Related papers: Extensional Higher-Order Paramodulation in Leo-III

Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…

Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…

Machine intelligence marks the ultimate dream of making machines' intelligence comparable to human beings. While recent progress in Large Language Models (LLMs) show substantial specific skills for a wide array of downstream tasks, they…

Large Language Models (LLMs) are often used as automated judges to evaluate text, but their effectiveness can be hindered by various unintentional biases. We propose using linear classifying probes, trained by leveraging differences between…

This paper develops a novel nested sequent proof-search methodology for intuitionistic tense logics (ITLs), supporting finite counter-model extraction. We introduce a new loop-checking method that detects repeating nested sequents using…

Post-training techniques combined with inference-time scaling significantly enhance the reasoning and alignment capabilities of large language models (LLMs). However, a fundamental tension arises: inference-time methods benefit from diverse…

Commonsense reasoning has long been considered as one of the holy grails of artificial intelligence. Most of the recent progress in the field has been achieved by novel machine learning algorithms for natural language processing. However,…

Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…

Inductive Logic Programming (ILP) provides interpretable rule learning in relational domains, yet remains limited in its ability to induce and reason with numerical constraints. Classical ILP systems operate over discrete predicates and…

We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of…

The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often…

Large language models (LLMs) exhibit strong reasoning capabilities but typically require expensive post-training to reach high performance. Recent test-time alignment methods offer a lightweight alternative, but have been explored mainly…

We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on…

Prompting and fine-tuning have emerged as two competing paradigms for augmenting language models with new capabilities, such as the use of tools. Prompting approaches are quick to set up but rely on providing explicit demonstrations of each…

Combining different forms of prompts with pre-trained large language models has yielded remarkable results on reasoning tasks (e.g. Chain-of-Thought prompting). However, along with testing on more complex reasoning, these methods also…

The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore…

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…

A key challenge in automated formal reasoning is the intractable search space, which grows exponentially with the depth of the proof. This branching is caused by the large number of candidate proof tactics which can be applied to a given…

Hammers are tools that provide general purpose automation for formal proof assistants. Despite the gaining popularity of the more advanced versions of type theory, there are no hammers for such systems. We present an extension of the…

Recently, latent reasoning has been introduced into large language models (LLMs) to leverage rich information within a continuous space. However, without stochastic sampling, these methods inevitably collapse to deterministic inference,…