Conceptually it is very attractive to believe that logic in a formal sense can solve the difficult problem of machine intelligence. Human cognition in its most accessible form follows a deductive format, which is precisely what formal logic models. Logic is frequently perceived as being to restrictive a representational system to achieve the goal of artificial intelligence. This is probably true, but Nilsson believes, as do I, that successful instances of artificial intelligence will incorporate multiple techniques or methodologies. It is thus important to understand these techniques, and in particular logic, and to independently to come to grips with their individual strengths and weaknesses. By understanding formal logic in the context of its application in solving problems in AI, with all the resultant strengths and weaknesses, that a better understanding of the these issues can be arrived at. One way of measuring the success of conceptualization system for a problem is that it reveals problematic areas rather than concealing them. Formal logic reveals many critical problems in AI, and more specifically in knowledge representation, that Nilsson believes must be addressed regardless of the methodology applied.

Nilsson presents three thesis that form the basis for a logical approach to AI (as he sees it):

Thesis 1: Intelligent machines will have knowledge of their environment.

Thesis 2: The most versatile intelligent machines will represent much of their knowledge about their environments declaratively.

Thesis 3: For the most versatile machines, the language in which declarative knowledge is represented must be at least as expressive as first-order predicate calculus.

Thesis 1 seems to be so basic that it need not be mentioned, but for thoroughness Nilsson includes it. I would go slightly further in that it is a good point to introduce the concept of belief models about the environment be introduced. Nilsson elaborates on this at later point in his paper when he introduces the "finite state machine" model of an intelligent agent interacting with the surrounding world. This builds on thesis 2 in that this model is mapping of percepts received by the machine onto its current state followed by the mapping of its current state to some action which is reflected in the surrounding world to start the loop off again. This might seem overly artificial, but Nilsson argues that if the model is good enough that it leads to the desired results, that it is sufficiently accurate.

Nilsson argues that thesis 2 is important as declarative knowledge (i.e. declarative sentences) is a much more effective way to represent knowledge than procedural knowledge. Nilsson supports this argument by say that one can separate the storage of knowledge from procedures that can be applied to the knowledge and this separation leads to the ability to use that knowledge in a much larger domain than if it was bound to some procedure. It would seem to me that this becomes even more clear when one tries to build metaphors and/or analogies, which require a high level of abstraction. (Which isn't to say that one can not abstract a procedure, this just requires that the declarative, i.e. data component of the procedure be abstracted out of the procedure rather than the procedure being abstracted out of the data.)

The value of logic in knowledge representation is that it is a powerful tool (i.e. language) for conceptualizing the (or a) world. That is to say that is a good tool for constructing "intended models" of the (or a) world. The fact that one chooses logic to do this is not, in general, because one cannot use other tools for constructing these models. Nilsson argues that one cannot avoid difficulty of what to say in a given language about a given problem. No, the "win" in using logic is that it is well developed and understood, and that if you, as a designer of a new language set out to represent a new problem you are faced with repeating what has already been done in logic.

Logic can be extended into domains that are not commonly thought of as domains where logic an be applied. This includes the area of "unsound inferences" where a strong model-theoretic justification can be made for a system (such as a minimal-model entailment as mentioned by Nilsson, or a "default"/"commonsense" reasoning system). Extensions to logic such as "chunking", learned procedures, or "vivification" can be used to increase the efficiency of the inference mechanism or avoid it all together.

Finally, Nilsson reviews some of the challenging problems currently extent, some of which he presents potential solutions (such as circumscription for abstract vs. specific problem representation) and others he refers the reader to literature (such as for the "frame-problem" and uncertain knowledge). These include abstract vs. specific problem representations (and the fact that no matter how specific a representation we choose to represent a problem we will never be able to conceive of all specific cases and encode them into the problem, i.e. "the potato up the tail pipe" case), change (i.e. the "frame problem", the knowledge representation must be robust enough to represent cause and effect with any resultant change to model of the world), uncertainty and embedded systems (i.e. reason effectively to solve a problem within some bounded amount of time). In each case Nilsson argues (and for those that he actually gives potential solutions, gives some reason to believe) that logic gives a firm foundation that can be extended to solve these problems. Nilsson also admits that we do not know if we can solve the problem of knowledge representation via declarative sentences, but based on the strengths already exhibited by logic and the general lack of a clear alternative, that the pursuit of the logical solution to knowledge representation has the best chance of success.