Related papers: Extensional Higher-Order Paramodulation in Leo-III
Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these…
This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover. The proof formalized is close to that of Hughes and Cresswell, but the system, based on a…
Large Language Models (LLMs) can acquire extensive world knowledge through pre-training on large corpora. However, due to exposure to low-quality data, LLMs may exhibit harmful behavior without aligning with human values. The dominant…
Tool-Integrated Reasoning (TIR) extends LLM capabilities by leveraging external environments. However, existing methods lack the deliberation during sequential tool invocation required for strategic planning and self-correction. While RL…
Large language models (LLMs) have increasingly leveraged tool invocation to enhance their reasoning capabilities. However, existing approaches typically tightly couple tool invocation with immediate execution. Such immediate tool…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
Does prompting a large language model (LLM) like GPT-3 with explanations improve in-context learning? We study this question on two NLP tasks that involve reasoning over text, namely question answering and natural language inference. We…
Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
Logical reasoning of text is an important ability that requires understanding the information present in the text, their interconnections, and then reasoning through them to infer new conclusions. Prior works on improving the logical…
Reasoning protocols such as Chain of Thought (CoT) and Tree of Thought (ToT) organize internal deliberation but lack an explicit mechanism for external questioning that elicits self-revision. We present FOR-Prompting (From Objection to…
The evolution of Large Language Model (LLM) reasoning is bottlenecked by the scarcity of high-quality process data. While self-alignment via endogenous rewards offers a solution, mining valid supervision faces three challenges: (1) Label…
OTTER is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyperresolution, UR-resolution, and binary paramodulation. Some of its other abilities and…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning.…
Large language models (LLMs) have recently achieved significant advances in reasoning and demonstrated their advantages in solving challenging problems. Yet, their effectiveness in the semiconductor display industry remains limited due to a…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to…
In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic. Our starting point is the observation that once embedded in the relational semantics of linear logic, the Church…
LLMs approach logical and mathematical reasoning through natural or symbolic languages. While natural language offers human-accessible flexibility but suffers from ambiguity, symbolic reasoning provides precise, machine-executable…