The question "Open questions in logic of artificial intelligence and programming?" touches on foundational and forward-looking issues in AI, computation, and logic. The response depends on how we interpret it—whether as a request for a survey of key problems or as a meta-question reflecting on AI's capacity to reason about its own logic and programming.

Here are some significant open questions across various dimensions:

1. Formal Logic and AI Reasoning

• Is there a universal logical framework for AI reasoning? Classical logic, modal logic, and non-monotonic logics each have strengths and weaknesses. Is a unifying theory possible?
• How can AI bridge symbolic and sub-symbolic reasoning? Deep learning lacks formal guarantees, while symbolic AI struggles with scalability. Hybrid approaches remain an open challenge.
• Can AI develop self-verifiable reasoning? Gödel’s incompleteness theorems suggest fundamental limits on formal systems. Can AI discover or bypass these in a meaningful way?

2. The Limits of AI and Computability

• What are the fundamental limits of AI decision-making? Can AI ever fully escape heuristic-based approximations, or is there a theoretical boundary similar to P ≠ NP?
• Can AI recognize its own limitations? Self-referentiality in AI raises issues akin to Russell’s Paradox and the Liar Paradox.
• Can AI systems truly exhibit metacognition? AI can optimize its learning algorithms, but can it meaningfully reflect on its own knowledge gaps?

3. AI and Programming Paradigms

• What is the 'natural' programming paradigm for AI? Traditional imperative, functional, and logic programming struggle to scale with AI’s needs. Do new paradigms like differentiable programming point the way forward?
• Can AI autonomously generate provably correct code? Formal verification is computationally expensive. Is there an AI-native way to guarantee correctness?
• Is programming fundamentally a human-centric process? If AI fully automates software development, does “programming” still exist as a human discipline?

4. Self-Reference and AI: A Meta-Question

If the original question is self-referential, it challenges AI to reflect on its own limitations in answering it. That in itself is an open problem—can an AI reason about open questions in AI logic, or is it always constrained by the formal structure of its own programming?

Perhaps the most profound open question is: Can AI ever escape the constraints of its own design and ask fundamentally new questions?