Related papers: Boolean perspectives of idioms and the Boyle deriv…
Idioms are unlike most phrases in two important ways. First, the words in an idiom have non-canonical meanings. Second, the non-canonical meanings of words in an idiom are contingent on the presence of other words in the idiom. Linguistic…
Existing sentence representations primarily encode what a sentence says, rather than how it is expressed, even though the latter is important for many applications. In contrast, we develop sentence representations that capture style and…
Recent years have witnessed a renewed interest in Boolean function in explaining binary classifiers in the field of explainable AI (XAI). The standard approach of Boolean function is propositional logic. We present a modal language of a…
We investigate the processing of idiomatic expressions in transformer-based language models using a novel set of techniques for circuit discovery and analysis. First discovering circuits via a modified path patching algorithm, we find that…
We revisit once again the connection between three notions of computation: monads, arrows and idioms (also called applicative functors). We employ monoidal categories of finitary functors and profunctors on finite sets as models of these…
We give a unified treatment of the model theory of various enrichments of infinite atomic Boolean algebras, with special attention to quantifier-eliminations, complete axiomatizations and decidability. A classical example is the enrichment…
Unlike literal expressions, idioms' meanings do not directly follow from their parts, posing a challenge for neural machine translation (NMT). NMT models are often unable to translate idioms accurately and over-generate compositional,…
Additive composition (Foltz et al, 1998; Landauer and Dumais, 1997; Mitchell and Lapata, 2010) is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this…
The concept of complementarity in combination with a non-Boolean calculus of propositions refers to a pivotal feature of quantum systems which has long been regarded as a key to their distinction from classical systems. But a non-Boolean…
The paper presents several combinatorial properties of the boolean cumulants. A corollary is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted for the case of boolean independence with…
Textual humor is enormously diverse and computational studies need to account for this range, including intentionally bad humor. In this paper, we curate and analyze a novel corpus of sentences from the Bulwer-Lytton Fiction Contest to…
Decompilers are important tools for reverse engineers that help them analyze software at a higher level of abstraction than assembly code. Unfortunately, because compilation is lossy, deterministic decompilers produce code that is missing…
We define lifting properties for universal algebras, which we study in this general context and then particularize to various such properties in certain classes of algebras. Next we focus on residuated lattices, in which we investigate…
The objects under inspection, on a given probability space, are noise(-type) Boolean algebras -- distributive non-empty sublattices of the lattice of all complete sub-$\sigma$-fields, whose every element admits an independent complement.…
We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\alpha), where \alpha is a Boolean variable. Intuitively, with Boolean dependence…
We present a fairly large, Potential Idiomatic Expression (PIE) dataset for Natural Language Processing (NLP) in English. The challenges with NLP systems with regards to tasks such as Machine Translation (MT), word sense disambiguation…
Unlike classical and free independence, the boolean and monotone notions of independence lack of the property of independent constants. In the scalar case, this leads to restrictions for the central limit theorems, as observed by F.…
In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We…
Idioms have long posed a challenge due to their unique linguistic properties, which set them apart from other common expressions. While recent studies have leveraged large language models (LLMs) to handle idioms across various tasks, e.g.,…
The symmetric difference in Boolean lattices can be defined in two different but equivalent forms. However, it can be introduced also in every bounded lattice with complementation where these two forms need not coincide. We study lattices…