Symbolic Artificial Intelligence

In artificial intelligence, symbolic synthetic intelligence (also referred to as classical expert system or logic-based expert system) [1] [2] is the term for the collection of all techniques in expert system research study that are based on high-level symbolic (human-readable) representations of problems, logic and search. [3] Symbolic AI used tools such as logic programs, production guidelines, semantic internet and frames, and it established 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 led to influential ideas in search, symbolic shows languages, representatives, multi-agent systems, the semantic web, and the strengths and limitations of formal understanding and reasoning systems.

Symbolic AI was the dominant paradigm of AI research study from the mid-1950s up until the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic methods would eventually prosper in a maker with synthetic general intelligence and considered this the supreme objective of their field. [citation required] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, led to unrealistic expectations and guarantees and was followed by the very first AI Winter as moneying dried up. [5] [6] A second boom (1969-1986) occurred with the rise of expert systems, their guarantee of capturing business proficiency, and a passionate business welcome. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later on frustration. [8] Problems with difficulties in knowledge acquisition, preserving large understanding bases, and brittleness in managing out-of-domain issues occurred. Another, 2nd, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers focused on attending to hidden problems in dealing with unpredictability and in knowledge acquisition. [10] Uncertainty was resolved with official approaches such as surprise Markov designs, Bayesian thinking, and analytical relational learning. [11] [12] Symbolic device learning dealt with the knowledge acquisition problem with contributions consisting of Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree learning, case-based learning, and inductive logic shows to learn relations. [13]

Neural networks, a subsymbolic technique, had 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 considered as effective up until about 2012: “Until Big Data ended up being commonplace, the basic agreement in the Al community was that the so-called neural-network method was helpless. Systems just didn’t work that well, compared to other approaches. … A transformation was available in 2012, when a number of individuals, including a team of scientists working with Hinton, exercised a way to utilize the power of GPUs to tremendously increase the power of neural networks.” [16] Over the next a number of years, deep learning had magnificent success in handling vision, speech recognition, speech synthesis, image generation, and device translation. However, since 2020, as fundamental difficulties with predisposition, description, comprehensibility, and robustness became more evident with deep learning approaches; an increasing number of AI scientists have actually required combining the very best of both the symbolic and neural network approaches [17] [18] and resolving areas that both approaches have problem with, such as sensible thinking. [16]

A brief history of symbolic AI to today day follows listed 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 differing a little for increased clarity.

The first AI summer: illogical vitality, 1948-1966

Success at early efforts in AI happened in three main locations: artificial neural networks, understanding representation, and heuristic search, adding to high expectations. This section summarizes Kautz’s reprise of early AI history.

Approaches inspired by human or animal cognition or behavior

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

An essential early symbolic AI program was the Logic theorist, written 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 generalized this work to produce a domain-independent issue solver, GPS (General Problem Solver). GPS resolved problems represented with official operators via state-space search using means-ends analysis. [21]

During the 1960s, symbolic methods accomplished terrific success at replicating smart habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was focused in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Each one developed its own design of research. Earlier techniques based on cybernetics or synthetic neural networks were abandoned 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, as well as cognitive science, operations research study and management science. Their research study team used the outcomes of mental experiments to establish programs that simulated the strategies that individuals utilized to solve issues. [22] [23] This tradition, focused at Carnegie Mellon University would ultimately culminate in the development of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific type of understanding that we will see later on used in expert systems, early symbolic AI researchers found another more general application of knowledge. These were called heuristics, general rules that assist a search in promising directions: “How can non-enumerative search be practical when the underlying issue is greatly hard? The technique advocated by Simon and Newell is to use heuristics: fast algorithms that might fail on some inputs or output suboptimal solutions.” [26] Another crucial advance was to find a method to use these heuristics that guarantees a solution will be discovered, if there is one, not holding up against the periodic fallibility of heuristics: “The A * algorithm offered a general frame for complete and optimum heuristically assisted search. A * is utilized as a subroutine within practically 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 knowledge representation and thinking

Early work covered both applications of formal reasoning emphasizing first-order reasoning, together with attempts to manage common-sense reasoning 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 mimic the precise systems of human idea, but might instead look for the essence of abstract thinking and problem-solving with reasoning, [27] regardless of whether people utilized the very same algorithms. [a] His laboratory at Stanford (SAIL) focused on utilizing formal logic to fix a wide array of issues, including understanding representation, planning and knowing. [31] Logic was also the focus of the work at the University of Edinburgh and elsewhere in Europe which resulted in the development of the programs language Prolog and the science of reasoning shows. [32] [33]

Modeling implicit sensible knowledge with frames and scripts: the “scruffies”

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that fixing tough issues in vision and natural language processing required ad hoc solutions-they argued that no simple and basic concept (like reasoning) would capture all the aspects of intelligent habits. Roger Schank described their “anti-logic” approaches as “shabby” (rather than 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 should 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 very first AI summertime, many individuals believed that machine intelligence could be accomplished in just a couple of years. The Defense Advance Research Projects Agency (DARPA) introduced programs to support AI research study to use AI to fix issues of nationwide security; in specific, to automate the translation of Russian to English for intelligence operations and to develop self-governing tanks for the battlefield. Researchers had begun to realize that achieving AI was going to be much harder than was supposed a years earlier, however a combination of hubris and disingenuousness led numerous university and think-tank scientists to accept financing with pledges of deliverables that they need to have known they might not fulfill. By the mid-1960s neither helpful natural language translation systems nor self-governing tanks had actually been created, and a significant backlash embeded in. New DARPA leadership canceled existing AI funding programs.

Outside of the United States, the most fertile ground for AI research was the UK. The AI winter in the UK was stimulated on not a lot by dissatisfied military leaders as by rival academics who saw AI researchers as charlatans and a drain on research study funding. A professor of applied 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 problems being worked on in AI would be much better dealt with by researchers from other disciplines-such as applied mathematics. The report likewise declared that AI successes on toy issues might never ever scale to real-world applications due to combinatorial explosion. [41]

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

Knowledge-based systems

As constraints with weak, domain-independent approaches became increasingly more obvious, [42] researchers from all three traditions started to develop knowledge into AI applications. [43] [7] The understanding revolution was driven by the awareness that understanding 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 highly domain-specific understanding. Ed Feigenbaum and Doug Lenat called this The Knowledge Principle:

( 1) The Knowledge Principle: if a program is to perform an intricate task well, it must understand a good deal about the world in which it operates.
( 2) A plausible extension of that concept, called the Breadth Hypothesis: there are two extra capabilities required for smart habits in unanticipated scenarios: drawing on progressively basic knowledge, and analogizing to particular however far-flung knowledge. [45]

Success with professional systems

This “understanding transformation” caused the advancement and release of specialist systems (introduced by Edward Feigenbaum), the very first commercially effective type of AI software. [46] [47] [48]

Key specialist systems were:

DENDRAL, which found the structure of organic particles from their chemical formula and mass spectrometer readings.
MYCIN, which identified bacteremia – and recommended additional lab tests, when essential – by translating lab outcomes, patient history, and physician observations. “With about 450 rules, MYCIN was able to carry out in addition to some experts, and substantially much better than junior physicians.” [49] INTERNIST and CADUCEUS which dealt with internal medication medical diagnosis. Internist attempted to capture the know-how of the chairman of internal medicine at the University of Pittsburgh School of Medicine while CADUCEUS might ultimately detect up to 1000 different diseases.
– GUIDON, which showed how a knowledge base constructed for expert problem solving might be repurposed for teaching. [50] XCON, to set up VAX computer systems, a then tiresome process that might use up to 90 days. XCON reduced the time to about 90 minutes. [9]
DENDRAL is thought about the first specialist system that depend on knowledge-intensive problem-solving. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

Among individuals at Stanford thinking about computer-based models of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genetics. When I informed him I desired an induction “sandbox”, he stated, “I have simply the one for you.” His lab 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 approaches, and he had an algorithm that was excellent at creating the chemical problem area.

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, creator of the chemical behind the birth control pill, and also one of the world’s most appreciated mass spectrometrists. Carl and his postdocs were world-class experts in mass spectrometry. We started to include to their knowledge, inventing 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 very good outcomes.

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

The other professional systems pointed out above came after DENDRAL. MYCIN exemplifies the timeless professional system architecture of a knowledge-base of guidelines combined to a symbolic thinking mechanism, consisting of using certainty factors to deal with uncertainty. GUIDON demonstrates how a specific knowledge base can be repurposed for a 2nd application, tutoring, and is an example of a smart tutoring system, a specific sort of knowledge-based application. Clancey showed that it was not enough merely to utilize MYCIN’s guidelines for direction, but that he likewise needed to include guidelines for dialogue management and trainee modeling. [50] XCON is considerable since of the millions of dollars it saved DEC, which activated the specialist system boom where most all significant corporations in the US had professional systems groups, to capture business expertise, preserve it, and automate it:

By 1988, DEC’s AI group had 40 specialist systems deployed, with more on the method. DuPont had 100 in usage and 500 in advancement. Nearly every major U.S. corporation had its own Al group and was either using or examining professional systems. [49]

Chess specialist understanding was encoded in Deep Blue. In 1996, this permitted IBM’s Deep Blue, with the aid 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

An essential element of the system architecture for all expert systems is the knowledge base, which shops truths and rules for analytical. [53] The simplest approach for an expert system understanding base is simply a collection or network of production guidelines. Production guidelines link signs in a relationship comparable to an If-Then declaration. The expert system processes the rules to make reductions and to determine what extra info it requires, i.e. what concerns to ask, using human-readable signs. For example, OPS5, CLIPS and their successors Jess and Drools operate in this fashion.

Expert systems can run in either a forward chaining – from evidence to conclusions – or backward chaining – from objectives to needed information and prerequisites – manner. More sophisticated knowledge-based systems, such as Soar can likewise perform meta-level thinking, that is thinking about their own thinking in terms of choosing how to resolve problems and monitoring the success of problem-solving techniques.

Blackboard systems are a second kind of knowledge-based or expert system architecture. They design a community of experts incrementally contributing, where they can, to fix an issue. The problem is represented in multiple levels of abstraction or alternate views. The specialists (knowledge sources) volunteer their services whenever they acknowledge they can contribute. Potential problem-solving actions are represented on a program that is upgraded as the problem circumstance modifications. A controller decides how useful each contribution is, and who should make the next analytical action. One example, the BB1 blackboard architecture [54] was originally influenced by studies of how human beings prepare to perform multiple jobs in a journey. [55] A development of BB1 was to use the very same blackboard model to fixing its control problem, i.e., its controller carried out meta-level reasoning with knowledge sources that kept track of how well a plan or the problem-solving was continuing and could change from one method to another as conditions – such as goals or times – altered. BB1 has been used in numerous domains: building and construction website planning, intelligent tutoring systems, and real-time patient tracking.

The second AI winter season, 1988-1993

At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were offering LISP makers specifically targeted to accelerate the development of AI applications and research. In addition, numerous synthetic intelligence business, such as Teknowledge and Inference Corporation, were offering skilled system shells, training, and consulting to corporations.

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

Many reasons can be offered for the arrival of the 2nd AI winter. The hardware business stopped working when much more economical general Unix workstations from Sun together with good compilers for LISP and Prolog came onto the marketplace. Many business deployments of specialist systems were stopped when they showed too costly to keep. Medical professional systems never ever captured on for several reasons: the difficulty in keeping them as much as date; the challenge for physician to discover how to utilize an overwelming variety of various specialist systems for different medical conditions; and maybe most crucially, the hesitation of physicians to rely on a computer-made medical diagnosis over their gut impulse, even for specific domains where the specialist systems might surpass an average medical professional. Equity capital money deserted AI almost over night. The world AI conference IJCAI hosted a massive and lavish trade show and countless nonacademic guests in 1987 in Vancouver; the primary AI conference the following year, AAAI 1988 in St. Paul, was a small and strictly academic affair. [9]

Including more rigorous structures, 1993-2011

Uncertain thinking

Both analytical approaches and extensions to logic were tried.

One statistical technique, concealed Markov models, had currently been popularized in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized using Bayesian Networks as a noise but efficient method of dealing with unsure thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian techniques were applied effectively in expert systems. [57] Even later on, in the 1990s, analytical relational knowing, an approach that combines likelihood with logical formulas, permitted likelihood 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 reasoning to assistance were likewise tried. For example, non-monotonic reasoning might be used with truth maintenance systems. A truth maintenance system tracked assumptions and validations for all inferences. It enabled reasonings to be withdrawn when assumptions were learnt to be incorrect or a contradiction was derived. Explanations might be offered for a reasoning by explaining which rules were applied to produce it and then continuing through underlying reasonings and guidelines all the method back to root assumptions. [58] Lofti Zadeh had actually presented a different sort of extension to handle the representation of vagueness. For instance, in deciding how “heavy” or “tall” a guy is, there is often no clear “yes” or “no” response, and a predicate for heavy or high would instead return values between 0 and 1. Those worths represented to what degree the predicates were real. His fuzzy logic even more provided a means for propagating mixes of these worths through logical solutions. [59]

Machine learning

Symbolic device discovering 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 produce plausible guideline hypotheses to check versus spectra. Domain and job knowledge reduced the number of prospects tested to a workable size. Feigenbaum described Meta-DENDRAL as

… the conclusion of my dream of the early to mid-1960s relating to theory formation. 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 knowledge to steer and prune the search. That knowledge got in there since we interviewed individuals. But how did the people get the understanding? By looking at thousands of spectra. So we desired a program that would look at countless spectra and infer the knowledge of mass spectrometry that DENDRAL could use to fix individual hypothesis formation issues. We did it. We were even able to publish new understanding of mass spectrometry in the Journal of the American Chemical Society, offering credit just in a footnote that a program, Meta-DENDRAL, really did it. We were able to do something that had been a dream: to have a computer system program come up with a new and publishable piece of science. [51]

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

Advances were made in understanding artificial intelligence theory, too. Tom Mitchell introduced version space learning which explains knowing as a search through an area of hypotheses, with upper, more general, and lower, more particular, boundaries including all feasible hypotheses constant with the examples seen so far. [62] More formally, Valiant introduced Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of artificial intelligence. [63]

Symbolic maker finding out included more than finding out by example. E.g., John Anderson provided a cognitive design of human knowing where skill practice leads to a collection of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a trainee might discover to apply “Supplementary angles are two angles whose steps sum 180 degrees” as several various procedural guidelines. E.g., one rule may state that if X and Y are supplemental and you know X, then Y will be 180 – X. He called his approach “understanding collection”. ACT-R has actually been utilized effectively to design elements of human cognition, such as discovering and retention. ACT-R is also utilized in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer shows, and algebra to school children. [64]

Inductive reasoning programming was another approach to finding out that enabled logic programs to be synthesized from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) could synthesize Prolog programs from examples. [65] John R. Koza used genetic algorithms to program synthesis to develop genetic programming, which he utilized to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger offered a more general approach to program synthesis that synthesizes a functional program in the course of proving its specs to be appropriate. [66]

As an option to logic, Roger Schank presented case-based thinking (CBR). The CBR method outlined in his book, Dynamic Memory, [67] focuses first on remembering crucial problem-solving cases for future use and generalizing them where proper. When faced with a new problem, CBR recovers the most similar previous case and adapts it to the specifics of the present problem. [68] Another alternative to logic, genetic algorithms and genetic programs are based upon an evolutionary model of knowing, where sets of rules are encoded into populations, the guidelines govern the habits of individuals, and selection of the fittest prunes out sets of unsuitable rules over lots of generations. [69]

Symbolic machine learning was used to finding out concepts, rules, heuristics, and problem-solving. Approaches, aside from those above, include:

1. Learning from direction or advice-i.e., taking human guideline, postured as suggestions, and figuring out how to operationalize it in specific scenarios. For instance, in a game of Hearts, discovering precisely how to play a hand to “prevent taking points.” [70] 2. Learning from exemplars-improving efficiency by accepting subject-matter professional (SME) feedback during training. When problem-solving stops working, querying the expert to either learn a new prototype for problem-solving or to discover a brand-new description as to precisely why one exemplar is more relevant than another. For example, the program Protos learned to diagnose tinnitus cases by interacting with an audiologist. [71] 3. Learning by analogy-constructing issue services based on comparable issues seen in the past, and then modifying their options to fit a new situation or domain. [72] [73] 4. Apprentice knowing systems-learning unique services to issues by observing human problem-solving. Domain knowledge describes why novel options are correct and how the service can be generalized. LEAP found out how to develop VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing tasks to bring out experiments and then gaining from the outcomes. Doug Lenat’s Eurisko, for instance, found out heuristics to beat human gamers at the Traveller role-playing game for two years in a row. [75] 6. Learning macro-operators-i.e., searching for beneficial macro-operators to be discovered from series of fundamental problem-solving actions. Good macro-operators simplify analytical by permitting problems to be solved at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now

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

Neuro-symbolic AI: incorporating neural and symbolic methods

Neuro-symbolic AI efforts to incorporate neural and symbolic architectures in a manner that addresses strengths and weak points of each, in a complementary fashion, in order to support robust AI efficient in reasoning, learning, and cognitive modeling. As argued by Valiant [77] and lots of others, [78] the efficient construction of abundant computational cognitive models requires the mix of sound symbolic thinking and efficient (machine) knowing designs. Gary Marcus, similarly, argues that: “We can not construct rich cognitive designs in an appropriate, automated method without the triumvirate of hybrid architecture, abundant anticipation, and advanced techniques for thinking.”, [79] and in specific: “To develop a robust, knowledge-driven approach to AI we need to have the machinery of symbol-manipulation in our toolkit. Too much of useful understanding is abstract to make do without tools that represent and control abstraction, and to date, the only machinery that we understand of that can manipulate such abstract understanding dependably is the apparatus of symbol adjustment. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have likewise argued for a synthesis. Their arguments are based upon a requirement to attend to the two kinds of thinking gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having two elements, System 1 and System 2. System 1 is quick, automated, intuitive and unconscious. System 2 is slower, detailed, and specific. System 1 is the kind used for pattern recognition while System 2 is far better suited for preparation, reduction, and deliberative thinking. In this view, deep knowing finest designs the first sort of believing while symbolic reasoning finest designs the 2nd kind and both are required.

Garcez and Lamb explain research in this location as being ongoing for at least the previous twenty years, [83] dating from their 2002 book on neurosymbolic knowing systems. [84] A series of workshops on neuro-symbolic reasoning has been held every year since 2005, see http://www.neural-symbolic.org/ for details.

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

The integration of the symbolic and connectionist paradigms of AI has actually been pursued by a reasonably small research community over the last 20 years and has actually yielded numerous substantial outcomes. Over the last years, neural symbolic systems have been shown efficient in conquering 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 shown capable of representing modal and temporal logics (d’Avila Garcez and Lamb, 2006) and fragments of first-order logic (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have actually been applied to a variety of problems in the areas of bioinformatics, control engineering, software application verification and adjustment, visual intelligence, ontology learning, and computer system games. [78]

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

– Symbolic Neural symbolic-is the existing approach of many neural designs in natural language processing, where words or subword tokens are both the ultimate input and output of large language designs. Examples consist of BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic techniques are used to call neural methods. In this case the symbolic approach is Monte Carlo tree search and the neural strategies discover how to assess game positions.
– Neural|Symbolic-uses a neural architecture to translate perceptual information as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to produce or label training information that is subsequently found out by a deep knowing model, e.g., to train a neural design for symbolic computation by utilizing a Macsyma-like symbolic mathematics system to produce or label examples.
– Neural _ Symbolic -uses a neural net that is created from symbolic rules. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR proof tree produced from knowledge base rules and terms. Logic Tensor Networks [86] likewise fall under this category.
– Neural [Symbolic] -permits a neural design to straight call a symbolic thinking engine, e.g., to carry out an action or evaluate a state.

Many crucial research 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 understanding be learned and reasoned about?
– How can abstract understanding that is hard to encode realistically be handled?

Techniques and contributions

This area supplies a summary of strategies and contributions in an overall context resulting in lots of other, more detailed articles in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered previously in the history area.

AI programming languages

The key AI programs language in the US throughout the last symbolic AI boom period was LISP. LISP is the second oldest programs language after FORTRAN and was produced in 1958 by John McCarthy. LISP offered the very first read-eval-print loop to support fast program advancement. Compiled functions might be easily blended with interpreted functions. Program tracing, stepping, and breakpoints were likewise provided, together with the capability to change worths or functions and continue from breakpoints or mistakes. It had the very first self-hosting compiler, suggesting that the compiler itself was initially composed in LISP and after that ran interpretively to assemble the compiler code.

Other essential developments originated by LISP that have actually infected other shows languages consist of:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

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

In contrast to the US, in Europe the essential AI programming language during that exact same period was Prolog. Prolog provided an integrated store of truths and clauses that could be queried by a read-eval-print loop. The shop could function as a knowledge base and the stipulations might act as rules or a limited form of reasoning. As a subset of first-order reasoning Prolog was based upon Horn clauses with a closed-world assumption-any realities not understood were considered false-and an unique name presumption for primitive terms-e.g., the identifier barack_obama was considered to describe precisely one item. Backtracking and unification are integrated to Prolog.

Alain Colmerauer and Philippe Roussel are credited as the developers of Prolog. Prolog is a type of reasoning programming, 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 detail see the section on the origins of Prolog in the PLANNER article.

Prolog is also a type of declarative programming. The reasoning stipulations that explain programs are directly translated to run the programs defined. No specific series of actions is required, as holds true with necessary programs languages.

Japan championed Prolog for its Fifth Generation Project, planning to develop unique hardware for high efficiency. Similarly, LISP devices were constructed to run LISP, however as the 2nd AI boom turned to bust these business might not take on new workstations that could now run LISP or Prolog natively at comparable speeds. See the history area for more information.

Smalltalk was another prominent AI programming language. For instance, 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 present standard Lisp dialect. CLOS is a Lisp-based object-oriented system that permits numerous inheritance, in addition to incremental extensions to both classes and metaclasses, thus offering a run-time meta-object procedure. [88]

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

Search

Search emerges in many type of issue resolving, consisting of preparation, restraint satisfaction, and playing games such as checkers, chess, and go. The very 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 approaches to represent understanding and after that reason with those representations have actually been examined. Below is a quick summary of approaches to understanding representation and automated thinking.

Knowledge representation

Semantic networks, conceptual graphs, frames, and logic are all methods to modeling understanding such as domain knowledge, analytical knowledge, 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 used for any domain while WordNet is a lexical resource that can also be considered as an ontology. YAGO integrates 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 presently being used.

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

First-order reasoning is more general than description reasoning. 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 used in reasoning programming languages such as Prolog. Extensions to first-order reasoning include temporal logic, to handle time; epistemic logic, to factor about agent knowledge; 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 utilized in combination with the Mace4 design checker. ACL2 is a theorem prover that can manage proofs by induction and is a descendant of the Boyer-Moore Theorem Prover, also called Nqthm.

Reasoning in knowledge-based systems

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

Forward chaining inference engines are the most typical, 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 unification, is used in Prolog.

A more flexible sort of analytical takes place when reasoning about what to do next happens, rather than merely choosing among the available actions. This kind of meta-level reasoning is utilized in Soar and in the BB1 chalkboard architecture.

Cognitive architectures such as ACT-R might have extra abilities, such as the ability to assemble frequently used understanding into higher-level pieces.

Commonsense reasoning

Marvin Minsky first proposed frames as a way of interpreting common visual situations, such as a workplace, and Roger Schank extended this idea to scripts for common routines, such as dining out. Cyc has tried to capture beneficial sensible knowledge and has “micro-theories” to manage specific type 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 potentially boil over, even though we may not know its temperature, its boiling point, or other details, such as climatic pressure.

Similarly, Allen’s temporal interval 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 constraint solvers.

Constraints and constraint-based thinking

Constraint solvers perform a more minimal sort of reasoning than first-order reasoning. They can streamline sets of spatiotemporal restraints, such as those for RCC or Temporal Algebra, along with resolving other kinds of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic programming can be utilized to fix scheduling issues, for example with restraint dealing with guidelines (CHR).

Automated planning

The General Problem Solver (GPS) cast planning as analytical utilized means-ends analysis to develop strategies. STRIPS took a various method, seeing planning as theorem proving. Graphplan takes a least-commitment technique to planning, rather than sequentially picking actions from an initial state, working forwards, or an objective state if working in reverse. Satplan is a technique to planning where a preparation issue is minimized to a Boolean satisfiability issue.

Natural language processing

Natural language processing focuses on dealing with language as data to perform jobs such as identifying topics without necessarily understanding the intended significance. Natural language understanding, in contrast, constructs a significance representation and utilizes that for further processing, such as addressing concerns.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all elements of natural language processing long managed by symbolic AI, but considering that enhanced by deep learning techniques. In symbolic AI, discourse representation theory and first-order logic have been utilized to represent sentence significances. Latent semantic analysis (LSA) and specific semantic analysis likewise offered vector representations of files. In the latter case, vector parts are interpretable as concepts named by Wikipedia posts.

New deep learning techniques based upon Transformer designs have actually now eclipsed these earlier symbolic AI approaches and attained cutting edge efficiency in natural language processing. However, Transformer designs are nontransparent 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 parts is nontransparent.

Agents and multi-agent systems

Agents are autonomous systems embedded in an environment they view and act on in some sense. Russell and Norvig’s basic textbook on expert system is organized to show agent architectures of increasing sophistication. [91] The elegance of representatives varies from basic reactive agents, to those with a design of the world and automated preparation capabilities, possibly a BDI representative, i.e., one with beliefs, desires, and objectives – or additionally a reinforcement finding out model found out over time to select actions – up to a mix of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep knowing for perception. [92]

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

Controversies emerged from early 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 welcomed AI however declined symbolic approaches-primarily connectionists-and those outside the field. Critiques from beyond the field were mainly from philosophers, on intellectual grounds, but likewise from funding companies, specifically throughout the two AI winter seasons.

The Frame Problem: knowledge representation challenges for first-order reasoning

Limitations were discovered in using simple first-order reasoning to reason about dynamic domains. Problems were found both with regards to identifying the prerequisites for an action to succeed and in providing axioms for what did not alter after an action was performed.

McCarthy and Hayes introduced the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Expert System.” [93] An easy example takes place in “proving 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 needed for other domain actions to specify what did not change.

A comparable issue, called the Qualification Problem, occurs in trying to identify the preconditions for an action to prosper. A boundless variety of pathological conditions can be envisioned, e.g., a banana in a tailpipe could prevent an automobile from operating properly.

McCarthy’s approach to fix the frame issue was circumscription, a sort of non-monotonic logic where reductions might be made from actions that require just specify what would alter while not having to clearly specify whatever that would not change. Other non-monotonic logics supplied truth upkeep systems that revised beliefs leading to contradictions.

Other ways of managing more open-ended domains consisted of probabilistic thinking systems and device knowing to discover brand-new principles and rules. McCarthy’s Advice Taker can be deemed a motivation here, as it might include brand-new understanding provided by a human in the form of assertions or guidelines. For instance, experimental symbolic maker discovering systems checked out the capability to take top-level natural language recommendations and to translate it into domain-specific actionable guidelines.

Similar to the problems in handling dynamic domains, sensible reasoning is likewise challenging to record in formal reasoning. Examples of common-sense reasoning include implicit thinking about how people believe or basic knowledge of daily events, items, and living animals. This type of understanding is taken for given and not viewed as noteworthy. Common-sense reasoning is an open area of research study and challenging both for symbolic systems (e.g., Cyc has actually attempted to catch essential parts of this knowledge over more than a years) and neural systems (e.g., self-driving cars that do not know not to drive into cones or not to hit pedestrians strolling a bicycle).

McCarthy viewed his Advice Taker as having common-sense, but his definition of sensible was different than the one above. [94] He specified a program as having good sense “if it instantly deduces for itself a sufficiently broad class of instant repercussions of anything it is told and what it already understands. “

Connectionist AI: philosophical obstacles and sociological conflicts

Connectionist methods consist of 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 advanced methods, such as Transformers, GANs, and other work in deep knowing.

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

1. Implementationism-where connectionist architectures implement the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected completely, and connectionist architectures underlie intelligence and are completely sufficient 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 neighborhood, explained the moderate connectionism view as basically suitable with current research study in neuro-symbolic hybrids:

The 3rd and last position I would like to analyze here is what I call the moderate connectionist view, a more eclectic view of the current argument in between connectionism and symbolic AI. Among 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 protected hybrid (partly symbolic, partially connectionist) systems. He claimed that (at least) two type of theories are required in order to study and model cognition. On the one hand, for some information-processing jobs (such as pattern recognition) connectionism has benefits over symbolic models. But on the other hand, for other cognitive procedures (such as serial, deductive thinking, and generative sign adjustment procedures) the symbolic paradigm provides appropriate models, and not just “approximations” (contrary to what extreme connectionists would declare). [97]

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

To think that we can simply desert symbol-manipulation is to suspend disbelief.

And yet, for the most part, that’s how most existing AI earnings. Hinton and many others have striven to eradicate symbols altogether. The deep learning hope-seemingly grounded not a lot in science, but in a sort of historical grudge-is that intelligent habits will emerge purely from the confluence of massive data and deep learning. Where classical computers and software application solve jobs by defining sets of symbol-manipulating guidelines committed to specific jobs, such as editing a line in a word processor or carrying out a computation in a spreadsheet, neural networks normally try to resolve jobs by analytical approximation and learning from examples.

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

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

…

Ever since, his anti-symbolic campaign has just increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep knowing in among science’s crucial journals, Nature. It closed with a direct attack on sign manipulation, calling not for reconciliation but for straight-out replacement. Later, Hinton told a gathering of European Union leaders that investing any more money in symbol-manipulating approaches was “a huge mistake,” comparing it to buying internal combustion engines in the period of electrical cars and trucks. [98]

Part of these disagreements may be due to unclear terms:

Turing award winner Judea Pearl offers a review of maker knowing which, sadly, conflates the terms artificial intelligence and deep knowing. Similarly, when Geoffrey Hinton refers to symbolic AI, the undertone of the term tends to be that of specialist systems dispossessed of any ability to discover. The use of the terms requires explanation. Artificial intelligence 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 learning algorithms). Equally, symbolic AI is not just about production guidelines written by hand. A proper meaning of AI issues understanding representation and reasoning, autonomous multi-agent systems, preparation and argumentation, in addition to knowing. [99]

Situated robotics: the world as a model

Another critique of symbolic AI is the embodied cognition method:

The embodied cognition technique declares that it makes no sense to consider the brain independently: cognition happens within a body, which is embedded in an environment. We require to study the system as a whole; the brain’s functioning exploits regularities in its environment, including the rest of its body. Under the embodied cognition technique, robotics, vision, and other sensors become main, not peripheral. [100]

Rodney Brooks invented behavior-based robotics, one method to embodied cognition. Nouvelle AI, another name for this approach, is deemed an alternative to both symbolic AI and connectionist AI. His technique turned down representations, either symbolic or distributed, as not just unneeded, however as harmful. Instead, he produced the subsumption architecture, a layered architecture for embodied agents. Each layer attains a various purpose and should work in the genuine world. For instance, the first robotic he describes in Intelligence Without Representation, has three layers. The bottom layer analyzes sonar sensors to prevent things. The middle layer triggers the robot to wander around when there are no challenges. The top layer causes the robot to go to more far-off locations for more exploration. Each layer can temporarily hinder or suppress a lower-level layer. He slammed AI researchers for specifying AI problems for their systems, when: “There is no tidy division in between perception (abstraction) and reasoning in the genuine world.” [101] He called his robots “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 extremely essential to evaluate the Creatures we build in the real world; i.e., in the same world that we human beings live in. It is devastating to fall under the temptation of checking them in a streamlined world initially, even with the best objectives of later moving activity to an unsimplified world.” [103] His emphasis on real-world screening remained in contrast to “Early work in AI focused on video games, geometrical problems, symbolic algebra, theorem proving, and other official systems” [104] and the usage of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has benefits, but has been criticized by the other methods. Symbolic AI has been criticized as disembodied, accountable to the credentials issue, and poor in managing the perceptual issues where deep learning excels. In turn, connectionist AI has been criticized as improperly fit for deliberative step-by-step problem solving, incorporating understanding, and handling preparation. Finally, Nouvelle AI excels in reactive and real-world robotics domains however has been slammed for problems in integrating learning and knowledge.

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

Overall, Dreyfus saw areas where AI did not have total responses and stated that Al is for that reason impossible; we now see a lot of these exact same areas going through ongoing research and advancement resulting in increased ability, not impossibility. [100]

Expert system.
Automated preparation and scheduling
Automated theorem proving
Belief modification
Case-based reasoning
Cognitive architecture
Cognitive science
Connectionism
Constraint programming
Deep learning
First-order logic
GOFAI
History of expert system
Inductive reasoning shows
Knowledge-based systems
Knowledge representation and reasoning
Logic shows
Machine knowing
Model monitoring
Model-based reasoning
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of artificial 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 do not care if it’s psychologically genuine”. [4] McCarthy restated his position in 2006 at the AI@50 conference where he stated “Artificial intelligence is not, by definition, simulation of human intelligence”. [28] Pamela McCorduck composes that there are “2 major branches of artificial intelligence: one aimed at producing intelligent habits despite how it was accomplished, and the other targeted at modeling intelligent procedures discovered in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig composed “Aeronautical engineering texts do not specify the goal of their field as making ‘devices 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 items 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.
^ 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.
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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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