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Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…

Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped…

The contribution of this paper is the development of the syntax and semantics of multi-sorted nominal abstract binding trees (abts), an extension of second order universal algebra to support symbol-indexed families of operators. Nominal…

Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…

Large language models have achieved high performance on various question answering (QA) benchmarks, but the explainability of their output remains elusive. Structured explanations, called entailment trees, were recently suggested as a way…

Building taxonomies is often a significant part of building an ontology, and many attempts have been made to automate the creation of such taxonomies from relevant data. The idea in such approaches is either that relevant definitions of the…

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…

The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…

Much recent work suggests that incorporating syntax information from dependency trees can improve task-specific transformer models. However, the effect of incorporating dependency tree information into pre-trained transformer models (e.g.,…

Tree-structured recursive neural networks (TreeRNNs) for sentence meaning have been successful for many applications, but it remains an open question whether the fixed-length representations that they learn can support tasks as demanding as…

Haskell functions are defined as a series of clauses consisting of patterns that are matched against the arguments in the order of definition. In case an input is not matched by any of the clauses, an error occurs. Therefore it is desirable…

The chain-structured long short-term memory (LSTM) has showed to be effective in a wide range of problems such as speech recognition and machine translation. In this paper, we propose to extend it to tree structures, in which a memory cell…

Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…

A syntax tree is a planar rooted tree where internal nodes are labeled on a graded set of generators. There is a natural notion of occurrence of contiguous pattern in such trees. We describe a way, given a set of generators $\mathfrak{G}$…

Linear sequences of words are implicitly represented in our brains by hierarchical structures that organize the composition of words in sentences. Linguists formalize different frameworks to model this hierarchy; two of the most common…

Treebanks traditionally treat punctuation marks as ordinary words, but linguists have suggested that a tree's "true" punctuation marks are not observed (Nunberg, 1990). These latent "underlying" marks serve to delimit or separate…

This paper introduces a refinement of the sequent calculus approach called cirquent calculus. While in Gentzen-style proof trees sibling (or cousin, etc.) sequents are disjoint sequences of formulas, in cirquent calculus they are permitted…

We present a new framework for compositional distributional semantics in which the distributional contexts of lexemes are expressed in terms of anchored packed dependency trees. We show that these structures have the potential to capture…

Human language is known to exhibit a nested, hierarchical structure, allowing us to form complex sentences out of smaller pieces. However, many state-of-the-art neural networks models such as Transformers have no explicit hierarchical…