Related papers: Tree Rewriting Calculi for Strictly Positive Logic…
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
This paper advances the theoretical understanding of active learning label complexity for decision trees as binary classifiers. We make two main contributions. First, we provide the first analysis of the disagreement coefficient for…
We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical…
Using Reinforcement Learning with Verifiable Rewards (RLVR) to optimize Large Language Models (LLMs) can be conceptualized as progressively editing a query's `Reasoning Tree'. This process involves exploring nodes (tokens) and dynamically…
Reframing a negative into a positive thought is at the crux of several cognitive approaches to mental health and psychotherapy that could be made more accessible by large language model-based solutions. Such reframing is typically…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
Large language models (LLMs), such as LLaMA, Alpaca, Vicuna, GPT-3.5 and GPT-4, have advanced the performance of AI systems on various natural language processing tasks to human-like levels. However, their generalisation and robustness when…
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…
Reinforcement learning (RL) training of large language models (LLMs) on unverifiable tasks is challenging even when a reasonable-quality reference answer is available. We propose a constrained RL training framework that (i) optimizes a…
We study rewriting systems whose underlying set of terms is equipped with a vector space structure over a given field. We introduce parallel rewriting relations, which are rewriting relations compatible with the vector space structure, as…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions…
Counterfactual explanations inform ways to achieve a desired outcome from a machine learning model. However, such explanations are not robust to certain real-world changes in the underlying model (e.g., retraining the model, changing…
To describe the transverse momentum spectrum of heavy color-singlet production, the joint resummation of threshold and transverse momentum logarithms is investigated. We obtain factorization theorems for various kinematic regimes valid to…
Logical fallacy uses invalid or faulty reasoning in the construction of a statement. Despite the prevalence and harmfulness of logical fallacies, detecting and classifying logical fallacies still remains a challenging task. We observe that…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…