Declarative programming supports software scalability and adaptability primarily through its high-level abstraction and separation of the 'what' from the 'how'. By focusing on specifying the desired outcomes rather than the specific steps to achieve them, declarative programming makes it easier to adapt and scale software systems. For example, in a declarative language like SQL used for database operations, the queries do not need to change even if the underlying database structure or scale changes, as long as the logical data relationships remain consistent. This abstraction allows developers to modify underlying implementations without needing to rewrite the high-level code, thus enhancing adaptability. Additionally, declarative programming often leads to more modular and reusable code. Since the code is not tightly coupled with the specific steps of computation, it can be more easily repurposed or integrated into different parts of a system or even different systems altogether. This modularity and reusability are key aspects that contribute to scalability, as they allow systems to grow and evolve without necessitating extensive rewrites or adjustments to the existing codebase.

Declarative programming handles complex logic and computations by abstracting the computational process, focusing instead on defining the logic and relationships of the data. This is achieved through a high-level description of what the desired outcome should be, rather than specifying how to compute it. For instance, in a declarative language like Prolog, used for logic programming, complex logic can be expressed in terms of rules and relationships, and the language's interpreter resolves the underlying computations to deduce the conclusions. Similarly, in functional programming, which is another type of declarative paradigm, complex computations are expressed through functions that transform data. These functions can be composed and chained to express intricate computational logic. However, this abstraction can sometimes lead to less efficient execution compared to imperative languages, where the developer has more control over the specifics of the computation process. Despite this, declarative programming excels in expressing and managing complex logic, especially in domains like AI, data analysis, and database operations, where the relationships and transformations of data are more critical than the specifics of the computational steps.

Error handling and debugging in declarative programming languages can be more abstract compared to imperative languages, due to the high-level nature of declarative code. In declarative programming, errors are often related to the logic of what is being declared, rather than how it is executed. For example, in SQL, errors might arise from incorrect query logic or data relationships, rather than syntax or procedural errors. Debugging, therefore, focuses on ensuring that the declarations correctly express the intended logic or outcome. This can sometimes be challenging, as the lack of explicit control flow makes it harder to trace and diagnose issues. Declarative languages often provide tools and mechanisms to inspect and test the declared logic. For instance, in functional programming languages, unit testing and function composition can be used to isolate and test specific parts of the logic. Similarly, in SQL, query analyzers and explain plans can help understand and optimize query performance. Despite these tools, debugging in declarative programming often requires a different mindset, focusing more on understanding the high-level logic and relationships rather than tracing procedural steps. This can be both an advantage and a challenge, depending on the complexity of the problem and the familiarity of the programmer with declarative concepts.

While declarative programming is versatile, it is not universally applicable for all types of applications. Its strength lies in situations where the problem can be clearly defined in terms of the desired outcome, such as in database querying (using SQL) or user interface design (using HTML/CSS). However, it has limitations in scenarios requiring explicit control of program flow, such as real-time systems, complex algorithms, or applications with intricate state management needs. In such cases, imperative programming might be more suitable. Declarative programming abstracts away the control flow, which can lead to inefficiencies in resource usage or performance, especially in systems where low-level control is crucial. Moreover, debugging can be more challenging in a declarative paradigm, as the abstraction of control flow makes it harder to trace the exact path the program takes, particularly in complex scenarios where the outcome is not as expected. Thus, while declarative programming is powerful in certain domains, it is not a one-size-fits-all solution and should be chosen based on the specific requirements and context of the application.

Declarative programming significantly enhances code maintainability through its high-level abstraction and separation of concerns. In this paradigm, the code is written in a way that describes what the outcome should be, rather than detailing how to achieve it. This results in code that is more readable and understandable. For example, in a declarative language like SQL, a query to retrieve data is written in terms of 'what' data is needed, not 'how' to traverse the database to find it. This makes the code less prone to errors and easier to modify. If a change is required, often only the declaration needs to be updated, not the underlying procedure. This abstraction also leads to fewer side effects, as the declarative code doesn't directly manipulate the program's state. Additionally, since the code is more focused on the desired outcome, it becomes more intuitive to understand and modify, thus reducing the learning curve for new developers and increasing the overall maintainability of the software.