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Topological collections allow to consider uniformly many data structures in programming languages and are handled by functions defined by pattern matching called transformations. We present two type systems for languages with topological…
A new approach to the problem of natural language understanding is proposed. The knowledge domain under consideration is the social behavior of people. English sentences are translated into set of predicates of a semantic database, which…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
In this paper we provide a conceptual overview of latent variable models within a probabilistic modeling framework, an overview that emphasizes the compositional nature and the interconnectedness of the seemingly disparate models commonly…
Natural language processing (NLP) can be done using either top-down (theory driven) and bottom-up (data driven) approaches, which we call mechanistic and phenomenological respectively. The approaches are frequently considered to stand in…
Verbs are important in semantic understanding of natural language. Traditional verb representations, such as FrameNet, PropBank, VerbNet, focus on verbs' roles. These roles are too coarse to represent verbs' semantics. In this paper, we…
We present a novel approach to construction of a formal semantics for a programming language. Our approach, using a parametric denotational semantics, allows the semantics to be easily extended to support new language features, and…
A natural next step in the evolution of constraint-based grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanism---to express syntactic theories purely in terms of the properties of…
This paper introduces how human languages can be studied in light of recent development of network theories. There are two directions of exploration. One is to study networks existing in the language system. Various lexical networks can be…
We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…
Making a linguistic theory is like making a programming language: one typically devises a type system to delineate the acceptable utterances and a denotational semantics to explain observations on their behavior. Via this connection, the…
In this paper, we show how game-theoretic work on conversation combined with a theory of discourse structure provides a framework for studying interpretive bias. Interpretive bias is an essential feature of learning and understanding but…
This thesis is about the problem of compositionality in distributional semantics. Distributional semantics presupposes that the meanings of words are a function of their occurrences in textual contexts. It models words as distributions over…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
Distributional semantics is the linguistic theory that a word's meaning can be derived from its distribution in natural language (i.e., its use). Language models are commonly viewed as an implementation of distributional semantics, as they…
Inspired by the inductive transfer learning on computer vision, many efforts have been made to train contextualized language models that boost the performance of natural language processing tasks. These models are mostly trained on large…
Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier…
In this paper I discuss both syntax and semantics of subjective probability. The semantics determines ways of testing probability statements. Among important varieties of subjective probabilities are intersubjective probabilities and…
We define and study logics in the framework of probabilistic team semantics and over metafinite structures. Our work is paralleled by the recent development of novel axiomatizable and tractable logics in team semantics that are closed under…
Among the several findings deriving from the application of complex network formalism to the investigation of natural phenomena, the fact that linguistic constructions follow power laws presents special interest for its potential…