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A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
Stochastic And-Or grammars (AOG) extend traditional stochastic grammars of language to model other types of data such as images and events. In this paper we propose a representation framework of stochastic AOGs that is agnostic to the type…
Written language is a complex communication signal capable of conveying information encoded in the form of ordered sequences of words. Beyond the local order ruled by grammar, semantic and thematic structures affect long-range patterns in…
Standard probabilistic models face fundamental challenges such as data scarcity, a large hypothesis space, and poor data transparency. To address these challenges, we propose a novel probabilistic model of data-driven temporal propositional…
This paper concerns the structure of meanings within natural language. Earlier, a framework named DisCoCirc was sketched that (1) is compositional and distributional (a.k.a. vectorial); (2) applies to general text; (3) captures linguistic…
In this study, we consider sequences drawn from time-homogeneous Markov chains and introduce a novel approach for estimating first hitting-time distributions to specified terminal states. Our method- ology is based on the…
The goal of this paper is to provide a complete representation of regional linguistic variation on a global scale. To this end, the paper focuses on removing three constraints that have previously limited work within…
The paper presents a language model that develops syntactic structure and uses it to extract meaningful information from the word history, thus enabling the use of long distance dependencies. The model assigns probability to every joint…
The pre-dominant approach to language modeling to date is based on recurrent neural networks. Their success on this task is often linked to their ability to capture unbounded context. In this paper we develop a finite context approach…
We extend the Markov chain tree theorem to general commutative semirings, and we generalize the state reduction algorithm to commutative semifields. This leads to a new universal algorithm, whose prototype is the state reduction algorithm…
We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…
In this paper, we introduce the fundamental notion of a Markov basis, which is one of the first connections between commutative algebra and statistics. The notion of a Markov basis is first introduced by Diaconis and Sturmfels (1998) for…
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…
Sequential Constraint Grammar (SCG) (Karlsson, 1990) and its extensions have lacked clear connections to formal language theory. The purpose of this article is to lay a foundation for these connections by simplifying the definition of…
This paper proposes a novel statistical approach to intelligent document retrieval. It seeks to offer a more structured and extensible mathematical approach to the term generalization done in the popular Latent Semantic Analysis (LSA)…
We propose and study a novel supervised approach to learning statistical semantic relatedness models from subjectively annotated training examples. The proposed semantic model consists of parameterized co-occurrence statistics associated…
The task of linearization is to find a grammatical order given a set of words. Traditional models use statistical methods. Syntactic linearization systems, which generate a sentence along with its syntactic tree, have shown state-of-the-art…
Traditional Relational Topic Models provide a way to discover the hidden topics from a document network. Many theoretical and practical tasks, such as dimensional reduction, document clustering, link prediction, benefit from this revealed…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…