PACS: Probabilistic Commonsense Reasoning Framework—A New Abductive Reasoning Approach for Modeling Individual Belief Differences

This article introduces the Probabilistic Abductive Commonsense Reasoning (PACS) algorithm. By explicitly modeling individual differences in commonsense beliefs, combining large language models (LLMs) and formal solvers to sample proofs, and aggregating commonsense beliefs from multiple individuals, it addresses the problem of formal reasoners lacking world knowledge and outperforms chain-of-thought and neuro-symbolic methods on several benchmarks.

Commonsense Dilemma in Neuro-Symbolic Reasoning

In recent years, neuro-symbolic frameworks have combined LLMs with formal logic solvers, but formal solvers lack commonsense world knowledge and cannot complete reasoning steps that humans find easy.

Blind Spots of Existing Solutions

Previous solutions used LLMs to provide commonsense assumptions, but they implicitly made the wrong assumption that commonsense is universally consistent. In reality, there are individual differences in commonsense beliefs (e.g., disagreements on "whether dogs are dangerous" or "whether spicy food is harmful"), and simply assuming a standard answer can easily lead to results that contradict intuition.

The core idea of the PACS framework is to explicitly model individual differences in commonsense beliefs and use probabilistic methods to aggregate multiple perspectives to judge whether a statement aligns with the commonsense of the majority.

Nature of Abductive Reasoning

Inferring the best explanation from observed results (e.g., inferring rain from wet ground) is a common pattern in commonsense reasoning.

Probabilistic Modeling

Model individual beliefs as probability distributions, acknowledge belief diversity, and capture distribution characteristics through sampling.

PACS executes three steps:

1. Belief Sampling: Use LLMs to generate commonsense assumption sets for multiple virtual individuals to capture the belief distribution;
2. Formal Proof: Combine formal solvers to construct logically valid reasoning proofs under each belief set;
3. Conclusion Aggregation: Statistically calculate the proportion of individuals supporting a certain conclusion to reflect the mainstream view.

PACS performs excellently in evaluations across multiple reasoning benchmarks:

• Outperforms chain-of-thought reasoning: Explicit formal reasoning and probabilistic commonsense modeling are more effective;
• Superior to neuro-symbolic methods: Flexible handling of commonsense disagreements leads to performance improvements;
• Beats search methods: The sampling-aggregation strategy balances effectiveness and efficiency.

PACS represents a paradigm shift: from pursuing absolutely correct reasoning to accepting probabilistic consensus.

• Human-like AI: Understand the influence of culture and experience on human reasoning;
• Domain Implications: Provide probabilistic modeling ideas for knowledge representation, decision-making, ethical judgment, etc.

Limitations of PACS and future exploration directions:

1. Sampling Efficiency: Reduce LLM call and solving costs, develop efficient sampling strategies;
2. Belief Calibration: Ensure the sampled belief distribution reflects human diversity and avoid biases in training data;
3. Dynamic Updates: Enable the system to adapt to changes in commonsense beliefs over time.

Through the probabilistic abductive reasoning framework, PACS bridges the gap between formal systems and commonsense knowledge, acknowledges commonsense diversity, captures group consensus through sampling and aggregation, leads on benchmarks, and opens up new paths for commonsense reasoning research.