Related papers: INDUCTION: Finite-Structure Concept Synthesis in F…
While large language models (LLMs) have shown progress in mathematical reasoning, they still face challenges in formalizing theorems that arise from instantiating abstract structures in concrete settings. With the goal of auto-formalizing…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
Structural priming is a cognitive phenomenon where exposure to a particular syntactic structure increases the likelihood of producing the same structure in subsequent utterances. While humans consistently demonstrate structural priming…
We introduce ABD, a benchmark for default-exception abduction over finite first-order worlds. Given a background theory with an abnormality predicate and a set of relational structures, a model must output a first-order formula that defines…
In this work, we investigate whether improving task clarity can enhance reasoning ability of large language models, focusing on theorem proving in Coq. We introduce a concept-level metric to evaluate task clarity and show that adding…
This paper introduces a unifying framework that links the Context-Content Uncertainty Principle (CCUP) with optimal transport (OT) via primal-dual inference. We propose that cognitive representations are not static encodings but active dual…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
Large language models (LLMs) with Chain-of-Thought (CoT) prompting achieve strong reasoning but often produce unnecessarily long explanations, increasing cost and sometimes reducing accuracy. Fair comparison of efficiency-oriented…
Architectural imperatives due to the slowing of Moore's Law, the broad acceptance of relaxed semantics and the O(n!) worst case verification complexity of generating sequential histories motivate a new approach to concurrent correctness.…
Long chain-of-thought (Long CoT) reasoning improves performance on multi-step problems, but it also induces overthinking: models often generate low-yield reasoning that increases inference cost and latency. This inefficiency is especially…
We present three syntactic forcing models for coherent logic. These are based on sites whose underlying category only depends on the signature of the coherent theory, and they do not presuppose that the logic has equality. As an application…
We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…
We present a novel learning framework to obtain finite-state controllers (FSCs) for partially observable Markov decision processes and illustrate its applicability for indefinite-horizon specifications. Our framework builds on oracle-guided…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as…
We propose cognitive prompting as a novel approach to guide problem-solving in large language models (LLMs) through structured, human-like cognitive operations, such as goal clarification, decomposition, filtering, abstraction, and pattern…
The focus of this work is to investigate unsupervised approaches to overcome quintessential challenges in designing task-oriented dialog schema: assigning intent labels to each dialog turn (intent clustering) and generating a set of intents…
Automating the translation of natural language to first-order logic (FOL) is crucial for knowledge representation and formal methods, yet remains challenging. We present a systematic evaluation of fine-tuned LLMs for this task, comparing…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…