2,311 research outputs found
Static and Dynamic Vector Semantics for Lambda Calculus Models of Natural Language
To appear in Journal of Language Modelling. Short versions presented in DSALT 2016, SaLMoM 2016, LACL 2016. A version presented in AC 2017To appear in Journal of Language Modelling. Short versions presented in DSALT 2016, SaLMoM 2016, LACL 2016. A version presented in AC 2017To appear in Journal of Language Modelling. Short versions presented in DSALT 2016, SaLMoM 2016, LACL 2016. A version presented in AC 2017Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In the vector models, the degree of co-occurrence of words in context determines how similar the meanings of words are. In this paper, we put these two models together and develop a vector semantics for language based on the simply typed lambda calculus models of natural language. We provide two types of vector semantics: a static one that uses techniques familiar from the truth conditional tradition and a dynamic one based on a form of dynamic interpretation inspired by Heim's context change potentials. We show how the dynamic model can be applied to entailment between a corpus and a sentence and we provide examples
Context Update for Lambdas and Vectors
Vector models of language are based on the contextual aspects of words
and how they co-occur in text. Truth conditional models focus on the
logical aspects of language, the denotations of phrases, and their
compositional properties. In the latter approach the denotation of a
sentence determines its truth conditions and can be taken to be a
truth value, a set of possible worlds, a context change
potential, or similar. In this short paper, we develop a vector
semantics for language based on the simply typed lambda calculus. Our
semantics uses techniques familiar from the truth conditional tradition
and is based on a form of dynamic interpretation inspired by
Heim's context updates
Density Matrices with Metric for Derivational Ambiguity
Recent work on vector-based compositional natural language semantics has
proposed the use of density matrices to model lexical ambiguity and (graded)
entailment (e.g. Piedeleu et al 2015, Bankova et al 2019, Sadrzadeh et al
2018). Ambiguous word meanings, in this work, are represented as mixed states,
and the compositional interpretation of phrases out of their constituent parts
takes the form of a strongly monoidal functor sending the derivational
morphisms of a pregroup syntax to linear maps in FdHilb. Our aims in this paper
are threefold. Firstly, we replace the pregroup front end by a Lambek
categorial grammar with directional implications expressing a word's
selectional requirements. By the Curry-Howard correspondence, the derivations
of the grammar's type logic are associated with terms of the (ordered) linear
lambda calculus; these terms can be read as programs for compositional meaning
assembly with density matrices as the target semantic spaces. Secondly, we
extend on the existing literature and introduce a symmetric, nondegenerate
bilinear form called a "metric" that defines a canonical isomorphism between a
vector space and its dual, allowing us to keep a distinction between left and
right implication. Thirdly, we use this metric to define density matrix spaces
in a directional form, modeling the ubiquitous derivational ambiguity of
natural language syntax, and show how this alows an integrated treatment of
lexical and derivational forms of ambiguity controlled at the level of the
interpretation.Comment: 24 pages, 10 figures. SemSpace 2019, to appear in J. of Applied
Logic
Monoidal computer III: A coalgebraic view of computability and complexity
Monoidal computer is a categorical model of intensional computation, where
many different programs correspond to the same input-output behavior. The
upshot of yet another model of computation is that a categorical formalism
should provide a much needed high level language for theory of computation,
flexible enough to allow abstracting away the low level implementation details
when they are irrelevant, or taking them into account when they are genuinely
needed. A salient feature of the approach through monoidal categories is the
formal graphical language of string diagrams, which supports visual reasoning
about programs and computations.
In the present paper, we provide a coalgebraic characterization of monoidal
computer. It turns out that the availability of interpreters and specializers,
that make a monoidal category into a monoidal computer, is equivalent with the
existence of a *universal state space*, that carries a weakly final state
machine for any pair of input and output types. Being able to program state
machines in monoidal computers allows us to represent Turing machines, to
capture their execution, count their steps, as well as, e.g., the memory cells
that they use. The coalgebraic view of monoidal computer thus provides a
convenient diagrammatic language for studying computability and complexity.Comment: 34 pages, 24 figures; in this version: added the Appendi
10252 Abstracts Collection -- Game Semantics and Program Verification
From 20th to 25th June 2010, the Dagstuhl Seminar
"Game Semantics and Program Verification\u27\u27 was held
in Schloss Dagstuhl - Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed.
Abstracts of the presentations given during the seminar
as well as abstracts of seminar results and ideas are put
together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
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