Tootfinder

Logical Reasoning with Outcome Reward Models for Test-Time Scaling
Ramya Keerthy Thatikonda, Wray Buntine, Ehsan Shareghi
https://arxiv.org/abs/2508.19903 https://

Logical Reasoning with Outcome Reward Models for Test-Time Scaling
Logical reasoning is a critical benchmark for evaluating the capabilities of large language models (LLMs), as it reflects their ability to derive valid conclusions from given premises. While the combination of test-time scaling with dedicated outcome or process reward models has opened up new avenues to enhance LLMs performance in complex reasoning tasks, this space is under-explored in deductive logical reasoning. We present a set of Outcome Reward Models (ORMs) for deductive reasoning. To tra…

Generative Logic: A New Computer Architecture for Deterministic Reasoning and Knowledge Generation
Nikolai Sergeev
https://arxiv.org/abs/2508.00017 https://

Generative Logic: A New Computer Architecture for Deterministic Reasoning and Knowledge Generation
We present Generative Logic (GL), a deterministic architecture that begins from user-supplied axiomatic definitions -- written in a minimalist Mathematical Programming Language (MPL) -- and systematically explores their deductive neighborhood. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; any time several expressions unify under an inference rule, a new fact is emitted with full provenance to its sources, yielding replayable, auditable pro…

Investigating Advanced Reasoning of Large Language Models via Black-Box Interaction
Congchi Yin, Tianyi Wu, Yankai Shu, Alex Gu, Yunhan Wang, Jun Shao, Xun Jiang, Piji Li
https://arxiv.org/abs/2508.19035

Investigating Advanced Reasoning of Large Language Models via Black-Box Interaction
Existing tasks fall short in evaluating reasoning ability of Large Language Models (LLMs) in an interactive, unknown environment. This deficiency leads to the isolated assessment of deductive, inductive, and abductive reasoning, neglecting the integrated reasoning process that is indispensable for humans discovery of real world. We introduce a novel evaluation paradigm, \textit{black-box interaction}, to tackle this challenge. A black-box is defined by a hidden function that maps a specific set…

Beyond Statistical Learning: Exact Learning Is Essential for General Intelligence
Andr\'as Gy\"orgy, Tor Lattimore, Nevena Lazi\'c, Csaba Szepesv\'ari
https://arxiv.org/abs/2506.23908

Beyond Statistical Learning: Exact Learning Is Essential for General Intelligence
Sound deductive reasoning -- the ability to derive new knowledge from existing facts and rules -- is an indisputably desirable aspect of general intelligence. Despite the major advances of AI systems in areas such as math and science, especially since the introduction of transformer architectures, it is well-documented that even the most advanced frontier systems regularly and consistently falter on easily-solvable deductive reasoning tasks. Hence, these systems are unfit to fulfill the dream o…

Synthesis Benchmarks for Automated Reasoning
M\'arton Hajdu, Petra Hozzov\'a, Laura Kov\'acs, Andrei Voronkov, Eva Maria Wagner, Richard Steven \v{Z}ilin\v{c}\'ik
https://arxiv.org/abs/2507.19827

Synthesis Benchmarks for Automated Reasoning
Program synthesis is the task of constructing a program conforming to a given specification. We focus on deductive synthesis, and in particular on synthesis problems with specifications given as $\forall\exists$-formulas, expressing the existence of an output corresponding to any input. So far there has been no canonical benchmark set for deductive synthesis using the $\forall\exists$-format and supporting the so-called uncomputable symbol restriction. This work presents such a data set, compos…

Unfolding Iterators: Specification and Verification of Higher-Order Iterators, in OCaml
Ion Chirica, M\'ario Pereira
https://arxiv.org/abs/2506.20310 h…

Unfolding Iterators: Specification and Verification of Higher-Order Iterators, in OCaml
Albeit being a central notion of every programming language, formally and modularly reasoning about iteration proves itself to be a non-trivial feat, specially in the context of higher-order iteration. In this paper, we present a generic approach to the specification and deductive verification of higher-order iterators, written in the OCaml language. Our methodology follows two key principles: first, the usage of the Gospel specification language to describe the general behaviour of any iterati…

Finite Axiomatizability by Disjunctive Existential Rules
Marco Calautti, Marco Console, Andreas Pieris
https://arxiv.org/abs/2508.11946 https://arxiv.org/p…

Finite Axiomatizability by Disjunctive Existential Rules
Rule-based languages lie at the core of several areas of central importance to databases and artificial intelligence such as deductive databases and knowledge representation and reasoning. Disjunctive existential rules (a.k.a. disjunctive tuple-generating dependencies in the database literature) form such a prominent rule-based language. The goal of this work is to pinpoint the expressive power of disjunctive existential rules in terms of insightful model-theoretic properties. More precisely, g…