics, the Dependency-based Compositional Semantics (DCS). We show theoretical evidence that the vector compositions in our model conform to the logic of DCS.…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on justification terms and equality predicate on terms. In…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
The neural architectures of language models are becoming increasingly complex, especially that of Transformers, based on the attention mechanism. Although their application to numerous natural language processing tasks has proven to be very…
Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped…
The integration of lexical semantics and pragmatics in the analysis of the meaning of natural lan- guage has prompted changes to the global framework derived from Montague. In those works, the original lexicon, in which words were assigned…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
Representing the semantics of words is a long-standing problem for the natural language processing community. Most methods compute word semantics given their textual context in large corpora. More recently, researchers attempted to…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Capturing the meaning of sentences has long been a challenging task. Current models tend to apply linear combinations of word features to conduct semantic composition for bigger-granularity units e.g. phrases, sentences, and documents.…
We discuss quantum non-locality and contextuality, emphasising logical and structural aspects. We also show how the same mathematical structures arise in various areas of classical computation.
Being inspired by the success of \texttt{word2vec} \citep{mikolov2013distributed} in capturing analogies, we study the conjecture that analogical relations can be represented by vector spaces. Unlike many previous works that focus on the…
Vector space word representations are learned from distributional information of words in large corpora. Although such statistics are semantically informative, they disregard the valuable information that is contained in semantic lexicons…
Formal, Distributional, and Grounded theories of computational semantics each have their uses and their drawbacks. There has been a shift to ground models of language by adding visual knowledge, and there has been a call to enrich models of…
We present an approach to combining distributional semantic representations induced from text corpora with manually constructed lexical-semantic networks. While both kinds of semantic resources are available with high lexical coverage, our…
Deep compositional models of meaning acting on distributional representations of words in order to produce vectors of larger text constituents are evolving to a popular area of NLP research. We detail a compositional distributional…
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by…
We show that context semantics can be fruitfully applied to the quantitative analysis of proof normalization in linear logic. In particular, context semantics lets us define the weight of a proof-net as a measure of its inherent complexity:…
We consider the problem of learning the semantics of composite algebraic expressions from examples. The outcome is a versatile framework for studying learning tasks that can be put into the following abstract form: The input is a partial…