Understanding the Question: The Kāraka theory is Pāṇini’s way of mapping the relationship between things (nouns) and actions (verbs). We need to identify the nature of this relationship.
Key Concepts and Approach: While "Cases" (Vibhakti) are morphological endings, Kārakas are the underlying semantic roles (like Agent, Object, Instrument) that these endings represent.
Detailed Solution:
Step 1: Defining Kāraka. A Kāraka is defined as "Kriyā-nimittaṃ kārakam" or "Kriyānvayi kārakam"—that which is instrumental in the performance of an action or has a direct semantic link to the verb.
Step 2: Types of Relations. There are 6 Kārakas: Kartṛ (Agent), Karman (Object), Karaṇa (Instrument), Sampradāna (Recipient), Apādāna (Source), and Adhikaraṇa (Locus).
Step 3: Semantic vs Morphological. A single Kāraka (semantic role) can be expressed by different cases (morphology). Because the theory focuses on the "role" in the action rather than just the spelling/ending, it is a semantic theory.
Conclusion: The Kāraka theory defines the semantic relation between a noun and a verb.