Related papers: Inductive Reasoning for Coinductive Types
\ac{CoT} prompting improves LLM accuracy on complex tasks but often increases token usage and inference cost. Existing ``Budget Forcing'' methods reduce cost via fine-tuning with heuristic length penalties, suppressing both essential…
Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…
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…
interpreters are tools to compute approximations for behaviors of a program. These approximations can then be used for optimisation or for error detection. In this paper, we show how to describe an abstract interpreter using the type-theory…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
Large language models make remarkable progress in reasoning capabilities. Existing works focus mainly on deductive reasoning tasks (e.g., code and math), while another type of reasoning mode that better aligns with human learning, inductive…
Answering logical queries on knowledge graphs (KG) poses a significant challenge for machine reasoning. The primary obstacle in this task stems from the inherent incompleteness of KGs. Existing research has predominantly focused on…
Despite recent successes of large pre-trained language models in solving reasoning tasks, their inference capabilities remain opaque. We posit that such models can be made more interpretable by explicitly generating interim inference rules,…
Large language models (LLMs) have achieved remarkable multi-step reasoning capabilities across various domains. However, LLMs still face distinct challenges in complex logical reasoning, as (1) proof-finding requires systematic exploration…
Chain-of-Thought (CoT) has unlocked advanced reasoning abilities of Large Language Models (LLMs) with intermediate steps, yet incurs prohibitive computational costs due to generation of extra tokens. Recent studies empirically show that…
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…
Traditional retrieval methods rely on transforming user queries into vector representations and retrieving documents based on cosine similarity within an embedding space. While efficient and scalable, this approach often fails to handle…
Chain-of-thought (CoT) prompting for language models demonstrates impressive performance across reasoning tasks, but typically needs labeled exemplars of the reasoning process. In this work, we introduce a new prompting approach, analogical…
Largely adopted by proof assistants, the conventional induction methods based on explicit induction schemas are non-reductive and local, at schema level. On the other hand, the implicit induction methods used by automated theorem provers…
Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) infinite data. Both instances of coinductive reasoning appeared in…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Due to the proliferation of short-form content and the rapid adoption of AI, opportunities for deep, reflective thinking have significantly diminished, undermining users' critical thinking and reducing engagement with the reasoning behind…
Chain-of-Thought (CoT) prompting can enhance the reasoning capabilities of large language models (LLMs), establishing itself as a primary approach to solving complex reasoning tasks. Existing CoT synthesis approaches usually focus on…
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…