402 research outputs found
A Study of Entanglement in a Categorical Framework of Natural Language
In both quantum mechanics and corpus linguistics based on vector spaces, the
notion of entanglement provides a means for the various subsystems to
communicate with each other. In this paper we examine a number of
implementations of the categorical framework of Coecke, Sadrzadeh and Clark
(2010) for natural language, from an entanglement perspective. Specifically,
our goal is to better understand in what way the level of entanglement of the
relational tensors (or the lack of it) affects the compositional structures in
practical situations. Our findings reveal that a number of proposals for verb
construction lead to almost separable tensors, a fact that considerably
simplifies the interactions between the words. We examine the ramifications of
this fact, and we show that the use of Frobenius algebras mitigates the
potential problems to a great extent. Finally, we briefly examine a machine
learning method that creates verb tensors exhibiting a sufficient level of
entanglement.Comment: In Proceedings QPL 2014, arXiv:1412.810
Algebraic proof theory for LE-logics
In this paper we extend the research programme in algebraic proof theory from
axiomatic extensions of the full Lambek calculus to logics algebraically
captured by certain varieties of normal lattice expansions (normal LE-logics).
Specifically, we generalise the residuated frames in [16] to arbitrary
signatures of normal lattice expansions (LE). Such a generalization provides a
valuable tool for proving important properties of LE-logics in full uniformity.
We prove semantic cut elimination for the display calculi D.LE associated with
the basic normal LE-logics and their axiomatic extensions with analytic
inductive axioms. We also prove the finite model property (FMP) for each such
calculus D.LE, as well as for its extensions with analytic structural rules
satisfying certain additional properties
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