TLDR: A longitudinal study evaluated the logical reasoning of frontier Large Language Models (LLMs) from 2023 to 2025, showing performance improvements attributed to hidden Chain of Thought prompting and the introduction of ‘thinking models’. The research also presented a neuro-symbolic architecture, combining smaller LLMs with an SMT solver (Z3), which achieved near-perfect accuracy at a significantly reduced computational cost, highlighting the efficiency of hybrid AI approaches for deductive reasoning.
A recent study delves into the evolving logical reasoning capabilities of Large Language Models (LLMs) over an eighteen-month period, from December 2023 to June 2025. The research, titled Large Language Models Imitate Logical Reasoning, but at what Cost?, was conducted by Lachlan McGinness and Peter Baumgartner from the Australian National University and Data61|CSIRO. It explores how frontier LLMs have improved in answering true or false questions from the PrOntoQA dataset and their adherence to reasoning strategies provided through in-context learning.
The study highlights a significant debate in the AI community: whether LLMs truly possess intelligent reasoning abilities or are merely advanced pattern recognition systems. While LLMs excel at generating plausible text and predicting the next token, their capacity for strict deductive reasoning has been a contentious topic. Symbolic AI approaches, such as Satisfiability Modulo Theory (SMT) solvers, are known for their rigorous deductive reasoning but lack the flexibility to process natural language inputs.
To bridge this gap, the researchers investigated two main approaches: ‘shallow embedding’ and ‘deep embedding’ of reasoning. Shallow embedding involves instructing LLMs with specific reasoning strategies through in-context learning, like Chain of Thought (CoT), Bottom Up, Top Down, and Magic Set Transformation. Deep embedding, on the other hand, involves LLMs translating natural language problems into a formal logical syntax that can then be solved by automated reasoning systems.
The longitudinal study tracked the performance of leading LLMs across three time points: December 2023 (GPT3, GPT4, Gemini), September 2024 (GPT4o, Claude Sonnet 3.5, Llama 3.1 405B), and June 2025 (DeepSeek R1, GPT-o3, Gemini 2.5Pro). They also examined smaller open-source models (Phi4, Gemma3 12B, Falcon 10B) in combination with an SMT solver called Z3.
A key finding was the notable improvement in LLM performance from 2023 to 2024, which the authors attribute to ‘hidden Chain of Thought’ prompting. This suggests that models were internally prompted or trained to automatically engage in step-by-step reasoning. The period between 2024 and 2025 saw further significant improvements with the introduction of ‘thinking models,’ which are explicitly trained to process information before generating a response. These models, such as Gemini 2.5 Pro and GPT-o3, achieved near-perfect scores on the PrOntoQA dataset.
However, this enhanced reasoning capability in large frontier models often comes at a substantial computational cost. The paper also explored a neuro-symbolic architecture where smaller LLMs (under 15 billion parameters) were used to translate natural language problems into a standardized logical form. This form was then parsed into a program for Z3, an SMT solver, to determine the satisfiability of the query. This neuro-symbolic approach demonstrated a significant reduction in computational cost while maintaining near-perfect performance, proving that LLMs can be effectively combined with symbolic AI for efficient and accurate reasoning.
The computational cost was approximated using FLOPs (floating-point operations), and the common approximation that inference FLOPs are double the product of active parameters and total tokens was found to be accurate within 10% for all experiments. The CPU time spent by Z3 was negligible compared to the GPU time required for running the small LLMs, reinforcing the efficiency of the hybrid approach.
Also Read:
- Verifiable Question Answering: Bridging LLMs and Formal Logic for Educational Systems
- Enhancing LLM Reasoning with Latent Thought Optimization
The study concludes that while advancements in LLM training and prompting have led to impressive reasoning imitation, particularly with the advent of ‘thinking models,’ a neuro-symbolic framework offers a compelling alternative. By leveraging LLMs’ strengths in natural language understanding and translation, combined with the rigorous deductive power of SMT solvers, high accuracy can be achieved at a fraction of the computational expense. This opens important avenues for future work, especially in applying this hybrid approach to more complex real-world problems and sophisticated automated theorem proving benchmarks.
