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We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces…
A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
Recursive neural models, which use syntactic parse trees to recursively generate representations bottom-up, are a popular architecture. But there have not been rigorous evaluations showing for exactly which tasks this syntax-based method is…
Coalgebras for analytic functors uniformly model graph-like systems where the successors of a state may admit certain symmetries. Examples of successor structure include ordered tuples, cyclic lists and multisets. Motivated by goals in…
Parse trees are fundamental syntactic structures in both computational linguistics and compilers construction. We argue in this paper that, in both fields, there are good incentives for model-checking sets of parse trees for some word…
Turi and Plotkin's bialgebraic semantics is an abstract approach to specifying the operational semantics of a system, by means of a distributive law between its syntax (encoded as a monad) and its dynamics (an endofunctor). This setup is…
Initial semantics aims to model inductive structures and their properties, and to provide them with recursion principles respecting these properties. An ubiquitous example is the fold operator for lists. We are concerned with initial…
We present the first parser for UCCA, a cross-linguistically applicable framework for semantic representation, which builds on extensive typological work and supports rapid annotation. UCCA poses a challenge for existing parsing techniques,…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
Programming physicists use, as all programmers, arrays, lists, tuples, records, etc., and this requires some change in their thought patterns while converting their formulae into some code, since the "data structures" operated upon, while…
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
Word representations induced from models with discrete latent variables (e.g.\ HMMs) have been shown to be beneficial in many NLP applications. In this work, we exploit labeled syntactic dependency trees and formalize the induction problem…
Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models…
Class algebra provides a natural framework for sharing of ISA hierarchies between users that may be unaware of each other's definitions. This permits data from relational databases, object-oriented databases, and tagged XML documents to be…
We present the results of an investigation into how the set of elementary trees of a Lexicalized Tree Adjoining Grammar can be represented in the lexical knowledge representation language DATR (Evans & Gazdar 1989a,b). The LTAG under…