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Large language models (LLMs) have demonstrated remarkable capabilities in natural language understanding, reasoning, and problem-solving across various domains. However, their ability to perform complex, multi-step reasoning task-essential…
Large language models (LLMs) have demonstrated strong mathematical reasoning capabilities but remain susceptible to hallucinations producing plausible yet incorrect statements especially in theorem proving, symbolic manipulation, and…
Large language models (LLMs) have advanced in text and vision, but their reasoning on audio remains limited. Most existing methods rely on dense audio embeddings, which are difficult to interpret and often fail on structured reasoning…
Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework…
Tabling is a powerful resolution mechanism for logic programs that captures their least fixed point semantics more faithfully than plain Prolog. In many tabling applications, we are not interested in the set of all answers to a goal, but…
Symbolic regression is a fundamental tool for discovering interpretable mathematical expressions from data, with broad applications across scientific and engineering domains. Recently, large language models (LLMs) have demonstrated strong…
Logic programming with tabling and constraints (TCLP, tabled constraint logic programming) has been shown to be more expressive and, in some cases, more efficient than LP, CLP, or LP with tabling. In this paper we provide insights regarding…
This paper addresses two limitations of large language models (LLMs) in solving complex problems: (1) their reasoning processes exhibit Bayesian-like stochastic generation, where each token is sampled from a context-dependent probability…
Chain-of-Thought (CoT) prompting has significantly improved the reasoning capabilities of large language models (LLMs). However, conventional CoT often relies on unstructured, flat reasoning chains that suffer from redundancy and suboptimal…
Due to their architecture and vast pre-training data, large language models (LLMs) demonstrate strong text classification performance. However, LLM output - here, the category assigned to a text - depends heavily on the wording of the…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
In solving a query, the SLD proof procedure for definite programs sometimes searches an infinite space for a non existing solution. For example, querying a planner for an unreachable goal state. Such programs motivate the development of…
We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited…
Large Language Models (LLMs), despite their remarkable capabilities, rely on singular, pre-dominant reasoning paradigms, hindering their performance on intricate problems that demand diverse cognitive strategies. To address this, we…
Mathematical reasoning is central to artificial intelligence, with applications in education, code generation, and research-level mathematical discovery. Mathematical competitions highlight two problem types: theorem proving, requiring…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
Generative large language models (LLMs) with instruct training such as GPT-4 can follow human-provided instruction prompts and generate human-like responses to these prompts. Apart from natural language responses, they have also been found…
Mechanized verification of liveness properties for infinite programs with effects and nondeterminism is challenging. Existing temporal reasoning frameworks operate at the level of models such as traces and automata. Reasoning happens at a…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
Generating semantically coherent text requires a robust internal representation of linguistic structures, which traditional embedding techniques often fail to capture adequately. A novel approach, Latent Lexical Projection (LLP), is…