Type theory of acyclic recursion and acyclic algorithms

Roussanka Loukanova

In my talk, I present Type Theory of Acyclic Recursion (TTAR) and Acyclic Algorithms (TTAA). TTAA supports algorithmic Syntax-Semantics Interfaces for varieties of approaches to computational grammar. Specifically, TTAA provides mathematical foundations and algorithmic semantics of computational grammar, including varieties of Constraint-Based Lexicalized Grammar (CBLG), such as HPSG, and MRS technique in and outside HPSG.

Dependent-Type Theory of Situated Information and Algorithms (TTofSIA / SIA) extends TTAA and provides mathematical foundations of partial information in relational data and algorithmic semantics of formal and natural languages, including for CBLG, HPSG, and MRS.

TTofSIA has potentials for algorithmic interfaces between computational grammar, algorithmic semantics, and Large Language Models (LLM), via Algorithmic Syntax-Semantics interfaces and numerical assessments, e.g., via mathematical probabilities and statistics. I demonstrate the prospective numerical assessments in TTofSIA by examples.