Related papers: A Note on One Less Known Class of Generated Residu…
We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…
Motivated by the classical ideas of generating functions for orthogonal polynomials, we initiate a new line of investigation on "generating operators" for a family of differential operators between two manifolds. We prove a novel formula of…
Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose…
Using the theory of Hilbert direct integrals, we introduce and study a monotonicity-preserving operation, termed the integral resolvent mixture. It combines arbitrary families of monotone operators acting on different spaces and linear…
We report the results of our classification-based machine translation model, built upon the framework of a recurrent neural network using gated recurrent units. Unlike other RNN models that attempt to maximize the overall conditional log…
Starting from involutive BE algebras, we redefine the orthomodular algebras, by introducing the notion of implicative-orthomodular algebras. We investigate properties of implicative-orthomodular algebras, and give characterizations of these…
We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal…
We construct a countable number of differential operators $\hat{L}_n$ that annihilate a generating function for intersection numbers of $\kappa$ classes on $\Moduli_g$ (the $\kappa$-potential). This produces recursions among intersection…
The question whether a set of formulae G implies a formula f is fundamental. The present paper studies the complexity of the above implication problem for propositional formulae that are built from a systematically restricted set of Boolean…
We propose an algorithm which for any recursive group $G$, given by its effectively enumerable generators and recursively enumerable relations, outputs an explicit embedding of $G$ into a finitely presented group directly written by its…
In designing generative models, it is commonly believed that in order to learn useful latent structure, we face a fundamental tension between expressivity and structure. In this paper we challenge this view by proposing a new approach to…
In contrast to problems of interference in (exogenous) treatments, models of interference in unit-specific (endogenous) outcomes do not usually produce a reduced-form representation where outcomes depend on other units' treatment status…
Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serves as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of…
In this note we focus on combinatorial aspects of plus-one generated line arrangements. We provide combinatorial constraints on such arrangements and we construct a polynomial that decodes the plus-one generated property. We present new…
This paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FLe-algebras). In particular,…
This paper uses computational experiments to explore the role of exposure in the emergence of construction grammars. While usage-based grammars are hypothesized to depend on a learner's exposure to actual language use, the mechanisms of…
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V^G-modules which occur as submodules of irreducible V-modules by using intertwining operators for…
While originally designed for unidirectional generative modeling, decoder-only large language models (LLMs) are increasingly being adapted for bidirectional modeling. However, unidirectional and bidirectional models are typically trained…
We introduce Transformer Grammars (TGs), a novel class of Transformer language models that combine (i) the expressive power, scalability, and strong performance of Transformers and (ii) recursive syntactic compositions, which here are…