What is the knowledge base paradigm and why do we need it ?

Declarative knowledge and its use for solving problems is studied in various fields such as knowledge representation and reasoning (KRR), computational logic and declarative problem solving paradigms. In the past half a century, an immense body of scientific knowledge about knowledge and its use for solving problems has been collected in these various domains. Yet, at this moment no coherent scientific approach to the study of knowledge and its use for problem solving has emerged. Scientific understanding is scattered over the many fields that study it.

One issue that fragments the study of knowledge and reasoning more than anything else is the type of inference (the type of reasoning with this knowledge). Historically, the study of logic was seen as the study of reasoning. This inference-centric view naturally leads to different logics specialized on specific forms of inference. To start with, classical first order logic (FO) is sometimes defined as the logic of deductive reasoning. But database languages (SQL, Datalog) are logics for query answering; constraint programming (CP) for constraint solving; answer set programming (ASP) for solving problems by computing answer sets, temporal logics for model checking, etc. All these logics differ strongly at the level of the underlying inference mechanism as well as on their syntax and on their scientific terminologies.

But knowledge is independent of the sort of reasoning task. Take the proposition:

During opening hours, at least one secretary is present at the entrance desk.

What task is this proposition to be used for? It could be used as a query to a scheduling database, or as a constraint in a scheduling problem, or as a property to be verified from a formal specification of a scheduling problem, or as a correctness property to be proven of a program that computes schedules. The proposition in itself is not bound to any specific problem or form of inference; yet, in the current state of the art, depending on the problem, the proposition needs to be rephrased in a logic that supports the required type of inference.

In fact, the proposition has a natural representation as the sentence in first order logic:

        ∀t : Open(t) ⇒ ∃s : Secretary(s) ∧ at(s, EntranceDesk, t).

Assume we want to solve a scheduling problem satisfying this formula. For a long time a “deductive” logic like FO was deemed unsuitable for such problem. Often this was blamed on the fact that deduction in FO is undecidable. However, the more essential reason is that the scheduling problem is simply not a deductive problem and FO theorem provers are useless. Instead, other declarative paradigms were developed for this such as CP.

The mix up of reasoning with the knowledge representation language is not a desirable situation; neither from a scientific point of view as it obscures the nature of knowledge and obfuscates it with the form of reasoning, nor from a pragmatical point of view as it forces the knowledge engineer to rephrase the same proposition in different logics to get different problems solved. What is needed is a knowledge-oriented scientific approach to study knowledge separated from inference and problem solving, that allows to study knowledge with scientific methods, that studies how to express knowledge as naturally and compactly as possible, and that studies the various sorts of problems that can be solved using a knowledge base. It leads to the idea to build software solutions by expressing domain knowledge in a symbolic knowledge base, and use it to solve a range of problems and tasks by applying various inference methods. Such a system is what we understand by the term ``a knowledge base system’’.

Why start from classical first order logic (FO)?

Classical first order logic dates from the late nineteenth century. Why use that logic? Because it’s language constructs \(\land, \lor, \neg, \Rightarrow , \Leftrightarrow, \forall, \exists\) are basic indispensable construct for expressing human knowledge. Moreover, FO’s formal semantics correctly captures their meaning.

Why extend FO?

Classical language is really a very small language, with only 7 language constructs. It can be improved for knowledge representation in many different ways.