3,079 research outputs found
Geometry of compositionality
Word embedding is a popular representation of words in vector space, and its geometry reveals the lexical semantics. This thesis further explores the interesting geometric properties of word embedding, and looks into its interaction with the context representation. We propose an innovative method to detect whether a given word or phrase is used literally in a specific context. This work focuses on three specific applications in natural language processing: idiomaticity, sarcasm and metaphor detection. Extensive experiments have shown that this embedding-based method achieves good performance in multiple languages
Compositional game theory
We introduce open games as a compositional foundation of economic game
theory. A compositional approach potentially allows methods of game theory and
theoretical computer science to be applied to large-scale economic models for
which standard economic tools are not practical. An open game represents a game
played relative to an arbitrary environment and to this end we introduce the
concept of coutility, which is the utility generated by an open game and
returned to its environment. Open games are the morphisms of a symmetric
monoidal category and can therefore be composed by categorical composition into
sequential move games and by monoidal products into simultaneous move games.
Open games can be represented by string diagrams which provide an intuitive but
formal visualisation of the information flows. We show that a variety of games
can be faithfully represented as open games in the sense of having the same
Nash equilibria and off-equilibrium best responses.Comment: This version submitted to LiCS 201
From holism to compositionality: memes and the evolution of segmentation, syntax, and signification in music and language
Steven Mithen argues that language evolved from an antecedent he terms “Hmmmmm, [meaning it was] Holistic, manipulative, multi-modal, musical and mimetic”. Owing to certain innate and learned factors, a capacity for segmentation and cross-stream mapping in early Homo sapiens broke the continuous line of Hmmmmm, creating discrete replicated units which, with the initial support of Hmmmmm, eventually became the semantically freighted words of modern language. That which remained after what was a bifurcation of Hmmmmm arguably survived as music, existing as a sound stream segmented into discrete units, although one without the explicit and relatively fixed semantic content of language. All three types of utterance – the parent Hmmmmm, language, and music – are amenable to a memetic interpretation which applies Universal Darwinism to what are understood as language and musical memes. On the basis of Peter Carruthers’ distinction between ‘cognitivism’ and ‘communicativism’ in language, and William Calvin’s theories of cortical information encoding, a framework is hypothesized for the semantic and syntactic associations between, on the one hand, the sonic patterns of language memes (‘lexemes’) and of musical memes (‘musemes’) and, on the other hand, ‘mentalese’ conceptual structures, in Chomsky’s ‘Logical Form’ (LF)
A probabilistic framework for analysing the compositionality of conceptual combinations
Conceptual combination performs a fundamental role in creating the broad
range of compound phrases utilised in everyday language. This article provides
a novel probabilistic framework for assessing whether the semantics of conceptual
combinations are compositional, and so can be considered as a function of
the semantics of the constituent concepts, or not. While the systematicity and
productivity of language provide a strong argument in favor of assuming compositionality,
this very assumption is still regularly questioned in both cognitive
science and philosophy. Additionally, the principle of semantic compositionality
is underspecified, which means that notions of both "strong" and "weak"
compositionality appear in the literature. Rather than adjudicating between
different grades of compositionality, the framework presented here contributes
formal methods for determining a clear dividing line between compositional and
non-compositional semantics. In addition, we suggest that the distinction between
these is contextually sensitive. Compositionality is equated with a joint probability distribution modeling how the constituent concepts in the combination
are interpreted. Marginal selectivity is introduced as a pivotal probabilistic
constraint for the application of the Bell/CH and CHSH systems of inequalities.
Non-compositionality is equated with a failure of marginal selectivity, or violation
of either system of inequalities in the presence of marginal selectivity. This
means that the conceptual combination cannot be modeled in a joint probability
distribution, the variables of which correspond to how the constituent concepts
are being interpreted. The formal analysis methods are demonstrated by applying
them to an empirical illustration of twenty-four non-lexicalised conceptual
combinations
Disquotationalism and the Compositional Principles
What Bar-On and Simmons call 'Conceptual Deflationism' is the thesis that truth is a 'thin' concept in the sense that it is not suited to play any explanatory role in our scientific theorizing. One obvious place it might play such a role is in semantics, so disquotationalists have been widely concerned to argued that 'compositional principles', such as
(C) A conjunction is true iff its conjuncts are true
are ultimately quite trivial and, more generally, that semantic theorists have misconceived the relation between truth, meaning, and logic. This paper argues, to the contrary, that even such simple compositional principles as (C) have substantial content that cannot be captured by deflationist 'proofs' of them. The key thought is that (C) is supposed, among other things, to affirm the truth-functionality of conjunction and that disquotationalists cannot, ultimately, make sense of truth-functionality.
This paper is something of a companion to "The Logical Strength of Compositional Principles"
The Geometry of Concurrent Interaction: Handling Multiple Ports by Way of Multiple Tokens (Long Version)
We introduce a geometry of interaction model for Mazza's multiport
interaction combinators, a graph-theoretic formalism which is able to
faithfully capture concurrent computation as embodied by process algebras like
the -calculus. The introduced model is based on token machines in which
not one but multiple tokens are allowed to traverse the underlying net at the
same time. We prove soundness and adequacy of the introduced model. The former
is proved as a simulation result between the token machines one obtains along
any reduction sequence. The latter is obtained by a fine analysis of
convergence, both in nets and in token machines
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