Related papers: A Tractable Extension of Linear Indexed Grammars
The evaluation of iterated primitives of powers of logarithms is expressed in closed form. The expressions contain polynomials with coefficients given in terms of the harmonic numbers and their generalizations. The logconcavity of these…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
The $N$th power of a polynomial matrix of fixed size and degree can be computed by binary powering as fast as multiplying two polynomials of linear degree in~$N$. When Fast Fourier Transform (FFT) is available, the resulting complexity is…
We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector…
We give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs-as-programs correspondence. Girard's seminal results, concerning elementary and light linear logic, achieve this…
While a great effort has concerned the development of fully integrated modular understanding systems, few researches have focused on the problem of unifying existing linguistic formalisms with cognitive processing models. The Situated…
Although pretrained language models (PLMs) can be prompted to perform a wide range of language tasks, it remains an open question how much this ability comes from generalizable linguistic understanding versus surface-level lexical patterns.…
We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a…
In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting. This approach is based on a partial order and a metric on term graphs. These…
We investigate the extent to which modern, neural language models are susceptible to structural priming, the phenomenon whereby the structure of a sentence makes the same structure more probable in a follow-up sentence. We explore how…
We investigate the expressive power of $\mathsf{MATLANG}$, a formal language for matrix manipulation based on common matrix operations and linear algebra. The language can be extended with the operation $\mathsf{inv}$ of inverting a matrix.…
We propose a generalization of Categorial Grammar in which lexical categories are defined by means of recursive constraints. In particular, the introduction of relational constraints allows one to capture the effects of (recursive) lexical…
We introduce a novel way to incorporate prior information into (semi-) supervised non-negative matrix factorization, which we call differentiable dictionary search. It enables general, highly flexible and principled modelling of mixtures…
We study cooperating distributed grammar systems working in hybrid modes in connection with the finite index restriction in two different ways: firstly, we investigate cooperating distributed grammar systems working in hybrid modes which…
We propose to employ the hierarchical coarse-grained structure in the artificial neural networks explicitly to improve the interpretability without degrading performance. The idea has been applied in two situations. One is a neural network…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
A temporal graph is a graph in which vertices communicate with each other at specific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is modeled by an edge from $A$ to $B$ with starting time "11 a.m." and duration "7…
Workflows constitute an important language to represent knowledge about processes, but also increasingly to reason on such knowledge. On the other hand, there is a limit to which time constraints between activities can be expressed.…
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…
The purpose of this article is to investigate triangularization and simultaneous triangularization of matrices over max algebras using graph theoretic methods. We establish a connection between commutators and commutants with simultaneous…