Logical Challenges in Artificial General Intelligence

The present thesis pertains to the research area of logic for artificial intelligence (AI), and is motivated by the critical role of automated reasoning in AI, particularly by the capacity of automated reasoning to support logical inference, problem-solving, and explainable decision-making. Automated reasoning serves as a fundamental building block of symbolic AI, and is essential for constructing general-purpose intelligent systems that can operate transparently and reliably. The current AI systems, such as Large Language Models (LLMs), rely on statistical correlations learned from vast datasets. This limits their capacity for robust and generalizable reasoning involving complex, novel, or counterfactual scenarios, and moreover, lacks trustworthy explanations of their outputs. To address these limitations, the emerging field of neural-symbolic AI seeks to integrate the statistical strengths of neural models with the structural rigor of symbolic reasoning. Automated reasoning, as a symbolic technique, remains central to these efforts, especially as AI applications increasingly demand higher standards of transparency, responsibility, and generalization. The field is therefore exploring a range of logical systems beyond classical logic—including non-monotonic, probabilistic, and modal logics—to better capture the uncertain, dynamic, and context-sensitive nature of human reasoning. The present thesis aims to advance symbolic formalizations in three key areas where current AI systems continue to struggle: conceptual reasoning, causal reasoning, and defeasible reasoning. These reasoning modes are vital for representing complex human knowledge structures, understanding causal relationships, and making decisions in the presence of incomplete or conflicting information. In the domain of conceptual reasoning, Formal Concept Analysis (FCA), description logic, and lattice-based logics are used to model conceptual hierarchies and category dynamics, to investigate how agents can generalize, classify, and compare concepts within dynamic knowledge systems. These tools allow for structured representation and reasoning with concepts. The present thesis investigates the application of LE-ALC, a logical framework which combines FCA and description logic, to ontology-mediated query answering, and illustrates how it can be used to answer different types of queries involving conceptual relationships. In the area of causal reasoning, the present thesis addresses the need for formal models that go beyond correlation to capture the semantics of interventions and counterfactuals. Building on Pearl’s Structural Causal Models (SCMs), the present thesis proposes a hybrid framework (causal Kripke models) that incorporates epistemic modalities in causal inference. This framework includes a formal definition of counterfactuals under minimal change conditions, avoiding erroneous causal attributions, and aligning more closely with intuitive human reasoning about cause and effect. Within the domain of defeasible reasoning, the present thesis extends the KLM framework, and defines three types of defeasible consequence relations within lattice-based logic. These include defeasible object-level entailment (where most members of a category belong to another category), defeasible feature-level entailment (where most attributes of a category apply to another category), and combined entailment over both objects and features. These allow for exception-tolerant reasoning across categories and features, supporting more human-like reasoning capabilities. In conclusion, the present thesis makes technical contributions to the development of symbolic frameworks that enhance the explainability and generalization abilities of AI systems. By formalizing conceptual, causal, and defeasible reasoning within lattice-based and modal logics, the contributions of the present thesis help to bridge the gap between data-driven learning and human-like inferential structures, contributing to the broader goal of building more transparent, trustworthy, and cognitively plausible AI.