Symbolic Artificial Intelligence

In artificial intelligence, symbolic expert system (also known as classical artificial intelligence or logic-based expert system) [1] [2] is the term for the collection of all approaches in synthetic intelligence research study that are based on high-level symbolic (human-readable) representations of problems, reasoning and search. [3] Symbolic AI utilized tools such as logic shows, production guidelines, semantic internet and frames, and it established applications such as knowledge-based systems (in specific, skilled systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to critical ideas in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and restrictions of formal knowledge and thinking systems.

Symbolic AI was the dominant paradigm of AI research study from the mid-1950s till the mid-1990s. [4] Researchers in the 1960s and the 1970s were convinced that symbolic approaches would ultimately succeed in developing a maker with artificial general intelligence and considered this the supreme goal of their field. [citation needed] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, led to unrealistic expectations and pledges and was followed by the first AI Winter as moneying dried up. [5] [6] A 2nd boom (1969-1986) happened with the rise of specialist systems, their pledge of catching business know-how, and a passionate business accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later on dissatisfaction. [8] Problems with problems in knowledge acquisition, keeping big understanding bases, and brittleness in handling out-of-domain problems developed. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers concentrated on dealing with underlying issues in handling uncertainty and in knowledge acquisition. [10] Uncertainty was resolved with formal methods such as hidden Markov models, Bayesian thinking, and analytical relational learning. [11] [12] Symbolic machine discovering dealt with the knowledge acquisition issue with contributions including Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree learning, case-based knowing, and inductive reasoning programming to find out relations. [13]

Neural networks, a subsymbolic technique, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt’s perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and operate in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not viewed as successful till about 2012: “Until Big Data ended up being commonplace, the general consensus in the Al community was that the so-called neural-network method was helpless. Systems just didn’t work that well, compared to other methods. … A transformation was available in 2012, when a variety of individuals, consisting of a group of researchers working with Hinton, exercised a method to utilize the power of GPUs to immensely increase the power of neural networks.” [16] Over the next several years, deep learning had magnificent success in handling vision, speech recognition, speech synthesis, image generation, and maker translation. However, because 2020, as intrinsic troubles with predisposition, description, comprehensibility, and effectiveness became more apparent with deep learning techniques; an increasing variety of AI researchers have required combining the very best of both the symbolic and neural network techniques [17] [18] and resolving areas that both techniques have problem with, such as sensible reasoning. [16]

A brief history of symbolic AI to the present day follows below. Time durations and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture [19] and the longer Wikipedia article on the History of AI, with dates and titles varying slightly for increased clarity.

The very first AI summertime: unreasonable enthusiasm, 1948-1966

Success at early attempts in AI occurred in three main locations: synthetic neural networks, understanding representation, and heuristic search, adding to high expectations. This section sums up Kautz’s reprise of early AI history.

Approaches influenced by human or animal cognition or behavior

Cybernetic techniques tried to duplicate the feedback loops in between animals and their environments. A robotic turtle, with sensors, motors for driving and guiding, and seven vacuum tubes for control, based on a preprogrammed neural web, was constructed as early as 1948. This work can be seen as an early precursor to later operate in neural networks, support knowing, and positioned robotics. [20]

An important early symbolic AI program was the Logic theorist, written by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it was able to show 38 primary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later on generalized this work to develop a domain-independent problem solver, GPS (General Problem Solver). GPS fixed issues represented with formal operators via state-space search utilizing means-ends analysis. [21]

During the 1960s, symbolic methods attained terrific success at replicating smart habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was focused in 4 institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Each one established its own design of research. Earlier methods based upon cybernetics or artificial neural networks were deserted or pressed into the background.

Herbert Simon and Allen Newell studied human analytical abilities and tried to formalize them, and their work laid the foundations of the field of artificial intelligence, along with cognitive science, operations research and management science. Their research group used the outcomes of mental experiments to develop programs that simulated the methods that individuals utilized to fix issues. [22] [23] This tradition, centered at Carnegie Mellon University would eventually culminate in the development of the Soar architecture in the middle 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific kinds of knowledge that we will see later on used in expert systems, early symbolic AI scientists found another more basic application of knowledge. These were called heuristics, guidelines that direct a search in appealing directions: “How can non-enumerative search be useful when the underlying problem is greatly difficult? The method promoted by Simon and Newell is to use heuristics: quick algorithms that might fail on some inputs or output suboptimal solutions.” [26] Another essential advance was to find a method to use these heuristics that guarantees an option will be discovered, if there is one, not enduring the occasional fallibility of heuristics: “The A * algorithm provided a general frame for total and optimum heuristically guided search. A * is utilized as a subroutine within almost every AI algorithm today however is still no magic bullet; its warranty of efficiency is purchased the cost of worst-case exponential time. [26]

Early work on understanding representation and thinking

Early work covered both applications of official reasoning highlighting first-order reasoning, together with efforts to handle common-sense thinking in a less official way.

Modeling formal thinking with logic: the “neats”

Unlike Simon and Newell, John McCarthy felt that machines did not require to replicate the precise mechanisms of human idea, but might instead attempt to find the essence of abstract thinking and analytical with logic, [27] despite whether individuals used the very same algorithms. [a] His lab at Stanford (SAIL) concentrated on utilizing formal reasoning to solve a wide range of problems, consisting of knowledge representation, planning and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and somewhere else in Europe which resulted in the advancement of the programs language Prolog and the science of logic programming. [32] [33]

Modeling implicit common-sense understanding with frames and scripts: the “scruffies”

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] found that fixing difficult problems in vision and natural language processing needed advertisement hoc solutions-they argued that no basic and general concept (like reasoning) would record all the aspects of intelligent habits. Roger Schank explained their “anti-logic” methods as “scruffy” (rather than the “cool” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “scruffy” AI, considering that they need to be constructed by hand, one complex principle at a time. [38] [39] [40]

The first AI winter season: crushed dreams, 1967-1977

The very first AI winter season was a shock:

During the first AI summer, lots of people thought that device intelligence might be attained in simply a couple of years. The Defense Advance Research Projects Agency (DARPA) introduced programs to support AI research study to utilize AI to fix issues of national security; in particular, to automate the translation of Russian to English for intelligence operations and to create autonomous tanks for the battlefield. Researchers had actually begun to recognize that achieving AI was going to be much harder than was expected a years previously, however a mix of hubris and disingenuousness led numerous university and think-tank scientists to accept funding with guarantees of deliverables that they must have known they might not meet. By the mid-1960s neither useful natural language translation systems nor self-governing tanks had actually been developed, and a dramatic reaction embeded in. New DARPA leadership canceled existing AI financing programs.

Beyond the United States, the most fertile ground for AI research was the UK. The AI winter in the United Kingdom was stimulated on not so much by disappointed military leaders as by competing academics who viewed AI scientists as charlatans and a drain on research study financing. A teacher of applied mathematics, Sir James Lighthill, was commissioned by Parliament to examine the state of AI research in the nation. The report mentioned that all of the problems being worked on in AI would be much better handled by scientists from other disciplines-such as used mathematics. The report also claimed that AI successes on toy issues might never scale to real-world applications due to combinatorial surge. [41]

The second AI summertime: understanding is power, 1978-1987

Knowledge-based systems

As constraints with weak, domain-independent approaches became a growing number of apparent, [42] researchers from all 3 customs began to construct knowledge into AI applications. [43] [7] The knowledge revolution was driven by the realization that knowledge underlies high-performance, domain-specific AI applications.

Edward Feigenbaum said:

– “In the understanding lies the power.” [44]
to explain that high performance in a specific domain needs both basic and extremely domain-specific understanding. Ed Feigenbaum and Doug Lenat called this The Knowledge Principle:

( 1) The Knowledge Principle: if a program is to perform a complicated job well, it should know a fantastic deal about the world in which it operates.
( 2) A possible extension of that principle, called the Breadth Hypothesis: there are 2 extra capabilities necessary for smart habits in unforeseen circumstances: falling back on increasingly basic knowledge, and analogizing to particular however distant understanding. [45]

Success with expert systems

This “knowledge revolution” resulted in the advancement and release of expert systems (introduced by Edward Feigenbaum), the first commercially effective type of AI software application. [46] [47] [48]

Key expert systems were:

DENDRAL, which found the structure of organic molecules from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and suggested additional lab tests, when necessary – by interpreting laboratory outcomes, patient history, and medical professional observations. “With about 450 guidelines, MYCIN had the ability to perform as well as some professionals, and considerably much better than junior doctors.” [49] INTERNIST and CADUCEUS which dealt with internal medication diagnosis. Internist attempted to catch the know-how of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS might eventually detect as much as 1000 different illness.
– GUIDON, which demonstrated how a knowledge base developed for professional problem solving could be repurposed for teaching. [50] XCON, to configure VAX computer systems, a then laborious process that might use up to 90 days. XCON decreased the time to about 90 minutes. [9]
DENDRAL is considered the first professional system that relied on knowledge-intensive analytical. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

One of the individuals at Stanford interested in computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I wanted an induction “sandbox”, he stated, “I have just the one for you.” His laboratory was doing mass spectrometry of amino acids. The concern was: how do you go from looking at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we started the DENDRAL Project: I was proficient at heuristic search techniques, and he had an algorithm that was proficient at producing the chemical issue area.

We did not have a grand vision. We worked bottom up. Our chemist was Carl Djerassi, creator of the chemical behind the birth control tablet, and likewise one of the world’s most appreciated mass spectrometrists. Carl and his postdocs were first-rate specialists in mass spectrometry. We began to add to their knowledge, creating knowledge of engineering as we went along. These experiments amounted to titrating DENDRAL increasingly more understanding. The more you did that, the smarter the program became. We had excellent outcomes.

The generalization was: in the understanding lies the power. That was the huge concept. In my career that is the substantial, “Ah ha!,” and it wasn’t the way AI was being done previously. Sounds simple, however it’s most likely AI’s most effective generalization. [51]

The other expert systems mentioned above came after DENDRAL. MYCIN exemplifies the classic specialist system architecture of a knowledge-base of rules combined to a symbolic thinking system, including the use of certainty aspects to manage uncertainty. GUIDON shows how a specific understanding base can be repurposed for a 2nd application, tutoring, and is an example of an intelligent tutoring system, a specific type of knowledge-based application. Clancey revealed that it was not adequate merely to utilize MYCIN’s guidelines for guideline, however that he also required to include guidelines for discussion management and student modeling. [50] XCON is significant due to the fact that of the countless dollars it saved DEC, which triggered the expert system boom where most all major corporations in the US had skilled systems groups, to capture corporate know-how, protect it, and automate it:

By 1988, DEC’s AI group had 40 specialist systems released, with more en route. DuPont had 100 in usage and 500 in development. Nearly every major U.S. corporation had its own Al group and was either utilizing or investigating expert systems. [49]

Chess professional understanding was encoded in Deep Blue. In 1996, this allowed IBM’s Deep Blue, with the assistance of symbolic AI, to win in a video game of chess against the world champ at that time, Garry Kasparov. [52]

Architecture of knowledge-based and expert systems

A crucial part of the system architecture for all specialist systems is the understanding base, which shops truths and rules for problem-solving. [53] The easiest method for a skilled system knowledge base is merely a collection or network of production guidelines. Production rules connect signs in a relationship similar to an If-Then statement. The expert system processes the rules to make deductions and to identify what extra information it needs, i.e. what questions to ask, using human-readable symbols. For example, OPS5, CLIPS and their followers Jess and Drools run in this fashion.

Expert systems can operate in either a forward chaining – from evidence to conclusions – or backwards chaining – from goals to needed information and prerequisites – manner. More advanced knowledge-based systems, such as Soar can also perform meta-level reasoning, that is reasoning about their own thinking in terms of deciding how to resolve issues and keeping track of the success of analytical methods.

Blackboard systems are a 2nd type of knowledge-based or skilled system architecture. They model a neighborhood of professionals incrementally contributing, where they can, to fix a problem. The issue is represented in numerous levels of abstraction or alternate views. The specialists (understanding sources) offer their services whenever they recognize they can contribute. Potential problem-solving actions are represented on a program that is upgraded as the issue situation modifications. A controller decides how useful each contribution is, and who should make the next problem-solving action. One example, the BB1 blackboard architecture [54] was originally inspired by research studies of how humans plan to carry out numerous jobs in a trip. [55] An innovation of BB1 was to apply the same blackboard design to solving its control issue, i.e., its controller carried out meta-level reasoning with knowledge sources that kept track of how well a strategy or the problem-solving was continuing and could switch from one technique to another as conditions – such as goals or times – changed. BB1 has actually been used in numerous domains: building site planning, intelligent tutoring systems, and real-time client monitoring.

The second AI winter, 1988-1993

At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were selling LISP devices specifically targeted to speed up the development of AI applications and research study. In addition, several expert system business, such as Teknowledge and Inference Corporation, were offering expert system shells, training, and consulting to corporations.

Unfortunately, the AI boom did not last and Kautz finest describes the second AI winter season that followed:

Many factors can be provided for the arrival of the second AI winter. The hardware business failed when far more cost-efficient basic Unix workstations from Sun together with excellent compilers for LISP and Prolog came onto the market. Many commercial deployments of specialist systems were terminated when they showed too costly to maintain. Medical specialist systems never caught on for numerous factors: the difficulty in keeping them as much as date; the challenge for doctor to learn how to utilize an overwelming variety of various expert systems for various medical conditions; and possibly most crucially, the unwillingness of medical professionals to rely on a computer-made diagnosis over their gut instinct, even for particular domains where the professional systems might outshine a typical doctor. Venture capital money deserted AI almost overnight. The world AI conference IJCAI hosted a massive and lavish exhibition and countless nonacademic participants in 1987 in Vancouver; the main AI conference the list below year, AAAI 1988 in St. Paul, was a small and strictly scholastic affair. [9]

Including more extensive structures, 1993-2011

Uncertain reasoning

Both analytical approaches and extensions to reasoning were attempted.

One analytical approach, hidden Markov designs, had currently been popularized in the 1980s for speech acknowledgment work. [11] Subsequently, in 1988, Judea Pearl popularized using Bayesian Networks as a noise however effective way of dealing with uncertain reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian methods were used successfully in professional systems. [57] Even later on, in the 1990s, analytical relational knowing, an approach that integrates possibility with rational solutions, permitted possibility to be integrated with first-order logic, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order logic to assistance were also tried. For example, non-monotonic thinking could be utilized with reality maintenance systems. A truth upkeep system tracked assumptions and validations for all inferences. It enabled inferences to be withdrawn when presumptions were discovered to be incorrect or a contradiction was obtained. Explanations might be attended to an inference by discussing which guidelines were used to develop it and then continuing through underlying inferences and guidelines all the method back to root assumptions. [58] Lofti Zadeh had introduced a different kind of extension to deal with the representation of vagueness. For example, in deciding how “heavy” or “tall” a man is, there is frequently no clear “yes” or “no” response, and a predicate for heavy or high would rather return values in between 0 and 1. Those worths represented to what degree the predicates were true. His fuzzy logic further offered a method for propagating combinations of these values through sensible formulas. [59]

Machine learning

Symbolic maker discovering techniques were investigated to resolve the understanding acquisition bottleneck. One of the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test method to create possible guideline hypotheses to test against spectra. Domain and task understanding minimized the number of candidates evaluated to a manageable size. Feigenbaum explained Meta-DENDRAL as

… the conclusion of my imagine the early to mid-1960s having to do with theory development. The conception was that you had a problem solver like DENDRAL that took some inputs and produced an output. In doing so, it used layers of understanding to steer and prune the search. That knowledge acted due to the fact that we talked to individuals. But how did individuals get the understanding? By taking a look at countless spectra. So we wanted a program that would look at countless spectra and infer the understanding of mass spectrometry that DENDRAL could utilize to solve individual hypothesis formation problems. We did it. We were even able to release new understanding of mass spectrometry in the Journal of the American Chemical Society, giving credit only in a footnote that a program, Meta-DENDRAL, in fact did it. We were able to do something that had actually been a dream: to have a computer system program created a new and publishable piece of science. [51]

In contrast to the knowledge-intensive approach of Meta-DENDRAL, Ross Quinlan invented a domain-independent method to analytical classification, decision tree knowing, beginning first with ID3 [60] and then later extending its capabilities to C4.5. [61] The choice trees developed are glass box, interpretable classifiers, with human-interpretable classification guidelines.

Advances were made in understanding device knowing theory, too. Tom Mitchell presented variation area learning which describes learning as an explore an area of hypotheses, with upper, more basic, and lower, more particular, limits including all practical hypotheses consistent with the examples seen so far. [62] More officially, Valiant presented Probably Approximately Correct Learning (PAC Learning), a framework for the mathematical analysis of maker learning. [63]

Symbolic maker learning encompassed more than learning by example. E.g., John Anderson supplied a cognitive design of human knowing where skill practice leads to a collection of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For example, a student may learn to apply “Supplementary angles are two angles whose steps sum 180 degrees” as numerous various procedural guidelines. E.g., one rule may say that if X and Y are additional and you know X, then Y will be 180 – X. He called his approach “understanding collection”. ACT-R has been used effectively to design elements of human cognition, such as learning and retention. ACT-R is also used in smart tutoring systems, called cognitive tutors, to successfully teach geometry, computer programs, and algebra to school kids. [64]

Inductive reasoning programs was another approach to discovering that permitted logic programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) might manufacture Prolog programs from examples. [65] John R. Koza used genetic algorithms to program synthesis to create hereditary programming, which he used to synthesize LISP programs. Finally, Zohar Manna and Richard Waldinger provided a more basic method to program synthesis that synthesizes a functional program in the course of proving its requirements to be correct. [66]

As an alternative to logic, Roger Schank introduced case-based thinking (CBR). The CBR technique described in his book, Dynamic Memory, [67] focuses first on remembering essential analytical cases for future use and generalizing them where proper. When confronted with a brand-new problem, CBR recovers the most comparable previous case and adjusts it to the specifics of the present problem. [68] Another alternative to logic, hereditary algorithms and genetic shows are based on an evolutionary design of knowing, where sets of rules are encoded into populations, the rules govern the behavior of individuals, and selection of the fittest prunes out sets of inappropriate guidelines over numerous generations. [69]

Symbolic device learning was applied to discovering concepts, rules, heuristics, and problem-solving. Approaches, aside from those above, consist of:

1. Learning from guideline or advice-i.e., taking human guideline, presented as guidance, and determining how to operationalize it in particular scenarios. For example, in a video game of Hearts, finding out precisely how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving efficiency by accepting subject-matter specialist (SME) feedback during training. When problem-solving fails, querying the specialist to either find out a brand-new prototype for analytical or to learn a new description regarding precisely why one prototype is more pertinent than another. For instance, the program Protos learned to detect tinnitus cases by interacting with an audiologist. [71] 3. Learning by analogy-constructing issue solutions based on comparable issues seen in the past, and then customizing their options to fit a new situation or domain. [72] [73] 4. Apprentice learning systems-learning novel services to problems by observing human analytical. Domain knowledge describes why unique services are correct and how the service can be generalized. LEAP found out how to design VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing jobs to perform experiments and after that gaining from the outcomes. Doug Lenat’s Eurisko, for instance, found out heuristics to beat human gamers at the Traveller role-playing video game for two years in a row. [75] 6. Learning macro-operators-i.e., looking for helpful macro-operators to be found out from series of fundamental analytical actions. Good macro-operators streamline analytical by permitting problems to be fixed at a more abstract level. [76]
Deep knowing and neuro-symbolic AI 2011-now

With the rise of deep learning, the symbolic AI approach has actually been compared to deep learning as complementary “… with parallels having been drawn many times by AI scientists in between Kahneman’s research study on human thinking and choice making – reflected in his book Thinking, Fast and Slow – and the so-called “AI systems 1 and 2″, which would in concept be designed by deep learning and symbolic reasoning, respectively.” In this view, symbolic thinking is more apt for deliberative reasoning, preparation, and explanation while deep knowing is more apt for fast pattern recognition in affective applications with noisy data. [17] [18]

Neuro-symbolic AI: integrating neural and symbolic techniques

Neuro-symbolic AI efforts to integrate neural and symbolic architectures in a manner that addresses strengths and weak points of each, in a complementary style, in order to support robust AI capable of thinking, learning, and cognitive modeling. As argued by Valiant [77] and many others, [78] the reliable construction of abundant computational cognitive models requires the mix of sound symbolic reasoning and efficient (device) knowing models. Gary Marcus, likewise, argues that: “We can not construct rich cognitive designs in a sufficient, automated method without the triune of hybrid architecture, abundant prior understanding, and advanced techniques for reasoning.”, [79] and in particular: “To build a robust, knowledge-driven technique to AI we should have the equipment of symbol-manipulation in our toolkit. Excessive of helpful knowledge is abstract to make do without tools that represent and control abstraction, and to date, the only machinery that we understand of that can control such abstract understanding dependably is the apparatus of sign manipulation. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based upon a requirement to attend to the 2 type of believing discussed in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having two components, System 1 and System 2. System 1 is fast, automatic, instinctive and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is the kind utilized for pattern acknowledgment while System 2 is far better matched for preparation, reduction, and deliberative thinking. In this view, deep knowing best designs the first kind of thinking while symbolic reasoning best designs the 2nd kind and both are required.

Garcez and Lamb explain research in this area as being continuous for a minimum of the past twenty years, [83] dating from their 2002 book on neurosymbolic learning systems. [84] A series of workshops on neuro-symbolic thinking has been held every year since 2005, see http://www.neural-symbolic.org/ for information.

In their 2015 paper, Neural-Symbolic Learning and Reasoning: Contributions and Challenges, Garcez et al. argue that:

The combination of the symbolic and connectionist paradigms of AI has actually been pursued by a relatively little research study community over the last 2 decades and has actually yielded several substantial outcomes. Over the last years, neural symbolic systems have actually been shown capable of overcoming the so-called propositional fixation of neural networks, as McCarthy (1988) put it in reaction to Smolensky (1988 ); see also (Hinton, 1990). Neural networks were shown efficient in representing modal and temporal logics (d’Avila Garcez and Lamb, 2006) and pieces of first-order logic (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have been used to a variety of issues in the locations of bioinformatics, control engineering, software verification and adjustment, visual intelligence, ontology learning, and computer video games. [78]

Approaches for integration are varied. Henry Kautz’s taxonomy of neuro-symbolic architectures, together with some examples, follows:

– Symbolic Neural symbolic-is the existing method of many neural models in natural language processing, where words or subword tokens are both the ultimate input and output of big language designs. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic methods are used to call neural techniques. In this case the symbolic technique is Monte Carlo tree search and the neural techniques find out how to assess game positions.
– Neural|Symbolic-uses a neural architecture to translate perceptual data as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to generate or identify training data that is consequently learned by a deep learning design, e.g., to train a neural design for symbolic calculation by utilizing a Macsyma-like symbolic mathematics system to create or label examples.
– Neural _ Symbolic -uses a neural internet that is created from symbolic guidelines. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR evidence tree produced from knowledge base rules and terms. Logic Tensor Networks [86] likewise fall into this category.
– Neural [Symbolic] -permits a neural model to directly call a symbolic thinking engine, e.g., to carry out an action or evaluate a state.

Many key research study concerns stay, such as:

– What is the very best method to incorporate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and extracted from them?
– How should common-sense understanding be found out and reasoned about?
– How can abstract knowledge that is difficult to encode logically be managed?

Techniques and contributions

This area supplies a summary of strategies and contributions in a general context causing lots of other, more comprehensive posts in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered previously in the history area.

AI shows languages

The crucial AI programming language in the US during the last symbolic AI boom duration was LISP. LISP is the second earliest shows language after FORTRAN and was created in 1958 by John McCarthy. LISP supplied the first read-eval-print loop to support fast program development. Compiled functions could be freely combined with translated functions. Program tracing, stepping, and breakpoints were also offered, in addition to the ability to change values or functions and continue from breakpoints or mistakes. It had the very first self-hosting compiler, implying that the compiler itself was initially composed in LISP and after that ran interpretively to assemble the compiler code.

Other essential developments pioneered by LISP that have spread out to other programming languages include:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

Programs were themselves data structures that other programs could run on, enabling the simple meaning of higher-level languages.

In contrast to the US, in Europe the crucial AI programs language during that exact same duration was Prolog. Prolog provided an integrated store of realities and clauses that might be queried by a read-eval-print loop. The shop could serve as a knowledge base and the stipulations could serve as guidelines or a restricted kind of logic. As a subset of first-order reasoning Prolog was based on Horn clauses with a closed-world assumption-any truths not known were considered false-and an unique name presumption for primitive terms-e.g., the identifier barack_obama was thought about to describe exactly one things. Backtracking and marriage are built-in to Prolog.

Alain Colmerauer and Philippe Roussel are credited as the innovators of Prolog. Prolog is a type of logic shows, which was developed by Robert Kowalski. Its history was likewise influenced by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of techniques. For more information see the area on the origins of Prolog in the PLANNER short article.

Prolog is also a type of declarative programming. The logic clauses that describe programs are directly analyzed to run the programs specified. No explicit series of actions is needed, as holds true with imperative shows languages.

Japan championed Prolog for its Fifth Generation Project, meaning to construct unique hardware for high performance. Similarly, LISP machines were developed to run LISP, however as the 2nd AI boom turned to bust these companies could not take on brand-new workstations that might now run LISP or Prolog natively at equivalent speeds. See the history area for more detail.

Smalltalk was another influential AI programs language. For example, it presented metaclasses and, along with Flavors and CommonLoops, influenced the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the current basic Lisp dialect. CLOS is a Lisp-based object-oriented system that permits several inheritance, in addition to incremental extensions to both classes and metaclasses, therefore providing a run-time meta-object procedure. [88]

For other AI programs languages see this list of programs languages for expert system. Currently, Python, a multi-paradigm programming language, is the most popular programs language, partially due to its comprehensive plan library that supports information science, natural language processing, and deep knowing. Python includes a read-eval-print loop, functional aspects such as higher-order functions, and object-oriented shows that consists of metaclasses.

Search

Search emerges in numerous sort of issue solving, including planning, constraint fulfillment, and playing games such as checkers, chess, and go. The best understood AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven provision knowing, and the DPLL algorithm. For adversarial search when playing video games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and reasoning

Multiple various methods to represent understanding and then factor with those representations have been investigated. Below is a quick introduction of approaches to understanding representation and automated reasoning.

Knowledge representation

Semantic networks, conceptual graphs, frames, and reasoning are all approaches to modeling knowledge such as domain understanding, analytical knowledge, and the semantic significance of language. Ontologies design key ideas and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be utilized for any domain while WordNet is a lexical resource that can likewise be viewed as an ontology. YAGO includes WordNet as part of its ontology, to align truths drawn out from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being utilized.

Description logic is a logic for automated classification of ontologies and for finding irregular classification information. OWL is a language used to represent ontologies with description reasoning. Protégé is an ontology editor that can check out in OWL ontologies and then check consistency with deductive classifiers such as such as HermiT. [89]

First-order reasoning is more basic than description logic. The automated theorem provers discussed below can prove theorems in first-order reasoning. Horn provision logic is more limited than first-order reasoning and is utilized in logic programming languages such as Prolog. Extensions to first-order logic include temporal reasoning, to deal with time; epistemic logic, to reason about agent understanding; modal logic, to deal with possibility and necessity; and probabilistic logics to manage logic and probability together.

Automatic theorem proving

Examples of automated theorem provers for first-order reasoning are:

Prover9.
ACL2.
Vampire.

Prover9 can be used in combination with the Mace4 model checker. ACL2 is a theorem prover that can deal with proofs by induction and is a descendant of the Boyer-Moore Theorem Prover, also known as Nqthm.

Reasoning in knowledge-based systems

Knowledge-based systems have an explicit understanding base, normally of guidelines, to enhance reusability throughout domains by separating procedural code and domain understanding. A different reasoning engine procedures rules and includes, deletes, or modifies an understanding store.

Forward chaining inference engines are the most common, and are seen in CLIPS and OPS5. Backward chaining happens in Prolog, where a more limited logical representation is used, Horn Clauses. Pattern-matching, particularly marriage, is utilized in Prolog.

A more flexible kind of problem-solving takes place when thinking about what to do next takes place, instead of just picking one of the offered actions. This type of meta-level thinking is utilized in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R might have additional capabilities, such as the ability to compile frequently used understanding into higher-level portions.

Commonsense reasoning

Marvin Minsky first proposed frames as a method of translating typical visual scenarios, such as an office, and Roger Schank extended this idea to scripts for typical regimens, such as eating in restaurants. Cyc has actually attempted to capture beneficial common-sense understanding and has “micro-theories” to handle specific kinds of domain-specific reasoning.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human thinking about ignorant physics, such as what happens when we heat up a liquid in a pot on the stove. We anticipate it to heat and perhaps boil over, even though we may not know its temperature, its boiling point, or other details, such as atmospheric pressure.

Similarly, Allen’s temporal period algebra is a simplification of reasoning about time and Region Connection Calculus is a simplification of reasoning about spatial relationships. Both can be solved with restraint solvers.

Constraints and constraint-based thinking

Constraint solvers carry out a more restricted type of reasoning than first-order logic. They can streamline sets of spatiotemporal restrictions, such as those for RCC or Temporal Algebra, along with fixing other type of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint reasoning programming can be utilized to fix scheduling problems, for instance with restraint dealing with rules (CHR).

Automated preparation

The General Problem Solver (GPS) cast preparation as analytical utilized means-ends analysis to develop plans. STRIPS took a different method, seeing preparation as theorem proving. Graphplan takes a least-commitment method to planning, instead of sequentially choosing actions from a preliminary state, working forwards, or an objective state if working backwards. Satplan is a technique to preparing where a planning problem is lowered to a Boolean satisfiability issue.

Natural language processing

Natural language processing concentrates on treating language as information to carry out jobs such as determining topics without always understanding the desired significance. Natural language understanding, in contrast, constructs a significance representation and utilizes that for more processing, such as responding to questions.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb phrase chunking are all aspects of natural language processing long dealt with by symbolic AI, but since improved by deep learning methods. In symbolic AI, discourse representation theory and first-order reasoning have been utilized to represent sentence significances. Latent semantic analysis (LSA) and specific semantic analysis also offered vector representations of documents. In the latter case, vector components are interpretable as concepts called by Wikipedia posts.

New deep knowing methods based on Transformer designs have now eclipsed these earlier symbolic AI techniques and obtained cutting edge efficiency in natural language processing. However, Transformer designs are nontransparent and do not yet produce human-interpretable semantic representations for sentences and files. Instead, they produce task-specific vectors where the significance of the vector elements is nontransparent.

Agents and multi-agent systems

Agents are autonomous systems embedded in an environment they perceive and act upon in some sense. Russell and Norvig’s standard textbook on expert system is organized to show representative architectures of increasing sophistication. [91] The sophistication of agents differs from easy reactive representatives, to those with a model of the world and automated preparation abilities, possibly a BDI agent, i.e., one with beliefs, desires, and intentions – or additionally a support finding out model learned over time to pick actions – as much as a combination of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep learning for understanding. [92]

In contrast, a multi-agent system includes multiple representatives that communicate amongst themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The representatives need not all have the exact same internal architecture. Advantages of multi-agent systems consist of the capability to divide work amongst the representatives and to increase fault tolerance when representatives are lost. Research issues include how agents reach consensus, distributed problem resolving, multi-agent learning, multi-agent planning, and dispersed restraint optimization.

Controversies arose from early in symbolic AI, both within the field-e.g., between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who embraced AI however declined symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were mostly from theorists, on intellectual premises, however also from financing firms, particularly throughout the 2 AI winters.

The Frame Problem: knowledge representation difficulties for first-order logic

Limitations were discovered in utilizing simple first-order reasoning to reason about vibrant domains. Problems were found both with concerns to enumerating the preconditions for an action to be successful and in providing axioms for what did not alter after an action was performed.

McCarthy and Hayes presented the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Expert System.” [93] A basic example happens in “showing that one individual could enter into discussion with another”, as an axiom asserting “if an individual has a telephone he still has it after searching for a number in the telephone book” would be needed for the deduction to prosper. Similar axioms would be needed for other domain actions to define what did not change.

A similar issue, called the Qualification Problem, takes place in attempting to identify the preconditions for an action to prosper. An unlimited number of pathological conditions can be thought of, e.g., a banana in a tailpipe could avoid a cars and truck from operating correctly.

McCarthy’s technique to fix the frame issue was circumscription, a type of non-monotonic logic where deductions could be made from actions that need only specify what would alter while not having to clearly define everything that would not change. Other non-monotonic logics supplied truth upkeep systems that revised beliefs leading to contradictions.

Other ways of handling more open-ended domains included probabilistic thinking systems and artificial intelligence to discover new principles and rules. McCarthy’s Advice Taker can be seen as a motivation here, as it might incorporate new understanding provided by a human in the type of assertions or rules. For instance, experimental symbolic device learning systems checked out the capability to take high-level natural language guidance and to analyze it into domain-specific actionable rules.

Similar to the issues in dealing with dynamic domains, common-sense reasoning is likewise hard to record in formal thinking. Examples of sensible reasoning consist of implicit thinking about how individuals think or general understanding of everyday events, objects, and living animals. This kind of knowledge is taken for granted and not viewed as noteworthy. Common-sense reasoning is an open area of research and challenging both for symbolic systems (e.g., Cyc has tried to capture essential parts of this knowledge over more than a decade) and neural systems (e.g., self-driving automobiles that do not know not to drive into cones or not to hit pedestrians walking a bicycle).

McCarthy viewed his Advice Taker as having sensible, however his definition of sensible was different than the one above. [94] He specified a program as having sound judgment “if it immediately deduces for itself a sufficiently large class of instant consequences of anything it is informed and what it already knows. “

Connectionist AI: philosophical challenges and sociological conflicts

Connectionist methods include earlier deal with neural networks, [95] such as perceptrons; operate in the mid to late 80s, such as Danny Hillis’s Connection Machine and Yann LeCun’s advances in convolutional neural networks; to today’s more sophisticated approaches, such as Transformers, GANs, and other work in deep knowing.

Three philosophical positions [96] have actually been outlined amongst connectionists:

1. Implementationism-where connectionist architectures execute the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is turned down absolutely, and connectionist architectures underlie intelligence and are fully sufficient to discuss it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are considered as complementary and both are needed for intelligence

Olazaran, in his sociological history of the debates within the neural network neighborhood, explained the moderate connectionism view as basically compatible with current research study in neuro-symbolic hybrids:

The third and last position I want to examine here is what I call the moderate connectionist view, a more eclectic view of the present debate between connectionism and symbolic AI. Among the scientists who has elaborated this position most clearly is Andy Clark, a theorist from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark safeguarded hybrid (partly symbolic, partially connectionist) systems. He declared that (at least) two type of theories are needed in order to study and design cognition. On the one hand, for some information-processing jobs (such as pattern recognition) connectionism has benefits over symbolic designs. But on the other hand, for other cognitive procedures (such as serial, deductive thinking, and generative sign adjustment processes) the symbolic paradigm provides sufficient models, and not only “approximations” (contrary to what extreme connectionists would claim). [97]

Gary Marcus has actually declared that the animus in the deep learning community against symbolic techniques now may be more sociological than philosophical:

To believe that we can simply desert symbol-manipulation is to suspend shock.

And yet, for the most part, that’s how most current AI earnings. Hinton and many others have actually striven to eliminate symbols altogether. The deep learning hope-seemingly grounded not so much in science, but in a sort of historic grudge-is that smart behavior will emerge simply from the confluence of massive information and deep knowing. Where classical computers and software application solve jobs by defining sets of symbol-manipulating guidelines dedicated to particular tasks, such as editing a line in a word processor or performing a calculation in a spreadsheet, neural networks generally attempt to solve jobs by analytical approximation and learning from examples.

According to Marcus, Geoffrey Hinton and his associates have actually been vehemently “anti-symbolic”:

When deep learning reemerged in 2012, it was with a sort of take-no-prisoners attitude that has characterized the majority of the last decade. By 2015, his hostility toward all things signs had completely crystallized. He lectured at an AI workshop at Stanford comparing signs to aether, among science’s greatest mistakes.

…

Since then, his anti-symbolic campaign has only increased in strength. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep knowing in one of science’s most crucial journals, Nature. It closed with a direct attack on symbol control, calling not for reconciliation however for outright replacement. Later, Hinton told a gathering of European Union leaders that investing any further money in symbol-manipulating approaches was “a substantial mistake,” comparing it to buying internal combustion engines in the period of electrical vehicles. [98]

Part of these disputes may be because of uncertain terms:

Turing award winner Judea Pearl offers a review of artificial intelligence which, unfortunately, conflates the terms device learning and deep knowing. Similarly, when Geoffrey Hinton describes symbolic AI, the connotation of the term tends to be that of specialist systems dispossessed of any capability to learn. Using the terminology is in requirement of clarification. Machine knowing is not confined to association rule mining, c.f. the body of work on symbolic ML and relational learning (the distinctions to deep learning being the option of representation, localist logical instead of distributed, and the non-use of gradient-based knowing algorithms). Equally, symbolic AI is not practically production guidelines composed by hand. A correct meaning of AI issues understanding representation and thinking, autonomous multi-agent systems, preparation and argumentation, in addition to knowing. [99]

Situated robotics: the world as a design

Another critique of symbolic AI is the embodied cognition approach:

The embodied cognition technique declares that it makes no sense to consider the brain separately: cognition takes place within a body, which is embedded in an environment. We need to study the system as a whole; the brain’s operating exploits consistencies in its environment, consisting of the rest of its body. Under the embodied cognition method, robotics, vision, and other sensors become central, not peripheral. [100]

Rodney Brooks created behavior-based robotics, one approach to embodied cognition. Nouvelle AI, another name for this approach, is considered as an alternative to both symbolic AI and connectionist AI. His method rejected representations, either symbolic or dispersed, as not only unnecessary, however as damaging. Instead, he created the subsumption architecture, a layered architecture for embodied representatives. Each layer attains a different purpose and should work in the real life. For example, the very first robot he explains in Intelligence Without Representation, has 3 layers. The bottom layer translates finder sensors to prevent items. The middle layer triggers the robot to roam around when there are no obstacles. The leading layer causes the robot to go to more distant locations for further exploration. Each layer can temporarily inhibit or reduce a lower-level layer. He slammed AI researchers for defining AI problems for their systems, when: “There is no clean division between perception (abstraction) and thinking in the real world.” [101] He called his robotics “Creatures” and each layer was “composed of a fixed-topology network of easy finite state makers.” [102] In the Nouvelle AI approach, “First, it is vitally important to check the Creatures we develop in the real life; i.e., in the exact same world that we human beings occupy. It is devastating to fall into the temptation of testing them in a streamlined world first, even with the finest intentions of later moving activity to an unsimplified world.” [103] His emphasis on real-world screening was in contrast to “Early operate in AI focused on video games, geometrical issues, symbolic algebra, theorem proving, and other official systems” [104] and the use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has advantages, but has been slammed by the other methods. Symbolic AI has actually been criticized as disembodied, accountable to the qualification issue, and poor in managing the affective problems where deep discovering excels. In turn, connectionist AI has been criticized as badly matched for deliberative detailed issue fixing, integrating understanding, and handling planning. Finally, Nouvelle AI masters reactive and real-world robotics domains but has been slammed for troubles in incorporating knowing and knowledge.

Hybrid AIs integrating several of these techniques are currently deemed the path forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw locations where AI did not have total answers and said that Al is therefore difficult; we now see a lot of these same areas undergoing continued research study and development leading to increased capability, not impossibility. [100]

Artificial intelligence.
Automated planning and scheduling
Automated theorem proving
Belief modification
Case-based reasoning
Cognitive architecture
Cognitive science
Connectionism
Constraint programming
Deep knowing
First-order logic
GOFAI
History of expert system
Inductive logic programs
Knowledge-based systems
Knowledge representation and thinking
Logic programs
Machine knowing
Model checking
Model-based reasoning
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of expert system
Physical sign systems hypothesis
Semantic Web
Sequential pattern mining
Statistical relational learning
Symbolic mathematics
YAGO ontology
WordNet

Notes

^ McCarthy once stated: “This is AI, so we don’t care if it’s psychologically genuine”. [4] McCarthy restated his position in 2006 at the AI@50 conference where he stated “Expert system is not, by meaning, simulation of human intelligence”. [28] Pamela McCorduck writes that there are “2 significant branches of expert system: one aimed at producing smart habits no matter how it was achieved, and the other targeted at modeling smart procedures found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig composed “Aeronautical engineering texts do not define the objective of their field as making ‘makers that fly so exactly like pigeons that they can deceive even other pigeons.'” [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). “Reconciling deep knowing with symbolic artificial intelligence: representing things and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). “Logic-Based Artificial Intelligence”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep learning with symbolic artificial intelligence: representing objects and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating errors”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten Zip Code Recognition”. Neural Computation. 1 (4 ): 541-551. doi:10.1162/ neco.1989.1.4.541. S2CID 41312633.
^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. “Thinking Fast and Slow in AI”. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. “AAAI Presidential Address: The State of AI”. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
^ Lenat, Douglas B; Feigenbaum, Edward A (1988 ). “On the limits of understanding”. Proceedings of the International Workshop on Expert System for Industrial Applications: 291-300. doi:10.1109/ AIIA.1988.13308. S2CID 11778085.
^ Russell & Norvig 2021, pp. 22-24.
^ McCorduck 2004, pp. 327-335, 434-435.
^ Crevier 1993, pp. 145-62, 197-203.
^ a b Russell & Norvig 2021, p. 23.
^ a b Clancey 1987.
^ a b Shustek, Len (2010 ). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-08-05.
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