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Symbolic Artificial Intelligence

In expert system, symbolic expert system (also called classical synthetic intelligence or logic-based artificial intelligence) [1] [2] is the term for the collection of all approaches in expert system research that are based upon top-level symbolic (human-readable) representations of problems, logic and search. [3] Symbolic AI used tools such as logic programs, production guidelines, semantic nets and frames, and it developed applications such as knowledge-based systems (in specific, professional systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm caused seminal ideas in search, symbolic programs languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of official understanding and reasoning systems.

Symbolic AI was the dominant paradigm of AI research from the mid-1950s up until the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic methods would ultimately prosper in producing a machine with synthetic basic intelligence and considered this the ultimate 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 impractical expectations and pledges and was followed by the first AI Winter as funding dried up. [5] [6] A second boom (1969-1986) took place with the increase of professional systems, their promise of recording business proficiency, and an enthusiastic business accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later on frustration. [8] Problems with troubles in knowledge acquisition, maintaining large understanding bases, and brittleness in dealing with out-of-domain problems arose. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers focused on dealing with underlying problems in handling uncertainty and in knowledge acquisition. [10] Uncertainty was addressed with official methods such as hidden Markov models, Bayesian reasoning, and analytical relational knowing. [11] [12] Symbolic device learning dealt with the knowledge acquisition issue with contributions consisting of Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree learning, case-based learning, and inductive reasoning programming to find out relations. [13]

Neural networks, a subsymbolic method, had actually been pursued from early days and reemerged highly 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 effective until about 2012: “Until Big Data became prevalent, the basic consensus in the Al community was that the so-called neural-network technique was hopeless. Systems just didn’t work that well, compared to other methods. … A revolution was available in 2012, when a variety of people, consisting of a group of scientists dealing with Hinton, exercised a method to use the power of GPUs to immensely increase the power of neural networks.” [16] Over the next numerous years, deep learning had incredible success in dealing with vision, speech acknowledgment, speech synthesis, image generation, and machine translation. However, considering that 2020, as inherent troubles with bias, description, comprehensibility, and robustness became more evident with deep learning approaches; an increasing variety of AI scientists have actually required integrating the best of both the symbolic and neural network approaches [17] [18] and attending to locations that both techniques have difficulty with, such as common-sense reasoning. [16]

A brief history of symbolic AI to today day follows listed below. Period and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture [19] and the longer Wikipedia short article on the History of AI, with dates and titles differing slightly for increased clearness.

The first AI summer: unreasonable liveliness, 1948-1966

Success at early attempts in AI occurred in 3 main areas: artificial neural networks, knowledge representation, and heuristic search, adding to high expectations. This area sums up Kautz’s reprise of early AI history.

Approaches influenced by human or animal cognition or habits

Cybernetic approaches tried to duplicate the feedback loops between animals and their environments. A robotic turtle, with sensing units, motors for driving and guiding, and 7 vacuum tubes for control, based upon a preprogrammed neural web, was built as early as 1948. This work can be viewed as an early precursor to later work in neural networks, reinforcement knowing, and situated robotics. [20]

A crucial early symbolic AI program was the Logic theorist, composed by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it had the ability to prove 38 elementary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later on generalized this work to create a domain-independent issue solver, GPS (General Problem Solver). GPS solved issues represented with official operators through state-space search utilizing means-ends analysis. [21]

During the 1960s, symbolic approaches accomplished terrific success at replicating smart habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was concentrated in four organizations in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Each one developed its own style of research study. Earlier methods based upon cybernetics or synthetic neural networks were deserted or pushed into the background.

Herbert Simon and Allen Newell studied human problem-solving abilities and attempted to formalize them, and their work laid the structures of the field of synthetic intelligence, in addition to cognitive science, operations research study and management science. Their research study group used the results of mental experiments to develop programs that simulated the methods that people utilized to fix issues. [22] [23] This tradition, focused at Carnegie Mellon University would ultimately culminate in the development of the Soar architecture in the middle 1980s. [24] [25]

Heuristic search

In addition to the highly specialized domain-specific type of knowledge that we will see later on used in professional systems, early symbolic AI researchers discovered another more general application of knowledge. These were called heuristics, guidelines that direct a search in appealing instructions: “How can non-enumerative search be useful when the underlying issue is greatly difficult? The approach advocated by Simon and Newell is to employ heuristics: fast algorithms that might fail on some inputs or output suboptimal options.” [26] Another essential advance was to discover a method to use these heuristics that ensures an option will be found, if there is one, not standing up to the occasional fallibility of heuristics: “The A * algorithm supplied a basic frame for complete and optimum heuristically guided search. A * is used as a subroutine within almost every AI algorithm today but is still no magic bullet; its warranty of efficiency is purchased at the expense of worst-case exponential time. [26]

Early deal with knowledge representation and reasoning

Early work covered both applications of official thinking stressing first-order logic, together with attempts to deal with common-sense thinking in a less official manner.

Modeling official thinking with logic: the “neats”

Unlike Simon and Newell, John McCarthy felt that machines did not need to simulate the precise mechanisms of human idea, however might instead look for the essence of abstract reasoning and analytical with reasoning, [27] regardless of whether individuals used the exact same algorithms. [a] His lab at Stanford (SAIL) concentrated on utilizing formal logic to solve a variety of problems, including understanding representation, planning and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and elsewhere in Europe which resulted in the advancement of the shows language Prolog and the science of logic programs. [32] [33]

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

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that solving challenging problems in vision and natural language processing required ad hoc solutions-they argued that no easy and basic principle (like reasoning) would capture all the elements of intelligent behavior. Roger Schank explained their “anti-logic” techniques as “scruffy” (instead of the “cool” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “shabby” AI, given that they must be developed by hand, one complex concept at a time. [38] [39] [40]

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

The first AI winter was a shock:

During the first AI summer, many individuals believed that machine intelligence could be achieved in simply a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research to utilize AI to resolve issues of nationwide security; in particular, to automate the translation of Russian to English for intelligence operations and to create self-governing tanks for the battlefield. Researchers had actually begun to understand that attaining AI was going to be much harder than was supposed a years previously, however a mix of hubris and disingenuousness led many university and think-tank scientists to accept financing with guarantees of deliverables that they must have understood they might not satisfy. By the mid-1960s neither helpful natural language translation systems nor self-governing tanks had been produced, and a dramatic backlash embeded in. New DARPA management canceled existing AI financing programs.

Beyond the United States, the most fertile ground for AI research study was the United Kingdom. The AI winter season in the UK was stimulated on not a lot by disappointed military leaders as by rival academics who saw AI scientists as charlatans and a drain on research financing. A teacher of used mathematics, Sir James Lighthill, was commissioned by Parliament to assess the state of AI research study in the country. The report specified that all of the issues being dealt with in AI would be better managed by scientists from other disciplines-such as applied mathematics. The report likewise declared that AI successes on toy problems might never ever scale to real-world applications due to combinatorial explosion. [41]

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

Knowledge-based systems

As limitations with weak, domain-independent methods ended up being more and more evident, [42] researchers from all 3 customs started to build knowledge into AI applications. [43] [7] The knowledge revolution was driven by the realization that understanding underlies high-performance, domain-specific AI applications.

Edward Feigenbaum said:

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

( 1) The Knowledge Principle: if a program is to carry out an intricate task well, it should understand a lot about the world in which it operates.
( 2) A possible extension of that principle, called the Breadth Hypothesis: there are 2 extra capabilities required for smart behavior in unforeseen circumstances: drawing on increasingly basic understanding, and analogizing to specific but far-flung knowledge. [45]

Success with expert systems

This “knowledge transformation” led to the advancement and deployment of expert systems (introduced by Edward Feigenbaum), the first commercially effective type of AI software. [46] [47] [48]

Key professional systems were:

DENDRAL, which found the structure of organic particles from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and recommended further lab tests, when necessary – by translating lab outcomes, client history, and physician observations. “With about 450 rules, MYCIN was able to carry out along with some professionals, and substantially better than junior doctors.” [49] INTERNIST and CADUCEUS which tackled internal medication diagnosis. Internist attempted to catch the knowledge of the chairman of internal medicine at the University of Pittsburgh School of Medicine while CADUCEUS might eventually identify as much as 1000 different diseases.
– GUIDON, which revealed how a knowledge base constructed for professional problem fixing could be repurposed for mentor. [50] XCON, to set up VAX computer systems, a then laborious procedure that could use up to 90 days. XCON decreased the time to about 90 minutes. [9]
DENDRAL is thought about the very 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:

Among the people at Stanford thinking about computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I desired an induction “sandbox”, he said, “I have simply the one for you.” His laboratory was doing mass spectrometry of amino acids. The concern was: how do you go from taking a look 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 approaches, and he had an algorithm that was good at generating the chemical problem space.

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, developer of the chemical behind the contraceptive pill, and also one of the world’s most appreciated mass spectrometrists. Carl and his postdocs were world-class professionals in mass spectrometry. We began to add to their understanding, inventing understanding of engineering as we went along. These experiments amounted to titrating DENDRAL more and more understanding. The more you did that, the smarter the program became. We had extremely great results.

The generalization was: in the understanding lies the power. That was the big concept. In my profession that is the big, “Ah ha!,” and it wasn’t the method AI was being done previously. Sounds simple, but it’s probably AI’s most powerful generalization. [51]

The other specialist systems pointed out above followed DENDRAL. MYCIN exemplifies the traditional expert system architecture of a knowledge-base of guidelines coupled to a symbolic reasoning mechanism, consisting of the usage of certainty aspects to handle uncertainty. GUIDON reveals how a specific knowledge base can be repurposed for a second application, tutoring, and is an example of a smart tutoring system, a particular sort of knowledge-based application. Clancey revealed that it was not sufficient just to utilize MYCIN’s rules for guideline, however that he likewise required to include rules for dialogue management and trainee modeling. [50] XCON is substantial due to the fact that of the countless dollars it saved DEC, which triggered the professional system boom where most all major corporations in the US had skilled systems groups, to catch business know-how, maintain it, and automate it:

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

Chess expert understanding was encoded in Deep Blue. In 1996, this allowed IBM’s Deep Blue, with the help of symbolic AI, to win in a game of chess versus the world champion at that time, Garry Kasparov. [52]

Architecture of knowledge-based and expert systems

A crucial element of the system architecture for all specialist systems is the knowledge base, which stores facts and rules for analytical. [53] The easiest approach for a professional system understanding base is simply a collection or network of production guidelines. Production rules connect symbols in a relationship similar to an If-Then declaration. The specialist system processes the guidelines to make deductions and to determine what extra information it needs, i.e. what questions to ask, utilizing human-readable signs. For instance, OPS5, CLIPS and their followers Jess and Drools operate in this fashion.

Expert systems can operate in either a forward chaining – from proof to conclusions – or backwards chaining – from goals to needed information and requirements – manner. Advanced knowledge-based systems, such as Soar can likewise carry out meta-level thinking, that is reasoning about their own thinking in terms of deciding how to solve issues and keeping an eye on the success of analytical strategies.

Blackboard systems are a 2nd kind of knowledge-based or skilled system architecture. They design a neighborhood of professionals incrementally contributing, where they can, to resolve an issue. The problem is represented in multiple levels of abstraction or alternate views. The experts (understanding sources) offer their services whenever they acknowledge they can contribute. Potential analytical actions are represented on a program that is updated as the problem situation modifications. A controller chooses how helpful each contribution is, and who must make the next analytical action. One example, the BB1 chalkboard architecture [54] was originally inspired by research studies of how people prepare to carry out several tasks in a trip. [55] A development of BB1 was to apply the very same blackboard model to solving its control problem, i.e., its controller performed meta-level reasoning with knowledge sources that kept an eye on how well a strategy or the analytical was continuing and might switch from one technique to another as conditions – such as goals or times – changed. BB1 has been used in numerous domains: building website planning, smart tutoring systems, and real-time patient tracking.

The 2nd AI winter season, 1988-1993

At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were selling LISP makers particularly targeted to speed up the development of AI applications and research. In addition, numerous artificial intelligence business, such as Teknowledge and Inference Corporation, were selling professional system shells, training, and consulting to corporations.

Unfortunately, the AI boom did not last and Kautz finest describes the 2nd AI winter that followed:

Many factors can be provided for the arrival of the 2nd AI winter. The hardware business failed when much more economical general Unix workstations from Sun together with excellent compilers for LISP and Prolog came onto the market. Many business deployments of professional systems were stopped when they proved too pricey to preserve. Medical specialist systems never caught on for several reasons: the trouble in keeping them approximately date; the difficulty for medical experts to learn how to use an overwelming variety of different expert systems for various medical conditions; and maybe most crucially, the hesitation of medical professionals to trust a computer-made medical diagnosis over their gut instinct, even for particular domains where the professional systems could outshine an average doctor. Venture capital money deserted AI practically overnight. The world AI conference IJCAI hosted a huge and lavish exhibition and thousands of nonacademic attendees in 1987 in Vancouver; the main AI conference the following year, AAAI 1988 in St. Paul, was a little and strictly academic affair. [9]

Including more extensive foundations, 1993-2011

Uncertain reasoning

Both analytical techniques and extensions to logic were attempted.

One statistical method, concealed Markov models, had already been popularized in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl promoted making use of Bayesian Networks as a noise however effective method of dealing with unsure thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian methods were applied successfully in expert systems. [57] Even later, in the 1990s, statistical relational knowing, an approach that combines probability with logical formulas, allowed possibility to be integrated with first-order reasoning, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order logic to support were also attempted. For instance, non-monotonic thinking could be used with truth maintenance systems. A reality upkeep system tracked presumptions and validations for all reasonings. It enabled reasonings to be withdrawn when assumptions were discovered to be incorrect or a contradiction was derived. Explanations might be attended to an inference by discussing which guidelines were used to produce it and then continuing through underlying inferences and guidelines all the way back to root assumptions. [58] Lofti Zadeh had actually presented a different type of extension to handle the representation of ambiguity. For instance, in deciding how “heavy” or “tall” a male is, there is regularly no clear “yes” or “no” answer, and a predicate for heavy or high would instead return worths between 0 and 1. Those values represented to what degree the predicates held true. His fuzzy reasoning further supplied a means for propagating mixes of these worths through logical formulas. [59]

Machine learning

Symbolic maker finding out approaches were examined to attend to the knowledge acquisition bottleneck. Among the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test method to create plausible guideline hypotheses to test against spectra. Domain and job knowledge reduced the number of prospects evaluated to a workable size. Feigenbaum described Meta-DENDRAL as

… the culmination of my dream of the early to mid-1960s relating to theory development. The conception was that you had an issue solver like DENDRAL that took some inputs and produced an output. In doing so, it utilized layers of knowledge to guide and prune the search. That understanding acted because we talked to individuals. But how did the people get the knowledge? By taking a look at thousands of spectra. So we wanted a program that would look at countless spectra and infer the knowledge of mass spectrometry that DENDRAL might utilize to solve specific 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 been a dream: to have a computer system program developed a brand-new and publishable piece of science. [51]

In contrast to the knowledge-intensive method of Meta-DENDRAL, Ross Quinlan created a domain-independent method to statistical category, decision tree knowing, starting initially with ID3 [60] and after that later on extending its capabilities to C4.5. [61] The choice trees created are glass box, interpretable classifiers, with human-interpretable classification rules.

Advances were made in understanding artificial intelligence theory, too. Tom Mitchell introduced version space learning which describes knowing as a search through a space of hypotheses, with upper, more general, and lower, more specific, limits including all practical hypotheses consistent with the examples seen so far. [62] More formally, Valiant presented Probably Approximately Correct Learning (PAC Learning), a framework for the mathematical analysis of artificial intelligence. [63]

Symbolic maker discovering encompassed more than discovering by example. E.g., John Anderson offered a cognitive model of human learning where skill practice results in a compilation of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a trainee might learn to use “Supplementary angles are 2 angles whose steps sum 180 degrees” as a number of various procedural guidelines. E.g., one guideline might say that if X and Y are extra and you understand X, then Y will be 180 – X. He called his technique “knowledge compilation”. ACT-R has been utilized successfully to design aspects of human cognition, such as learning and retention. ACT-R is also used in intelligent tutoring systems, called cognitive tutors, to effectively teach geometry, computer system programs, and algebra to school kids. [64]

Inductive logic programs was another method to discovering that enabled logic programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) might synthesize Prolog programs from examples. [65] John R. Koza used hereditary algorithms to program synthesis to produce hereditary shows, which he used to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger offered a more basic technique to program synthesis that synthesizes a practical program in the course of proving its specs to be appropriate. [66]

As an option to reasoning, Roger Schank introduced case-based thinking (CBR). The CBR approach described in his book, Dynamic Memory, [67] focuses first on keeping in mind crucial problem-solving cases for future usage and generalizing them where appropriate. When faced with a brand-new issue, CBR recovers the most similar previous case and adapts it to the specifics of the current issue. [68] Another option to logic, genetic algorithms and hereditary programs are based upon an evolutionary design of knowing, where sets of guidelines are encoded into populations, the guidelines govern the habits of people, and choice of the fittest prunes out sets of inappropriate rules over lots of generations. [69]

Symbolic artificial intelligence was used to finding out ideas, rules, heuristics, and problem-solving. Approaches, aside from those above, include:

1. Learning from direction or advice-i.e., taking human instruction, impersonated advice, and identifying how to operationalize it in particular circumstances. For instance, in a video game of Hearts, discovering exactly how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving efficiency by accepting subject-matter professional (SME) feedback during training. When analytical stops working, querying the professional to either find out a new exemplar for analytical or to learn a new explanation as to exactly why one exemplar is more pertinent than another. For example, the program Protos discovered to detect ringing in the ears cases by communicating with an audiologist. [71] 3. Learning by analogy-constructing issue solutions based upon similar problems seen in the past, and after that modifying their services to fit a brand-new situation or domain. [72] [73] 4. Apprentice learning systems-learning novel services to issues by observing human problem-solving. Domain knowledge describes why novel solutions are right and how the solution can be generalized. LEAP found out how to develop VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., developing tasks to perform experiments and then learning from the outcomes. Doug Lenat’s Eurisko, for example, learned heuristics to beat human gamers at the Traveller role-playing game for two years in a row. [75] 6. Learning macro-operators-i.e., browsing for useful macro-operators to be gained from sequences of basic analytical actions. Good macro-operators simplify analytical by permitting issues to be resolved at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now

With the increase of deep knowing, the symbolic AI technique has been compared to deep learning as complementary “… with parallels having been drawn lot of times by AI scientists in between Kahneman’s research on human reasoning and choice making – shown 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 reasoning is more apt for deliberative thinking, planning, and explanation while deep knowing is more apt for quick pattern acknowledgment in perceptual applications with noisy information. [17] [18]

Neuro-symbolic AI: integrating neural and symbolic approaches

Neuro-symbolic AI efforts to incorporate 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 efficient in thinking, discovering, and cognitive modeling. As argued by Valiant [77] and many others, [78] the reliable construction of abundant computational cognitive designs demands the combination of sound symbolic reasoning and efficient (maker) learning models. Gary Marcus, likewise, argues that: “We can not construct abundant cognitive models in a sufficient, automated method without the triumvirate of hybrid architecture, abundant anticipation, and sophisticated strategies for reasoning.”, [79] and in specific: “To develop a robust, knowledge-driven technique to AI we should have the machinery of symbol-manipulation in our toolkit. Excessive of useful understanding is abstract to make do without tools that represent and control abstraction, and to date, the only equipment that we understand of that can manipulate such abstract understanding dependably is the device of symbol control. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based on a need to resolve the two kinds of believing talked about in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having two components, System 1 and System 2. System 1 is fast, automated, instinctive and unconscious. System 2 is slower, detailed, and explicit. System 1 is the kind utilized for pattern recognition while System 2 is far better matched for planning, deduction, and deliberative thinking. In this view, deep learning finest models the very first type of believing while symbolic thinking finest designs the second kind and both are required.

Garcez and Lamb explain research in this location as being ongoing for at least the past twenty years, [83] dating from their 2002 book on neurosymbolic knowing systems. [84] A series of workshops on neuro-symbolic reasoning has actually 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 20 years and has actually yielded numerous considerable outcomes. Over the last decade, neural symbolic systems have actually been revealed capable of overcoming the so-called propositional fixation of neural networks, as McCarthy (1988) put it in response to Smolensky (1988 ); see also (Hinton, 1990). Neural networks were revealed capable of 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 applied to a number of issues in the areas of bioinformatics, control engineering, software application confirmation and adjustment, visual intelligence, ontology learning, and computer system games. [78]

Approaches for combination are varied. Henry Kautz’s taxonomy of neuro-symbolic architectures, in addition to some examples, follows:

– Symbolic Neural symbolic-is the present method of lots of neural models in natural language processing, where words or subword tokens are both the supreme 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 strategies. In this case the symbolic approach is Monte Carlo tree search and the neural strategies discover how to examine game positions.
– Neural|Symbolic-uses a neural architecture to interpret affective data as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to generate or label training data that is subsequently discovered by a deep knowing design, e.g., to train a neural design for symbolic computation by utilizing a Macsyma-like symbolic mathematics system to develop or identify examples.
– Neural _ Symbolic -uses a neural internet that is produced from symbolic rules. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR evidence tree created from understanding base rules and terms. Logic Tensor Networks [86] also fall under this classification.
– Neural [Symbolic] -permits a neural design to straight call a symbolic reasoning engine, e.g., to carry out an action or assess a state.

Many essential research study questions remain, such as:

– What is the very best way to incorporate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and extracted from them?
– How should common-sense knowledge be learned and reasoned about?
– How can abstract knowledge that is difficult to encode realistically be dealt with?

Techniques and contributions

This section offers a summary of strategies and contributions in a total context leading to numerous other, more in-depth articles in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered previously in the history section.

AI programs languages

The key AI shows language in the US during the last symbolic AI boom period was LISP. LISP is the 2nd oldest programming language after FORTRAN and was created in 1958 by John McCarthy. LISP offered the first read-eval-print loop to support quick program development. Compiled functions might be easily blended with translated functions. Program tracing, stepping, and breakpoints were likewise provided, along with the capability to alter worths or functions and continue from breakpoints or mistakes. It had the first self-hosting compiler, suggesting that the compiler itself was originally written in LISP and after that ran interpretively to compile the compiler code.

Other key innovations originated by LISP that have actually spread out to other programs languages consist of:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

Programs were themselves information structures that other programs might run on, permitting the simple definition of higher-level languages.

In contrast to the US, in Europe the crucial AI programs language throughout that same period was Prolog. Prolog supplied an integrated store of facts and clauses that could be queried by a read-eval-print loop. The store could serve as an understanding base and the stipulations might act as guidelines or a limited form of logic. As a subset of first-order logic Prolog was based upon Horn clauses with a closed-world assumption-any truths not known were thought about false-and a special name assumption for primitive terms-e.g., the identifier barack_obama was considered to refer to exactly one object. Backtracking and marriage are integrated to Prolog.

Alain Colmerauer and Philippe Roussel are credited as the developers of Prolog. Prolog is a form of logic programs, which was invented by Robert Kowalski. Its history was likewise affected 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 post.

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

Japan promoted Prolog for its Fifth Generation Project, intending to develop unique hardware for high performance. Similarly, LISP devices were developed to run LISP, however as the 2nd AI boom turned to bust these business might not contend with new workstations that might now run LISP or Prolog natively at similar speeds. See the history area for more information.

Smalltalk was another influential AI programs language. For instance, it presented metaclasses and, in addition to Flavors and CommonLoops, affected the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the existing basic Lisp dialect. CLOS is a Lisp-based object-oriented system that allows several inheritance, in addition to incremental extensions to both classes and metaclasses, therefore supplying a run-time meta-object protocol. [88]

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

Search

Search emerges in many type of issue solving, consisting of planning, constraint complete satisfaction, and playing games such as checkers, chess, and go. The very best known 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 clause learning, and the DPLL algorithm. For adversarial search when playing games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and thinking

Multiple different techniques to represent knowledge and after that factor with those representations have been examined. Below is a fast introduction of approaches to understanding representation and automated reasoning.

Knowledge representation

Semantic networks, conceptual graphs, frames, and reasoning are all approaches to modeling understanding such as domain knowledge, analytical understanding, and the semantic significance of language. Ontologies design essential 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 also be deemed an ontology. YAGO incorporates WordNet as part of its ontology, to line up realities extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being utilized.

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

First-order logic is more basic than description logic. The automated theorem provers discussed below can show theorems in first-order logic. Horn stipulation reasoning is more limited than first-order logic and is utilized in reasoning programs languages such as Prolog. Extensions to first-order logic include temporal reasoning, to manage time; epistemic logic, to reason about agent understanding; modal reasoning, to manage possibility and need; and probabilistic reasonings to manage reasoning and possibility together.

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

Prover9 can be used in combination with the Mace4 design checker. ACL2 is a theorem prover that can handle evidence by induction and is a descendant of the Boyer-Moore Theorem Prover, likewise called Nqthm.

Reasoning in knowledge-based systems

Knowledge-based systems have a specific knowledge base, typically of guidelines, to enhance reusability throughout domains by separating procedural code and domain knowledge. A separate reasoning engine procedures guidelines and adds, deletes, or modifies an understanding store.

Forward chaining reasoning engines are the most common, and are seen in CLIPS and OPS5. Backward chaining happens in Prolog, where a more minimal rational representation is utilized, Horn Clauses. Pattern-matching, specifically unification, is used in Prolog.

A more versatile kind of problem-solving happens when reasoning about what to do next occurs, rather than simply selecting one of the readily available actions. This type of meta-level reasoning is utilized in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R might have extra capabilities, such as the capability to put together frequently utilized knowledge into higher-level chunks.

Commonsense reasoning

Marvin Minsky initially proposed frames as a method of interpreting typical visual scenarios, such as a workplace, and Roger Schank extended this concept to scripts for common routines, such as eating in restaurants. Cyc has actually attempted to capture useful sensible knowledge and has “micro-theories” to manage specific kinds of domain-specific reasoning.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] estimates human reasoning about naive physics, such as what takes place when we warm a liquid in a pot on the stove. We expect it to heat and perhaps boil over, despite the fact that we might not know its temperature level, its boiling point, or other information, such as air pressure.

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

Constraints and constraint-based thinking

Constraint solvers carry out a more limited type of reasoning than first-order logic. They can simplify 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 issues, and so on. Constraint logic programs can be utilized to fix scheduling issues, for instance with restraint managing rules (CHR).

Automated planning

The General Problem Solver (GPS) cast planning as analytical utilized means-ends analysis to develop plans. STRIPS took a various method, viewing planning as theorem proving. Graphplan takes a least-commitment method to planning, rather than sequentially selecting actions from a preliminary state, working forwards, or an objective state if working in reverse. Satplan is an approach to planning where a planning issue is lowered to a Boolean satisfiability issue.

Natural language processing

Natural language processing concentrates on dealing with language as information to perform jobs such as identifying subjects without always understanding the desired significance. Natural language understanding, in contrast, constructs a significance representation and uses that for further processing, such as addressing concerns.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all aspects of natural language processing long managed by symbolic AI, however given that enhanced by deep knowing methods. In symbolic AI, discourse representation theory and first-order logic have been used to represent sentence significances. Latent semantic analysis (LSA) and explicit semantic analysis likewise provided vector representations of documents. In the latter case, vector parts are interpretable as concepts named by Wikipedia articles.

New deep learning approaches based upon Transformer models have actually now eclipsed these earlier symbolic AI methods and attained advanced efficiency in natural language processing. However, Transformer designs are opaque and do not yet produce human-interpretable semantic representations for sentences and documents. Instead, they produce task-specific vectors where the meaning of the vector elements is opaque.

Agents and multi-agent systems

Agents are self-governing systems embedded in an environment they view and act upon in some sense. Russell and Norvig’s standard book on synthetic intelligence is arranged to reflect representative architectures of increasing elegance. [91] The elegance of representatives differs from simple reactive agents, to those with a design of the world and automated preparation capabilities, potentially a BDI representative, i.e., one with beliefs, desires, and objectives – or additionally a reinforcement discovering design discovered with time to pick actions – approximately a mix of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep knowing for perception. [92]

On the other hand, a multi-agent system consists of several representatives that communicate amongst themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The representatives require not all have the very same internal architecture. Advantages of multi-agent systems consist of the capability to divide work among the representatives and to increase fault tolerance when representatives are lost. Research issues consist of how representatives reach consensus, distributed issue fixing, multi-agent knowing, multi-agent preparation, and dispersed restraint optimization.

Controversies arose from at an early stage in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who embraced AI however turned down symbolic approaches-primarily connectionists-and those outside the field. Critiques from beyond the field were mostly from thinkers, on intellectual grounds, however likewise from financing agencies, particularly during the 2 AI winter seasons.

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

Limitations were discovered in using simple first-order logic to reason about dynamic domains. Problems were found both with concerns to specifying the preconditions for an action to succeed and in offering axioms for what did not alter after an action was carried out.

McCarthy and Hayes presented the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Artificial Intelligence.” [93] A basic example occurs in “showing that a person person could get 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 required for the deduction to prosper. Similar axioms would be required for other domain actions to specify what did not change.

A comparable issue, called the Qualification Problem, happens in trying to mention the prerequisites for an action to succeed. An unlimited number of pathological conditions can be thought of, e.g., a banana in a tailpipe could prevent an automobile from running correctly.

McCarthy’s approach to fix the frame issue was circumscription, a type of non-monotonic logic where deductions could be made from actions that require just define what would change while not having to clearly specify whatever that would not alter. Other non-monotonic reasonings offered fact maintenance systems that modified beliefs resulting in contradictions.

Other methods of managing more open-ended domains included probabilistic reasoning systems and machine learning to discover new ideas and rules. McCarthy’s Advice Taker can be seen as an inspiration here, as it could include brand-new understanding provided by a human in the type of assertions or guidelines. For example, speculative symbolic maker finding out systems explored the capability to take top-level natural language advice and to analyze it into domain-specific actionable guidelines.

Similar to the issues in handling vibrant domains, sensible reasoning is likewise challenging to catch in official thinking. Examples of sensible thinking include implicit reasoning about how people believe or basic understanding of daily occasions, items, and living animals. This sort of understanding is considered approved and not seen as noteworthy. Common-sense reasoning is an open location 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 cars that do not understand not to drive into cones or not to strike pedestrians strolling a bicycle).

McCarthy viewed his Advice Taker as having common-sense, however his definition of common-sense was different than the one above. [94] He defined a program as having good sense “if it instantly deduces for itself a sufficiently large class of immediate effects of anything it is told and what it already knows. “

Connectionist AI: philosophical obstacles and sociological conflicts

Connectionist approaches consist of earlier deal with neural networks, [95] such as perceptrons; work 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 advanced approaches, such as Transformers, GANs, and other work in deep learning.

Three philosophical positions [96] have actually been described among connectionists:

1. Implementationism-where connectionist architectures execute the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected absolutely, and connectionist architectures underlie intelligence and are totally enough to describe 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 controversies within the neural network community, described the moderate connectionism deem essentially suitable with current research study in neuro-symbolic hybrids:

The third and last position I would like to take a look at here is what I call the moderate connectionist view, a more eclectic view of the existing argument in between connectionism and symbolic AI. One of the scientists who has elaborated this position most clearly is Andy Clark, a thinker from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark safeguarded hybrid (partly symbolic, partially connectionist) systems. He claimed that (a minimum of) 2 type of theories are needed in order to study and model cognition. On the one hand, for some information-processing jobs (such as pattern acknowledgment) connectionism has benefits over symbolic designs. But on the other hand, for other cognitive procedures (such as serial, deductive reasoning, and generative sign control processes) the symbolic paradigm provides appropriate designs, and not just “approximations” (contrary to what extreme connectionists would claim). [97]

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

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

And yet, for the a lot of part, that’s how most present AI proceeds. Hinton and many others have actually striven to banish symbols entirely. The deep knowing hope-seemingly grounded not a lot in science, but in a sort of historic grudge-is that smart habits will emerge simply from the confluence of enormous information and deep knowing. Where classical computers and software solve jobs by specifying sets of symbol-manipulating guidelines devoted to specific tasks, such as editing a line in a word processor or carrying out a computation in a spreadsheet, neural networks usually try to resolve jobs by statistical approximation and finding out from examples.

According to Marcus, Geoffrey Hinton and his colleagues have been emphatically “anti-symbolic”:

When deep knowing reemerged in 2012, it was with a type of take-no-prisoners mindset that has identified the majority of the last decade. By 2015, his hostility toward all things signs had completely taken shape. He lectured at an AI workshop at Stanford comparing symbols to aether, among science’s biggest mistakes.

…

Since then, his anti-symbolic campaign has actually only increased in strength. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep learning in among science’s essential journals, Nature. It closed with a direct attack on sign manipulation, calling not for reconciliation but for straight-out replacement. Later, Hinton informed an event of European Union leaders that investing any additional cash in symbol-manipulating methods was “a big mistake,” comparing it to purchasing internal combustion engines in the age of electrical cars. [98]

Part of these disputes might be because of unclear terminology:

Turing award winner Judea Pearl uses a review of artificial intelligence which, regrettably, conflates the terms artificial intelligence and deep learning. Similarly, when Geoffrey Hinton describes symbolic AI, the undertone of the term tends to be that of expert systems dispossessed of any ability to find out. Using the terms requires explanation. Artificial intelligence is not restricted to association rule mining, c.f. the body of work on symbolic ML and relational knowing (the distinctions to deep learning being the choice of representation, localist rational instead of distributed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not almost production rules written by hand. An appropriate definition of AI concerns understanding representation and reasoning, self-governing multi-agent systems, preparation and argumentation, in addition to learning. [99]

Situated robotics: the world as a model

Another review of symbolic AI is the embodied cognition technique:

The embodied cognition method claims that it makes no sense to consider the brain independently: cognition occurs within a body, which is embedded in an environment. We require to study the system as a whole; the brain’s functioning exploits consistencies in its environment, including the rest of its body. Under the embodied cognition method, robotics, vision, and other sensors end up being central, not peripheral. [100]

Rodney Brooks invented behavior-based robotics, one approach to embodied cognition. Nouvelle AI, another name for this approach, is seen as an alternative to both symbolic AI and connectionist AI. His method turned down representations, either symbolic or dispersed, as not only unneeded, but as detrimental. Instead, he produced the subsumption architecture, a layered architecture for embodied agents. Each layer attains a different function and needs to work in the real life. For instance, the first robotic he describes in Intelligence Without Representation, has three layers. The bottom layer analyzes sonar sensors to avoid things. The middle layer causes the robot to roam around when there are no barriers. The leading layer triggers the robotic to go to more far-off places for more exploration. Each layer can briefly inhibit or suppress a lower-level layer. He slammed AI researchers for specifying AI issues for their systems, when: “There is no tidy department between understanding (abstraction) and thinking in the real life.” [101] He called his robotics “Creatures” and each layer was “composed of a fixed-topology network of easy finite state machines.” [102] In the Nouvelle AI technique, “First, it is extremely crucial to test the Creatures we construct in the real life; i.e., in the very same world that we people populate. It is disastrous to fall into the temptation of checking them in a streamlined world initially, even with the very best intentions of later transferring activity to an unsimplified world.” [103] His emphasis on real-world screening remained in contrast to “Early operate in AI focused on games, geometrical problems, symbolic algebra, theorem proving, and other official systems” [104] and making use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has benefits, however has been criticized by the other methods. Symbolic AI has actually been criticized as disembodied, responsible to the qualification issue, and bad in dealing with the perceptual issues where deep finding out excels. In turn, connectionist AI has been slammed as poorly suited for deliberative step-by-step issue solving, integrating understanding, and dealing with planning. Finally, Nouvelle AI masters reactive and real-world robotics domains but has been criticized for problems in incorporating learning and knowledge.

Hybrid AIs incorporating one or more of these techniques are presently deemed the course forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw areas where AI did not have total responses and said that Al is therefore difficult; we now see numerous of these same areas going through ongoing research study and advancement causing increased capability, not impossibility. [100]

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

Notes

^ McCarthy once stated: “This is AI, so we don’t care if it’s mentally real”. [4] McCarthy restated his position in 2006 at the AI@50 conference where he said “Artificial intelligence is not, by definition, simulation of human intelligence”. [28] Pamela McCorduck writes that there are “2 major branches of expert system: one intended at producing smart habits despite how it was accomplished, and the other targeted at modeling smart processes found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not define the objective of their field as making ‘makers that fly so exactly like pigeons that they can trick even other pigeons.'” [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). “Reconciling deep learning with symbolic expert system: representing items 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 Expert System”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep knowing with symbolic expert system: 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 mistakes”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
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^ 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.
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^ 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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