The Rise and Fall of Symbolic AI Philosophical presuppositions of AI by Ranjeet Singh

Most recently, an extension to arbitrary (irregular) graphs then became extremely popular as Graph Neural Networks (GNNs). Driven heavily by the empirical success, DL then largely moved away from the original biological brain-inspired models of perceptual intelligence to “whatever works in practice” kind of engineering approach. In essence, the concept evolved into a very generic methodology of using gradient descent to optimize parameters of almost arbitrary nested functions, for which many like to rebrand the field yet again as differentiable programming. This view then made even more space for all sorts of new algorithms, tricks, and tweaks that have been introduced under various catchy names for the underlying functional blocks (still consisting mostly of various combinations of basic linear algebra operations). Historically, the two encompassing streams of symbolic and sub-symbolic stances to AI evolved in a largely separate manner, with each camp focusing on selected narrow problems of their own.

Powered by such a structure, the DSN model is expected to learn like humans, because of its unique characteristics. First, it is universal, using the same structure to store any knowledge. Second, it can learn symbols from the world and construct the deep symbolic networks automatically, by utilizing the fact that real world objects have been naturally separated by singularities.

Evidence for Perceptual Manipulations Theory

Maruyama et al. (2012) argue on the basis of fMRI and MEG evidence that mathematical expressions like these are parsed quickly by visual cortex, using mechanisms that are shared with non-mathematical spatial perception tasks. On one hand, students can think about such problems syntactically, as a specific instance of the more general logical form “All Xs are Ys; All Ys are Zs; Therefore, all Xs are Zs.” On the other hand, they might think about them semantically—as relations between subsets, for example. In an analogous fashion, two prominent scientific attempts to explain how students are able to solve symbolic reasoning problems can be distinguished according to their emphasis on syntactic or semantic properties. Full logical expressivity means that LNNs support an expressive form of logic called first-order logic.

But how is it that “primitive” sensorimotor processes can give rise to some of the most sophisticated mathematical behaviors? Unlike many traditional accounts, PMT does not presuppose that mathematical and logical rules must be internally represented in order to be followed. Analogous to the syntactic approach above, computationalism holds that the capacity for symbolic reasoning is carried out by mental processes of syntactic rule-based symbol-manipulation. In its canonical form, these processes take place in a general-purpose “central reasoning system” that is functionally encapsulated from dedicated and modality-specific sensorimotor “modules” (Fodor, 1983; Sloman, 1996; Pylyshyn, 1999; Anderson, 2007).

Moreover, they lack the ability to reason on an abstract level, which makes it difficult to implement high-level cognitive functions such as transfer learning, analogical reasoning, and hypothesis-based reasoning. Finally, their operation is largely opaque to humans, rendering them unsuitable for domains in which verifiability is important. In this paper, we propose an end-to-end reinforcement learning architecture comprising a neural back end and a symbolic front end with the potential to overcome each of these shortcomings. As proof-of-concept, we present a preliminary implementation of the architecture and apply it to several variants of a simple video game. We show that the resulting system – though just a prototype – learns effectively, and, by acquiring a set of symbolic rules that are easily comprehensible to humans, dramatically outperforms a conventional, fully neural DRL system on a stochastic variant of the game. Symbolic AI is a branch of artificial intelligence that uses symbols and rules to represent knowledge and reasoning processes.

His approach highlights how symbolic reasoning can enhance the ability of generative systems to create accurate depictions, something modern LLMs still need to work on. As seen recently with Stability AI’s release of Stable Diffusion 3 Medium, the latest AI image-synthesis model has been heavily criticized online for generating anatomically incorrect images. Despite advancements in AI, these visual abominations underscore the ongoing challenges in accurately depicting human forms, a problem Cohen’s symbolic approach addressed over half a century ago. One is based on possible worlds; the other is based on symbolic manipulation of expressions. Yet, for “well-behaved” logics, it turns out that logical entailment and provability are identical – a set of premises logically entails a conclusion if and only if the conclusion is provable from the premises.

For another, even a single individual may rely on different strategies in different situations, depending on the particular notations being employed at the time. Some of the relevant strategies may cross modalities, and be applicable in various mathematical domains; others may exist only within a single modality and within a limited formal context. Although in this particular case such cross-domain mapping leads to a formal error, it need not always be mistaken—as when understanding that “~~X” is equivalent to “X,” just as “??x” is equal to “x.” In some contexts, such perceptual strategies lead to mathematical success. In other contexts, however, the same strategies lead to mathematical failure. People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning—as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion.

Symbolic Reasoning (Symbolic AI) and Machine Learning

Even if the number of worlds is infinite, it is possible in such logics to produce a finite proof of the conclusion, i.e. we can determine logical entailment without going through all possible worlds. Symbolic AI involves the explicit embedding of human knowledge and behavior rules into computer programs. The practice showed a lot of promise in the early decades of AI research.

This idea has also been later extended by providing corresponding algorithms for symbolic knowledge extraction back from the learned network, completing what is known in the NSI community as the “neural-symbolic learning cycle”. Meanwhile, with the progress in computing power and amounts of available data, another approach to AI has begun to gain momentum. Statistical machine learning, originally targeting “narrow” problems, such as regression and classification, has begun to penetrate the AI field.

Expert systems are monotonic; that is, the more rules you add, the more knowledge is encoded in the system, but additional rules can’t undo old knowledge. Monotonic basically means one direction; i.e. when one thing goes up, another thing goes up. Because machine learning algorithms can be retrained on new data, and will revise their parameters based on that new data, they are better at encoding tentative knowledge that can be retracted later if necessary; i.e. if they need to learn something new, like when data is non-stationary. Because machine learning algorithms can be retrained on new data, and will revise their parameters based on that new data, they are better at encoding tentative knowledge that can be retracted later if necessary. Think of them as a secret alphabet where ‘?’ stands for ‘and’, ‘?’ for ‘or’, and so on. Then you’ll translate regular sentences into these symbols, kind of like learning a new language.

The brain regions involved in high-level cognitive tasks do not overlap with those used for language, suggesting that language serves primarily as a communication code. Language facilitates the transfer of information rather than being the substrate for complex thought processes. The study remarks, “Many individuals with acquired brain damage exhibit difficulties in reasoning and problem-solving but appear to have full command of their linguistic abilities,” reinforcing that undamaged language abilities do not imply intact thought??. Despite their differences, there are many commonalities among these logics. In particular, in each case, there is a language with a formal syntax and a precise semantics; there is a notion of logical entailment; and there are legal rules for manipulating expressions in the language. Logic eliminates these difficulties through the use of a formal language for encoding information.

Given four girls, there are sixteen possible instances of the likes relation – Abby likes Abby, Abby likes Bess, Abby likes Cody, Abby likes Dana, Bess likes Abby, and so forth. There are 216 (65,536) possible combinations of these true-false possibilities, and so there are 216 possible worlds. It is used primarily by mathematicians in proving complicated theorems in geometry or number theory. It is all about writing formal proofs to be published in scholarly papers that have little to do with everyday life.

Although other versions of computationalism do not posit a strict distinction between central and sensorimotor processing, they do generally assume that sensorimotor processing can be safely “abstracted away” (e.g., Kemp et al., 2008; Perfors et al., 2011). These mental symbols and expressions are then operated on by syntactic rules that instantiate mathematical and logical principles, and that are typically assumed to take the form of productions, laws, or probabilistic causal structures (Newell and Simon, 1976; Sloman, 1996; Anderson, 2007). Once a solution is computed, it is converted back into a publicly observable (i.e., written or spoken) linguistic or notational formalism.

Using symbolic AI, everything is visible, understandable and explainable, leading to what is called a ‘transparent box’ as opposed to the ‘black box’ created by machine learning. In a nutshell, symbolic AI involves the explicit embedding of human knowledge and behavior rules into computer programs. Interestingly, we note that the simple logical XOR function is actually still challenging to learn properly even in modern-day deep learning, which we will discuss in the follow-up article. However, the black-box nature of classic neural models, with most confirmations on their learning abilities being done empirically rather than analytically, renders some direct integration with the symbolic systems, possibly providing the missing capabilities, rather complicated.

Consequently, all these methods are merely approximations of the true underlying relational semantics. It has now been argued by many that a combination of deep learning with the high-level reasoning capabilities present in the symbolic, logic-based approaches is necessary to progress towards more general AI systems [9,11,12]. The concept of neural networks (as they were called before the deep learning “rebranding”) has actually been around, with various ups and downs, for a few decades already. It dates all the way back to 1943 and the introduction of the first computational neuron [1].

In talking about Logic, we now have two notions – logical entailment and provability. A set of premises logically entails a conclusion if and only if every possible world that satisfies the premises also satisfies the conclusion. A sentence is provable from a set of premises if and only if there is a finite sequence of sentences in which every element is either a premise or the result of applying a deductive rule of inference to earlier members in the sequence. First of all, correctness in logical reasoning is determined by the logical operators in our sentences, not the objects and relationships mentioned in those sentences. Second, the conclusion is guaranteed to be true only if the premises are true. We start with a look at the essential elements of logic – logical sentences, logical entailment, and logical proofs.

The language of Logic can be used to encode regulations and business rules, and automated reasoning techniques can be used to analyze such regulations for inconsistency and overlap. Logical spreadsheets generalize traditional spreadsheets to include logical constraints as well as traditional arithmetic formulas. For example, in scheduling applications, we might have timing constraints or restrictions on who can reserve which rooms. In the domain of travel reservations, we might have constraints on adults and infants.

When you provide it with a new image, it will return the probability that it contains a cat. There have been several efforts to create complicated symbolic AI systems that encompass the multitudes of rules of certain domains. Called expert systems, these symbolic AI models use hardcoded knowledge and rules to tackle complicated tasks such as medical diagnosis.

Thinking correctly and effectively requires training in Logic, just as writing well requires training in English and composition. Without explicit training, we are likely to be unsure of our conclusions; we are prone to make mistakes; and we are apt to be fooled by others. Artificial intelligence software was used to enhance the grammar, flow, and readability of this article’s text. “Pushing symbols,” Proceedings of the 31st Annual Conference of the Cognitive Science Society. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

As you can easily imagine, this is a very heavy and time-consuming job as there are many many ways of asking or formulating the same question. And if you take into account that a knowledge base usually holds on average 300 intents, you now see how repetitive maintaining a knowledge base can be when using machine learning. For instance, one prominent idea was to encode the (possibly infinite) interpretation structures of a logic program by (vectors of) real numbers and represent the relational inference as a (black-box) mapping between these, based on the universal approximation theorem. However, this assumes the unbound relational information to be hidden in the unbound decimal fractions of the underlying real numbers, which is naturally completely impractical for any gradient-based learning.

With this paradigm shift, many variants of the neural networks from the ’80s and ’90s have been rediscovered or newly introduced. Benefiting from the substantial increase in the parallel processing power of modern GPUs, and the ever-increasing amount of available data, deep learning has been steadily paving its way to completely dominate the (perceptual) ML. Discover how integrating symbolic reasoning into AI can enhance its capabilities.

External symbolic notations need not be translated into internal representational structures, but neither does all mathematical reasoning occur by manipulating perceived notations on paper. Rather, complex visual and auditory processes such as affordance learning, perceptual pattern-matching and perceptual grouping of notational structures produce simplified representations of the mathematical problem, simplifying the task faced by the rest of the symbolic reasoning system. Perceptual processes exploit the typically well-designed features of physical notations to automatically reduce and simplify difficult, routine formal chores, and so are themselves constitutively involved in the capacity for symbolic reasoning. On our view, therefore, much of the capacity for symbolic reasoning is implemented as the perception, manipulation and modal and cross-modal representation of externally perceived notations. That is, they assume that all transformations that involve changes in semantic structure take place “internally,” over Mentalese expressions, mental models, metaphors or simulations, and that sensorimotor interactions with physical notations involve (at most) a change in representational format.

So the main challenge, when we think about GOFAI and neural nets, is how to ground symbols, or relate them to other forms of meaning that would allow computers to map the changing raw sensations of the world to symbols and then reason about them. These dynamic models finally enable to skip the preprocessing step of turning the relational representations, such as interpretations of a relational logic program, into the fixed-size vector (tensor) format. They do so by effectively reflecting the variations in the input data structures into variations in the structure of the neural model itself, constrained by some shared parameterization (symmetry) scheme reflecting the respective model prior. While the aforementioned correspondence between the propositional logic formulae and neural networks has been very direct, transferring the same principle to the relational setting was a major challenge NSI researchers have been traditionally struggling with. The issue is that in the propositional setting, only the (binary) values of the existing input propositions are changing, with the structure of the logical program being fixed. And while these concepts are commonly instantiated by the computation of hidden neurons/layers in deep learning, such hierarchical abstractions are generally very common to human thinking and logical reasoning, too.

More advanced knowledge-based systems, such as Soar can also perform meta-level reasoning, that is reasoning about their own reasoning in terms of deciding how to solve problems and monitoring the success of problem-solving strategies. This page includes some recent, notable research that attempts to combine deep learning with symbolic learning to answer those questions. Symbolic logic is a system that takes sentences apart and shows the connections between their pieces using symbols. By doing this, you can find out whether the sentence is set up in a way that makes logical sense. The beauty of symbolic logic is that it turns arguments into almost a puzzle that you can piece together. It’s like translating a sentence into a secret code where each symbol has a specific meaning.

These pioneers crafted symbolic logic into the precise, finely tuned tool that it is today, comparable to a mathematician’s trusty set of formulas and equations. Note the similarity to the propositional and relational machine learning we discussed in the last article. Perhaps surprisingly, the correspondence between the neural and logical calculus has been well established throughout history, Chat GPT due to the discussed dominance of symbolic AI in the early days. Functional Logic takes us one step further by providing a means for describing worlds with infinitely many objects. The resulting logic is much more powerful than Propositional Logic and Relational Logic. Unfortunately, as we shall see, some of the nice computational properties of the first two logics are lost as a result.

With the rules of logic, you can move these symbols around, swap them, or combine them in different ways to explore the argument. It’s a little like following a recipe where the rules are your ingredients and steps. You end up with a clear idea of whether the argument holds up to scrutiny. Since its foundation as an academic discipline in 1955, Artificial Intelligence (AI) research field has been divided into different camps, of which symbolic AI and machine learning. While symbolic AI used to dominate in the first decades, machine learning has been very trendy lately, so let’s try to understand each of these approaches and their main differences when applied to Natural Language Processing (NLP). However, in the meantime, a new stream of neural architectures based on dynamic computational graphs became popular in modern deep learning to tackle structured data in the (non-propositional) form of various sequences, sets, and trees.

During the first AI summer, many people thought that machine intelligence could be achieved in just a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research to use AI to solve problems of national security; in particular, to automate the translation of Russian to English for intelligence operations and to create autonomous tanks for the battlefield. By the mid-1960s neither useful natural language translation systems nor autonomous tanks had been created, and a dramatic backlash set in. This is easy to think of as a boolean circuit (neural network) sitting on top of a propositional interpretation (feature vector). However, the relational program input interpretations can no longer be thought of as independent values over a fixed (finite) number of propositions, but an unbound set of related facts that are true in the given world (a “least Herbrand model”). Consequently, also the structure of the logical inference on top of this representation can no longer be represented by a fixed boolean circuit.

Furthermore, it can generalize to novel rotations of images that it was not trained for. In this vein, since many forms of advanced mathematical reasoning rely on graphical representations and geometric principles, it would be surprising to find that perceptual and sensorimotor processes are not involved in a constitutive way. Therefore, by accounting for symbolic reasoning—perhaps the most abstract of all forms of mathematical reasoning—in perceptual and sensorimotor terms, we have attempted to lay the groundwork for an account of mathematical and logical reasoning more generally.

We know that all Accords are Hondas, and we know that all Hondas are Japanese cars. Consequently, we can conclude that all Accords are Japanese cars. what is symbolic reasoning Ideally, when we have enough sentences, we know exactly how things stand. Of course, in general, there are more than two possible worlds to consider.

Given the syntax and semantics of this formal language, we can give a precise definition for the notion of logical conclusion. Moreover, we can establish precise reasoning rules that produce all and only logical conclusions. Deep neural networks are also very suitable for reinforcement learning, AI models that develop their behavior through numerous trial and error. This is the kind of AI that masters complicated games such as Go, StarCraft, and Dota. Also, some tasks can’t be translated to direct rules, including speech recognition and natural language processing.

It wasn’t until the 1980’s, when the chain rule for differentiation of nested functions was introduced as the backpropagation method to calculate gradients in such neural networks which, in turn, could be trained by gradient descent methods. For that, however, researchers had to replace the originally used binary threshold units with differentiable activation functions, such as the sigmoids, which started digging a gap between the neural networks and their crisp logical interpretations. This only escalated with the arrival of the deep learning (DL) era, with which the field got completely dominated by the sub-symbolic, continuous, distributed representations, seemingly ending the story of symbolic AI.

Symbols in the language represent “conditions” in the world, and complex sentences in the language express interrelationships among these conditions. The primary operators are Boolean connectives, such as and, or, and not. Today, the prospect of automated reasoning has moved from the realm of possibility to that of practicality, with the creation of logic technology in the form of automated reasoning systems, such as Vampire, Prover9, the Prolog Technology Theorem Prover, and others. Such complexities and ambiguities can sometimes be humorous if they lead to interpretations the author did not intend. See the examples below for some infamous newspaper headlines with multiple interpretations.

Stacking these on top of each other into layers then became quite popular in the 1980s and ’90s already. However, at that time they were still mostly losing the competition against the more established, and better theoretically substantiated, learning models like SVMs. We see Neuro-symbolic AI as a pathway to achieve artificial general intelligence.

2) The two problems may overlap, and solving one could lead to solving the other, since a concept that helps explain a model will also help it recognize certain patterns in data using fewer examples. As a consequence, the Botmaster’s job is completely different when using Symbolic AI technology than with Machine Learning-based technology as he focuses on writing new content for the knowledge base rather than utterances of existing content. He also has full transparency on how to fine-tune the engine when it doesn’t work properly as he’s been able to understand why a specific decision has been made and has the tools to fix it.

In situations like this, which world should we use in answering questions? Even though a set of sentences does not determine a unique world, there are some sentences that have the same truth value in every world that satisfies the given sentences, and we can use that value in answering questions. Once we know which world is correct, we can see that some sentences must be true even though they are not included in the premises we are given. For example, in the first world we saw above, we can see that Bess likes Cody, even though we are not told this fact explicitly.

By writing logical sentences, each informant can express exactly what he or she knows – no more, no less. The following sentences are examples of different types of logical sentences. The first sentence is straightforward; it tells us directly that Dana likes Cody. The second and third sentences tell us what is not true without saying what is true.

Even in philosophy’s diverse landscape, from ethics to metaphysics, it’s a versatile tool for disentangling some exceptionally knotty problems. Note the similarity to the use of background knowledge in the Inductive Logic Programming approach to Relational ML here. Although Logic is a single field of study, there is more than one logic in this field. In the three main units of this book, we look at three different types of logic, each more sophisticated than the one before.

The Disease Ontology is an example of a medical ontology currently being used. In contrast to the US, in Europe the key AI programming language during that same period was Prolog. Prolog provided a built-in store of facts and clauses that could be queried by a read-eval-print loop. The store could act as a knowledge base and the clauses could act as rules or a restricted form of logic. As a subset of first-order logic Prolog was based on Horn clauses with a closed-world assumption—any facts not known were considered false—and a unique name assumption for primitive terms—e.g., the identifier barack_obama was considered to refer to exactly one object.

Automated reasoning tools can be used to simulate designs and in some cases validate that these designs meet their specification. Such tools can also be used to diagnose failures and to develop testing programs. Of all types of reasoning, deduction is the only one that guarantees its conclusions in all cases, it produces only those conclusions that are logically entailed by one’s premises. The philosopher Bertrand Russell summed this situation up as follows.

Although translational accounts may eventually be elaborated to accommodate this evidence, it is far more easily and naturally accommodated by accounts which, like PMT, attribute a constitutive role to perceptual processing. While emphasizing the ways in which notations are acted upon, however, proponents of the cyborg view rarely consider how such notations are perceived. Sometimes, this neglect is intentional, as when the utility of cognitive artifacts is explained by stating that they become assimilated into a “body schema” in which “sensorimotor capacities function without… the necessity of perceptual monitoring” (Gallagher, 2005, p. 25). At other times, this neglect seems to be unintended, however, and subject to corrective elaboration. Hinton and many others have tried hard to banish symbols altogether.

However, there have also been some major disadvantages including computational complexity, inability to capture real-world noisy problems, numerical values, and uncertainty. Due to these problems, most of the symbolic AI approaches remained in their elegant theoretical forms, and never really saw any larger practical adoption in applications (as compared to what we see today). You can foun additiona information about ai customer service and artificial intelligence and NLP. By conceptualizing database tables as sets of simple sentences, it is possible to use Logic in support of database systems. For example, the language of Logic can be used to define virtual views of data in terms of explicitly stored tables, and it can be used to encode constraints on databases. Automated reasoning techniques can be used to compute new tables, to detect problems, and to optimize queries.

We propose the Neuro-Symbolic Concept Learner (NS-CL), a model that learns visual concepts, words, and semantic parsing of sentences without explicit supervision on any of them; instead, our model learns by simply looking at images and reading paired questions and answers. Our model builds an object-based scene representation and translates sentences into executable, symbolic programs. To bridge the learning of two modules, we use a neuro-symbolic reasoning module that executes these programs on the latent scene representation. Analog to the human concept learning, given the parsed program, the perception module learns visual concepts based on the language description of the object being referred to. Meanwhile, the learned visual concepts facilitate learning new words and parsing new sentences.

Knowledge-based systems have an explicit knowledge base, typically of rules, to enhance reusability across domains by separating procedural code and domain knowledge. A separate inference engine processes rules and adds, deletes, or modifies a knowledge store. The automated theorem provers discussed below can prove theorems in first-order logic. Horn clause logic is more restricted than first-order logic and is used in logic programming languages such as Prolog. Extensions to first-order logic include temporal logic, to handle time; epistemic logic, to reason about agent knowledge; modal logic, to handle possibility and necessity; and probabilistic logics to handle logic and probability together. Expert systems can operate in either a forward chaining – from evidence to conclusions – or backward chaining – from goals to needed data and prerequisites – manner.

• In this regard, there is a strong analogy between the methods of Formal Logic and those of high school algebra.
• The study remarks, “Many individuals with acquired brain damage exhibit difficulties in reasoning and problem-solving but appear to have full command of their linguistic abilities,” reinforcing that undamaged language abilities do not imply intact thought??.
• Yet it is rarely offered as a standalone course, making it more difficult for students to succeed and get better quality jobs.
• Early work covered both applications of formal reasoning emphasizing first-order logic, along with attempts to handle common-sense reasoning in a less formal manner.
• OOP languages allow you to define classes, specify their properties, and organize them in hierarchies.

Therefore, the key to understanding the human capacity for symbolic reasoning in general will be to characterize typical sensorimotor strategies, and to understand the particular conditions in which those strategies are successful or unsuccessful. For other AI programming languages see this list of programming languages for artificial intelligence. Currently, Python, a multi-paradigm programming language, is the most popular programming language, partly due to its extensive https://chat.openai.com/ package library that supports data science, natural language processing, and deep learning. Python includes a read-eval-print loop, functional elements such as higher-order functions, and object-oriented programming that includes metaclasses. Henry Kautz,[19] Francesca Rossi,[81] and Bart Selman[82] have also argued for a synthesis. Their arguments are based on a need to address the two kinds of thinking discussed in Daniel Kahneman’s book, Thinking, Fast and Slow.

One difficult problem encountered by symbolic AI pioneers came to be known as the common sense knowledge problem. In addition, areas that rely on procedural or implicit knowledge such as sensory/motor processes, are much more difficult to handle within the Symbolic AI framework. In these fields, Symbolic AI has had limited success and by and large has left the field to neural network architectures (discussed in a later chapter) which are more suitable for such tasks. In sections to follow we will elaborate on important sub-areas of Symbolic AI as well as difficulties encountered by this approach. Building on the foundations of deep learning and symbolic AI, we have developed software that can answer complex questions with minimal domain-specific training. Our initial results are encouraging – the system achieves state-of-the-art accuracy on two datasets with no need for specialized training.

This lead towards the connectionist paradigm of AI, also called non-symbolic AI which gave rise to learning and neural network-based approaches to solve AI. They also assume complete world knowledge and do not perform as well on initial experiments testing learning and reasoning. One of the main stumbling blocks of symbolic AI, or GOFAI, was the difficulty of revising beliefs once they were encoded in a rules engine.