Symbolic Artificial Intelligence

In expert system, symbolic expert system (also referred to as classical artificial intelligence or logic-based synthetic intelligence) [1] [2] is the term for the collection of all techniques in artificial intelligence research that are based on high-level symbolic (human-readable) representations of problems, reasoning and search. [3] Symbolic AI used tools such as logic programs, production rules, semantic internet 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 preparation and scheduling systems. The Symbolic AI paradigm caused seminal ideas in search, symbolic programming 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 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 producing a maker with synthetic general intelligence and considered this the ultimate objective of their field. [citation needed] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, caused impractical expectations and promises and was followed by the very first AI Winter as moneying dried up. [5] [6] A 2nd boom (1969-1986) accompanied the increase of expert systems, their guarantee of catching corporate knowledge, and a passionate business accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later on frustration. [8] Problems with troubles in understanding acquisition, preserving big understanding bases, and brittleness in managing out-of-domain problems developed. Another, 2nd, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists concentrated on resolving underlying problems in handling uncertainty and in understanding acquisition. [10] Uncertainty was addressed with official techniques such as concealed Markov models, Bayesian thinking, and analytical relational knowing. [11] [12] Symbolic machine discovering addressed the knowledge acquisition issue with contributions including Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree knowing, case-based learning, and inductive logic programming to learn relations. [13]

Neural networks, a subsymbolic technique, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt’s perceptron knowing work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and work 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 general agreement in the Al community was that the so-called neural-network approach was hopeless. Systems just didn’t work that well, compared to other techniques. … A revolution came in 2012, when a variety of individuals, consisting of a team of researchers dealing with Hinton, worked out a method to utilize the power of GPUs to immensely increase the power of neural networks.” [16] Over the next numerous years, deep knowing had spectacular success in handling vision, speech recognition, speech synthesis, image generation, and device translation. However, considering that 2020, as intrinsic troubles with bias, explanation, comprehensibility, and toughness ended up being more obvious with deep knowing techniques; an increasing variety of AI researchers have actually called for combining the finest of both the symbolic and neural network methods [17] [18] and resolving areas that both techniques have trouble with, such as common-sense thinking. [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 post on the History of AI, with dates and titles differing somewhat for increased clarity.

The very first AI summer: unreasonable spirit, 1948-1966

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

Approaches inspired by human or animal cognition or habits

Cybernetic approaches tried to reproduce the feedback loops in between animals and their environments. A robotic turtle, with sensing units, motors for driving and steering, and seven vacuum tubes for control, based on a preprogrammed neural internet, was built as early as 1948. This work can be viewed as an early precursor to later work in neural networks, reinforcement learning, and located robotics. [20]

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

During the 1960s, symbolic methods accomplished terrific success at replicating smart behavior 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) University of Edinburgh. Each one developed its own design of research study. Earlier approaches based on cybernetics or artificial neural networks were deserted or pressed into the background.

Herbert Simon and Allen Newell studied human analytical skills and attempted to formalize them, and their work laid the foundations of the field of synthetic intelligence, in addition to cognitive science, operations research and management science. Their research study team utilized the outcomes of psychological experiments to establish programs that simulated the strategies that people used to solve problems. [22] [23] This tradition, centered 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 highly specialized domain-specific sort of understanding that we will see later on utilized in expert systems, early symbolic AI researchers found another more basic application of knowledge. These were called heuristics, guidelines of thumb that direct a search in promising instructions: “How can non-enumerative search be useful when the underlying issue is greatly hard? The method advocated by Simon and Newell is to utilize heuristics: fast algorithms that might fail on some inputs or output suboptimal solutions.” [26] Another important advance was to find a way to use these heuristics that guarantees a solution will be discovered, if there is one, not enduring the occasional fallibility of heuristics: “The A * algorithm offered a general frame for total and optimum heuristically guided search. A * is utilized as a subroutine within almost every AI algorithm today however is still no magic bullet; its assurance of efficiency is bought at the cost of worst-case exponential time. [26]

Early deal with knowledge representation and reasoning

Early work covered both applications of formal reasoning stressing first-order logic, along with attempts to handle common-sense thinking in a less official way.

Modeling formal thinking with logic: the “neats”

Unlike Simon and Newell, John McCarthy felt that machines did not need to simulate the exact systems of human thought, however might rather look for the essence of abstract reasoning and analytical with reasoning, [27] despite whether people utilized the exact same algorithms. [a] His laboratory at Stanford (SAIL) concentrated on using official reasoning to fix a wide array of problems, consisting of understanding representation, planning and knowing. [31] Logic was also the focus of the work at the University of Edinburgh and in other places in Europe which led to the advancement of the programming language Prolog and the science of reasoning programming. [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 problems in vision and natural language processing required ad hoc solutions-they argued that no easy and basic concept (like logic) would catch all the elements of intelligent habits. Roger Schank described their “anti-logic” techniques as “scruffy” (instead of the “neat” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “scruffy” AI, since they should be constructed by hand, one complex idea at a time. [38] [39] [40]

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

The very first AI winter was a shock:

During the first AI summer, lots of people believed that device intelligence could be accomplished in simply a couple of years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research study to use AI to solve problems of nationwide security; in specific, to automate the translation of Russian to English for intelligence operations and to produce autonomous tanks for the battlefield. Researchers had begun to recognize that attaining AI was going to be much more difficult than was expected a decade earlier, but a combination of hubris and disingenuousness led lots of university and think-tank scientists to accept funding with promises of deliverables that they should have known they might not meet. By the mid-1960s neither helpful natural language translation systems nor self-governing tanks had actually been created, and a dramatic reaction embeded in. New DARPA leadership canceled existing AI financing programs.

Outside of the United States, the most fertile ground for AI research study was the United Kingdom. The AI winter in the United Kingdom was spurred on not so much by disappointed military leaders as by rival academics who saw AI scientists as charlatans and a drain on research financing. A professor of used mathematics, Sir James Lighthill, was commissioned by Parliament to evaluate the state of AI research in the nation. The report mentioned that all of the problems being dealt with in AI would be much better managed by researchers from other disciplines-such as used mathematics. The report likewise declared that AI successes on toy problems might never ever scale to real-world applications due to combinatorial surge. [41]

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

Knowledge-based systems

As constraints with weak, domain-independent methods ended up being a growing number of obvious, [42] scientists from all 3 traditions started to construct understanding into AI applications. [43] [7] The understanding transformation was driven by the awareness that understanding underlies high-performance, domain-specific AI applications.

Edward Feigenbaum said:

– “In the knowledge lies the power.” [44]
to describe that high efficiency in a particular domain needs both general 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 a complex job well, it must understand a good deal about the world in which it runs.
( 2) A plausible extension of that concept, called the Breadth Hypothesis: there are two additional capabilities needed for intelligent behavior in unexpected circumstances: falling back on increasingly general understanding, and analogizing to particular but far-flung knowledge. [45]

Success with expert systems

This “knowledge revolution” led to the development and implementation of specialist systems (presented by Edward Feigenbaum), the very first commercially successful form of AI software. [46] [47] [48]

Key professional systems were:

DENDRAL, which discovered the structure of natural molecules from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and recommended more laboratory tests, when required – by analyzing laboratory outcomes, patient history, and doctor observations. “With about 450 guidelines, MYCIN was able to carry out along with some experts, and considerably much better than junior physicians.” [49] INTERNIST and CADUCEUS which dealt with internal medication diagnosis. Internist attempted to catch the proficiency of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS might ultimately detect up to 1000 various diseases.
– GUIDON, which demonstrated how an understanding base developed for specialist issue fixing might be repurposed for teaching. [50] XCON, to set up VAX computers, a then laborious process that might take up to 90 days. XCON reduced the time to about 90 minutes. [9]
DENDRAL is thought about the first professional system that count on knowledge-intensive problem-solving. It is described listed below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

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

We did not have a grand vision. We worked bottom up. Our chemist was Carl Djerassi, creator of the chemical behind the contraceptive pill, and also among the world’s most respected mass spectrometrists. Carl and his postdocs were first-rate experts in mass spectrometry. We began to contribute to their understanding, creating knowledge of engineering as we went along. These experiments totaled up to titrating DENDRAL more and more knowledge. The more you did that, the smarter the program ended up being. We had great results.

The generalization was: in the knowledge lies the power. That was the huge idea. In my career that is the huge, “Ah ha!,” and it wasn’t the method AI was being done formerly. Sounds simple, however it’s probably AI‘s most effective generalization. [51]

The other professional systems pointed out above followed DENDRAL. MYCIN exhibits the traditional professional system architecture of a knowledge-base of rules paired to a symbolic thinking system, including making use of certainty factors to handle unpredictability. GUIDON reveals how an explicit understanding base can be repurposed for a second application, tutoring, and is an example of a smart tutoring system, a specific sort of knowledge-based application. Clancey showed that it was not adequate simply to utilize MYCIN’s rules for direction, but that he likewise needed to include guidelines for dialogue management and trainee modeling. [50] XCON is substantial due to the fact that of the millions of dollars it conserved DEC, which activated the expert system boom where most all major corporations in the US had professional systems groups, to capture corporate proficiency, preserve it, and automate it:

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

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

Architecture of knowledge-based and skilled systems

A crucial component of the system architecture for all specialist systems is the knowledge base, which stores realities and guidelines for problem-solving. [53] The easiest approach for a skilled system knowledge base is merely a collection or network of production rules. Production guidelines link signs in a relationship similar to an If-Then declaration. The expert system processes the guidelines to make reductions and to identify what additional details it needs, i.e. what concerns to ask, using human-readable signs. For example, OPS5, CLIPS and their successors Jess and Drools run in this fashion.

Expert systems can run in either a forward chaining – from proof to conclusions – or backwards chaining – from goals to needed data and prerequisites – way. More advanced knowledge-based systems, such as Soar can also carry out meta-level reasoning, that is thinking about their own thinking in regards to choosing how to fix problems and keeping an eye on the success of analytical strategies.

Blackboard systems are a second sort of knowledge-based or professional system architecture. They model a neighborhood of experts incrementally contributing, where they can, to solve a problem. The issue is represented in numerous levels of abstraction or alternate views. The experts (knowledge sources) volunteer their services whenever they acknowledge they can contribute. Potential problem-solving actions are represented on an agenda that is upgraded as the issue circumstance changes. A controller chooses how helpful each contribution is, and who should make the next analytical action. One example, the BB1 blackboard architecture [54] was originally inspired by studies of how people prepare to perform multiple tasks in a trip. [55] An innovation of BB1 was to apply the exact same blackboard model to solving its control problem, i.e., its controller carried out meta-level thinking with knowledge sources that monitored how well a strategy or the problem-solving was continuing and could change from one strategy to another as conditions – such as goals or times – changed. BB1 has been applied in several domains: construction website preparation, smart 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 devices specifically targeted to speed up the advancement of AI applications and research study. In addition, several artificial intelligence business, such as Teknowledge and Inference Corporation, were offering professional system shells, training, and seeking advice from to corporations.

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

Many factors can be offered for the arrival of the second AI winter. The hardware companies stopped working when a lot more cost-efficient general Unix workstations from Sun together with great compilers for LISP and Prolog came onto the marketplace. Many commercial deployments of expert systems were terminated when they proved too expensive to preserve. Medical professional systems never ever captured on for a number of reasons: the problem in keeping them up to date; the difficulty for physician to find out how to use a bewildering variety of various professional systems for various medical conditions; and perhaps most crucially, the unwillingness of medical professionals to rely on a computer-made medical diagnosis over their gut impulse, even for particular domains where the specialist systems could outshine an average medical professional. Venture capital money deserted AI almost overnight. The world AI conference IJCAI hosted a massive and lavish trade show and thousands of nonacademic participants in 1987 in Vancouver; the primary AI conference the following year, AAAI 1988 in St. Paul, was a little and strictly scholastic affair. [9]

Including more rigorous structures, 1993-2011

Uncertain reasoning

Both analytical approaches and extensions to reasoning were attempted.

One analytical approach, hidden Markov designs, had actually currently been popularized in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized using Bayesian Networks as a noise however efficient method of managing unsure thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian methods were applied effectively in professional systems. [57] Even later on, in the 1990s, analytical relational learning, a technique that integrates possibility with sensible formulas, allowed likelihood to be combined 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 attempted. For example, non-monotonic thinking could be used with fact maintenance systems. A reality maintenance system tracked presumptions and validations for all reasonings. It enabled reasonings to be withdrawn when presumptions were discovered to be incorrect or a contradiction was obtained. Explanations might be offered a reasoning by describing which rules were applied to create it and after that continuing through underlying inferences and rules all the method back to root assumptions. [58] Lofti Zadeh had presented a various sort of extension to handle the representation of vagueness. For example, in choosing how “heavy” or “tall” a man is, there is frequently no clear “yes” or “no” answer, and a predicate for heavy or high would rather return values between 0 and 1. Those worths represented to what degree the predicates were real. His fuzzy reasoning even more provided a way for propagating combinations of these worths through rational formulas. [59]

Artificial intelligence

Symbolic machine finding out techniques were examined to resolve the understanding acquisition bottleneck. One of the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test strategy to generate plausible guideline hypotheses to evaluate versus spectra. Domain and task knowledge lowered the number of candidates tested to a workable size. Feigenbaum described Meta-DENDRAL as

… the culmination of my imagine the early to mid-1960s pertaining 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 understanding got in there because we talked to people. But how did individuals get the knowledge? By looking at thousands of spectra. So we desired a program that would look at countless spectra and presume the understanding of mass spectrometry that DENDRAL could utilize to resolve specific hypothesis formation problems. We did it. We were even able to release brand-new understanding of mass spectrometry in the Journal of the American Chemical Society, giving 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 created a brand-new and publishable piece of science. [51]

In contrast to the knowledge-intensive approach of Meta-DENDRAL, Ross Quinlan invented a domain-independent technique to statistical category, decision tree knowing, starting first with ID3 [60] and then later extending its abilities to C4.5. [61] The decision trees produced are glass box, interpretable classifiers, with human-interpretable classification rules.

Advances were made in understanding maker knowing theory, too. Tom Mitchell presented variation space knowing which explains knowing as an explore an area of hypotheses, with upper, more general, and lower, more particular, limits incorporating all feasible hypotheses consistent 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 machine learning included more than learning by example. E.g., John Anderson provided a cognitive design of human knowing where ability practice leads to a compilation of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a student may discover to apply “Supplementary angles are 2 angles whose steps sum 180 degrees” as a number of various procedural guidelines. E.g., one rule may say that if X and Y are additional and you know X, then Y will be 180 – X. He called his approach “understanding collection”. ACT-R has actually been utilized effectively to model elements of human cognition, such as finding out and retention. ACT-R is likewise used in smart tutoring systems, called cognitive tutors, to successfully teach geometry, computer programming, and algebra to school children. [64]

Inductive logic programming was another approach to learning that enabled logic programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) might manufacture Prolog programs from examples. [65] John R. Koza used hereditary algorithms to program synthesis to produce genetic shows, which he used to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger offered a more basic method to program synthesis that manufactures a functional program in the course of showing its specifications to be correct. [66]

As an alternative to logic, Roger Schank introduced case-based reasoning (CBR). The CBR approach outlined in his book, Dynamic Memory, [67] focuses initially on remembering crucial problem-solving cases for future use and generalizing them where suitable. When confronted with a new problem, CBR retrieves the most comparable previous case and adjusts it to the specifics of the present issue. [68] Another alternative to reasoning, genetic algorithms and hereditary programs are based on an evolutionary design of learning, where sets of rules are encoded into populations, the rules govern the habits of people, and choice of the fittest prunes out sets of unsuitable rules over many generations. [69]

Symbolic machine learning was applied to discovering concepts, rules, heuristics, and problem-solving. Approaches, besides those above, include:

1. Learning from direction or advice-i.e., taking human instruction, posed as recommendations, and figuring out how to operationalize it in specific scenarios. For instance, in a game of Hearts, discovering exactly how to play a hand to “prevent taking points.” [70] 2. Learning from exemplars-improving performance by accepting subject-matter specialist (SME) feedback during training. When problem-solving stops working, querying the professional to either learn a new exemplar for analytical or to find out a brand-new explanation regarding exactly why one exemplar is more appropriate than another. For instance, the program Protos found out to diagnose ringing in the ears cases by connecting with an audiologist. [71] 3. Learning by analogy-constructing problem options based on comparable problems seen in the past, and after that customizing their options to fit a new situation or domain. [72] [73] 4. Apprentice knowing systems-learning unique solutions to problems by observing human problem-solving. Domain understanding describes why unique services are proper and how the solution can be generalized. LEAP found out how to design VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., creating jobs to carry out experiments and after that gaining from the results. Doug Lenat’s Eurisko, for instance, learned heuristics to beat human players at the Traveller role-playing video game for 2 years in a row. [75] 6. Learning macro-operators-i.e., searching for helpful macro-operators to be gained from series of basic problem-solving actions. Good macro-operators simplify analytical by enabling 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 method has been compared to deep learning as complementary “… with parallels having been drawn lots of times by AI researchers between Kahneman’s research study on human reasoning and decision making – shown in his book Thinking, Fast and Slow – and the so-called “AI systems 1 and 2″, which would in principle be designed by deep learning and symbolic reasoning, respectively.” In this view, symbolic reasoning is more apt for deliberative thinking, planning, and description while deep knowing is more apt for fast pattern recognition in affective applications with loud information. [17] [18]

Neuro-symbolic AI: incorporating neural and symbolic techniques

Neuro-symbolic AI attempts 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, learning, and cognitive modeling. As argued by Valiant [77] and numerous others, [78] the effective building and construction of abundant computational cognitive designs requires the combination of sound symbolic thinking and effective (maker) knowing designs. Gary Marcus, likewise, argues that: “We can not construct abundant cognitive models in an adequate, automatic way without the triune of hybrid architecture, abundant prior understanding, and sophisticated strategies for thinking.”, [79] and in specific: “To construct a robust, knowledge-driven approach to AI we must have the equipment of symbol-manipulation in our toolkit. Too much of useful knowledge is abstract to make do without tools that represent and manipulate abstraction, and to date, the only machinery that we understand of that can control such abstract understanding dependably is the device of sign adjustment. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based upon a requirement to resolve the 2 type of thinking discussed in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having two parts, System 1 and System 2. System 1 is quickly, automated, instinctive and unconscious. System 2 is slower, step-by-step, and specific. System 1 is the kind utilized for pattern acknowledgment while System 2 is far much better matched for planning, deduction, and deliberative thinking. In this view, deep knowing best models the very first type of thinking while symbolic thinking finest designs the 2nd kind and both are required.

Garcez and Lamb explain research in this location as being ongoing for a minimum of the past twenty years, [83] dating from their 2002 book on neurosymbolic learning systems. [84] A series of workshops on neuro-symbolic reasoning has been held every year given that 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 been pursued by a fairly little research study community over the last 2 years and has actually yielded several considerable outcomes. Over the last years, neural symbolic systems have actually been shown capable of getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in response to Smolensky (1988 ); see likewise (Hinton, 1990). Neural networks were revealed efficient in 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 been applied to a variety of issues in the locations of bioinformatics, control engineering, software application confirmation and adaptation, visual intelligence, ontology learning, and video game. [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 current approach of many neural models in natural language processing, where words or subword tokens are both the supreme input and output of big language models. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic strategies are used to call neural strategies. In this case the symbolic approach is Monte Carlo tree search and the neural methods learn how to assess video game positions.
– Neural|Symbolic-uses a neural architecture to analyze perceptual data as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to generate or identify training data that is consequently learned by a deep learning design, e.g., to train a neural design for symbolic computation by utilizing a Macsyma-like symbolic mathematics system to create or identify examples.
– Neural _ Symbolic -uses a neural net that is produced 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 guidelines and terms. Logic Tensor Networks [86] likewise fall under this classification.
– Neural [Symbolic] -allows a neural design to directly call a symbolic reasoning engine, e.g., to perform an action or assess a state.

Many essential research study questions remain, such as:

– What is the very best way to integrate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and drawn out from them?
– How should sensible knowledge be discovered and reasoned about?
– How can abstract understanding that is tough to encode rationally be handled?

Techniques and contributions

This area supplies an overview of methods and contributions in a general context resulting in numerous other, more comprehensive articles in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered earlier in the history area.

AI shows languages

The crucial AI programming language in the US throughout the last symbolic AI boom period was LISP. LISP is the 2nd oldest programming language after FORTRAN and was produced in 1958 by John McCarthy. LISP offered the very first read-eval-print loop to support rapid program advancement. Compiled functions might be freely mixed with analyzed functions. Program tracing, stepping, and breakpoints were likewise supplied, along with the capability to alter values or functions and continue from breakpoints or errors. It had the first self-hosting compiler, implying that the compiler itself was initially written in LISP and then ran interpretively to assemble the compiler code.

Other essential developments originated by LISP that have actually spread out to 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, allowing the simple meaning of higher-level languages.

In contrast to the US, in Europe the key AI programs language during that same duration was Prolog. Prolog offered an integrated shop of truths and clauses that might be queried by a read-eval-print loop. The shop could function as an understanding base and the provisions might act as rules or a limited kind of reasoning. As a subset of first-order logic Prolog was based upon Horn provisions with a closed-world assumption-any facts not known were considered false-and a special name presumption for primitive terms-e.g., the identifier barack_obama was considered to refer to exactly one things. Backtracking and marriage are integrated to Prolog.

Alain Colmerauer and Philippe Roussel are credited as the innovators of Prolog. Prolog is a kind of logic shows, which was developed by Robert Kowalski. Its history was also affected by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of methods. For more detail see the area on the origins of Prolog in the PLANNER post.

Prolog is also a type of declarative programming. The reasoning stipulations that explain programs are straight translated to run the programs defined. No explicit series of actions is needed, as is the case with crucial programs languages.

Japan promoted Prolog for its Fifth Generation Project, planning to construct unique hardware for high efficiency. Similarly, LISP devices were constructed to run LISP, however as the second AI boom turned to bust these companies might not complete with brand-new workstations that might now run LISP or Prolog natively at equivalent speeds. See the history section for more detail.

Smalltalk was another prominent AI programs language. For instance, it introduced 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, hence providing a run-time meta-object protocol. [88]

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

Search

Search occurs in lots of kinds of problem solving, including preparation, constraint complete satisfaction, and playing video 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 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 different techniques to represent understanding and after that reason with those representations have been examined. Below is a quick introduction of approaches to knowledge representation and automated reasoning.

Knowledge representation

Semantic networks, conceptual graphs, frames, and logic are all techniques to modeling knowledge such as domain knowledge, analytical understanding, and the semantic significance of language. Ontologies model essential principles 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 likewise be considered as an ontology. YAGO integrates WordNet as part of its ontology, to align facts drawn out from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being used.

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

First-order logic is more basic than description logic. The automated theorem provers gone over below can show theorems in first-order reasoning. Horn stipulation logic is more limited than first-order logic and is used in logic programming languages such as Prolog. Extensions to first-order reasoning include temporal logic, to manage time; epistemic logic, to factor about agent understanding; modal reasoning, to manage possibility and need; and probabilistic logics to handle reasoning and probability together.

Automatic theorem proving

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

Prover9.
ACL2.
Vampire.

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

Reasoning in knowledge-based systems

Knowledge-based systems have an explicit knowledge base, usually of rules, to enhance reusability throughout domains by separating procedural code and domain understanding. A different inference engine procedures rules 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 takes place in Prolog, where a more limited sensible representation is used, Horn Clauses. Pattern-matching, particularly marriage, is utilized in Prolog.

A more flexible kind of analytical occurs when reasoning about what to do next occurs, instead of just selecting one of the offered actions. This sort of meta-level reasoning is utilized in Soar and in the BB1 chalkboard architecture.

Cognitive architectures such as ACT-R may have additional capabilities, such as the ability to put together frequently utilized understanding into higher-level chunks.

Commonsense thinking

Marvin Minsky first proposed frames as a method of interpreting common visual situations, such as a workplace, and Roger Schank extended this idea to scripts for common regimens, such as dining out. Cyc has actually attempted to record helpful sensible understanding and has “micro-theories” to manage particular type of domain-specific thinking.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human reasoning about naive physics, such as what happens when we heat a liquid in a pot on the stove. We expect it to heat and perhaps boil over, even though we may not know its temperature, its boiling point, or other information, 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 thinking about spatial relationships. Both can be fixed with restraint solvers.

Constraints and constraint-based thinking

Constraint solvers perform a more restricted sort 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 issues, such as Wordle, Sudoku, cryptarithmetic issues, and so on. Constraint logic shows can be utilized to fix scheduling issues, for example with restraint managing guidelines (CHR).

Automated planning

The General Problem Solver (GPS) cast preparation as problem-solving used means-ends analysis to produce strategies. STRIPS took a various method, viewing preparation as theorem proving. Graphplan takes a least-commitment technique to planning, instead of sequentially choosing actions from a preliminary state, working forwards, or a goal state if working backwards. Satplan is a technique to planning where a planning problem is reduced to a Boolean satisfiability issue.

Natural language processing

Natural language processing concentrates on dealing with language as information to perform tasks such as determining subjects without necessarily comprehending the desired significance. Natural language understanding, in contrast, constructs a significance representation and uses that for more processing, such as responding to questions.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb phrase chunking are all aspects of natural language processing long dealt with by symbolic AI, but considering that improved by deep learning techniques. In symbolic AI, discourse representation theory and first-order reasoning have been used to represent sentence significances. Latent semantic analysis (LSA) and explicit semantic analysis likewise offered vector representations of files. In the latter case, vector elements are interpretable as concepts named by Wikipedia articles.

New deep knowing methods based on Transformer designs have actually now eclipsed these earlier symbolic AI approaches and attained advanced performance in natural language processing. However, Transformer models 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 components is nontransparent.

Agents and multi-agent systems

Agents are self-governing systems embedded in an environment they perceive and act on in some sense. Russell and Norvig’s basic book on expert system is arranged to show representative architectures of increasing sophistication. [91] The sophistication of representatives differs from simple reactive representatives, to those with a model of the world and automated preparation capabilities, potentially a BDI representative, i.e., one with beliefs, desires, and objectives – or additionally a reinforcement finding out design discovered with time to choose actions – as much as a combination of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep knowing for understanding. [92]

In contrast, a multi-agent system includes several representatives that communicate amongst themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The representatives need not all have the same internal architecture. Advantages of multi-agent systems include the capability to divide work among the agents and to increase fault tolerance when agents are lost. Research issues include how representatives reach consensus, distributed problem fixing, multi-agent learning, multi-agent preparation, and dispersed constraint 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 between those who embraced AI however rejected symbolic approaches-primarily connectionists-and those outside the field. Critiques from outside of the field were primarily from philosophers, on intellectual grounds, however likewise from funding firms, specifically throughout the two AI winters.

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

Limitations were found in using easy first-order logic to factor about dynamic domains. Problems were found both with concerns to identifying the preconditions for an action to succeed and in offering axioms for what did not change after an action was performed.

McCarthy and Hayes presented the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Artificial Intelligence.” [93] An easy example takes place in “proving that a person person might enter into conversation with another”, as an axiom asserting “if an individual has a telephone he still has it after looking up a number in the telephone directory” would be required for the deduction to be successful. Similar axioms would be needed for other domain actions to define what did not alter.

A comparable problem, called the Qualification Problem, happens in attempting to enumerate the preconditions for an action to succeed. An unlimited variety of pathological conditions can be envisioned, e.g., a banana in a tailpipe might prevent a car from running correctly.

McCarthy’s approach to fix the frame issue was circumscription, a type of non-monotonic reasoning where deductions might be made from actions that require just define what would alter while not having to clearly define everything that would not alter. Other non-monotonic reasonings supplied fact upkeep systems that modified beliefs resulting in contradictions.

Other methods of dealing with more open-ended domains consisted of probabilistic thinking systems and machine learning to discover brand-new concepts and guidelines. McCarthy’s Advice Taker can be viewed as a motivation here, as it could include brand-new understanding provided by a human in the type of assertions or rules. For example, speculative symbolic machine learning systems checked out the ability to take high-level natural language advice and to analyze it into domain-specific actionable rules.

Similar to the problems in handling vibrant domains, sensible thinking is likewise challenging to record in official reasoning. Examples of sensible thinking include implicit reasoning about how people think or basic knowledge of everyday events, items, and living creatures. This kind of understanding is taken for granted and not deemed noteworthy. Common-sense reasoning is an open location of research study and challenging both for symbolic systems (e.g., Cyc has attempted to catch crucial parts of this understanding over more than a years) and neural systems (e.g., self-driving vehicles that do not know not to drive into cones or not to strike pedestrians strolling a bike).

McCarthy viewed his Advice Taker as having sensible, but his definition of sensible was various than the one above. [94] He specified a program as having good sense “if it automatically deduces for itself a sufficiently wide class of instant consequences of anything it is told and what it already knows. “

Connectionist AI: philosophical obstacles and sociological disputes

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

Three philosophical positions [96] have been outlined among connectionists:

1. Implementationism-where connectionist architectures carry out the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is declined totally, and connectionist architectures underlie intelligence and are fully adequate to explain it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are deemed complementary and both are needed for intelligence

Olazaran, in his sociological history of the debates within the neural network community, described the moderate connectionism consider as essentially suitable with existing 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 dispute between connectionism and symbolic AI. One of the researchers who has elaborated this position most clearly is Andy Clark, a philosopher from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark safeguarded hybrid (partially symbolic, partly connectionist) systems. He declared that (at least) two type of theories are needed in order to study and design cognition. On the one hand, for some information-processing jobs (such as pattern recognition) connectionism has benefits over symbolic designs. But on the other hand, for other cognitive procedures (such as serial, deductive reasoning, and generative sign manipulation processes) the symbolic paradigm offers appropriate designs, and not just “approximations” (contrary to what radical connectionists would claim). [97]

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

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

And yet, for the most part, that’s how most current AI proceeds. Hinton and lots of others have attempted difficult to eliminate symbols altogether. The deep learning hope-seemingly grounded not a lot in science, however in a sort of historic grudge-is that smart behavior will emerge simply from the confluence of massive data and deep knowing. Where classical computers and software application resolve jobs by defining sets of symbol-manipulating rules dedicated to specific jobs, such as editing a line in a word processor or carrying out an estimation in a spreadsheet, neural networks normally attempt to resolve tasks by analytical approximation and learning from examples.

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

When deep learning reemerged in 2012, it was with a kind of take-no-prisoners mindset that has actually defined most of the last years. By 2015, his hostility towards all things signs had fully taken shape. He lectured at an AI workshop at Stanford comparing symbols to aether, one of science’s biggest errors.

…

Ever since, his anti-symbolic project has actually just increased in strength. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep learning in one of science’s essential journals, Nature. It closed with a direct attack on sign manipulation, calling not for reconciliation but for outright replacement. Later, Hinton informed an event of European Union leaders that investing any additional cash in symbol-manipulating techniques was “a big mistake,” likening it to purchasing internal combustion engines in the period of electric automobiles. [98]

Part of these disagreements might be because of unclear terminology:

Turing award winner Judea Pearl uses a critique of device knowing which, unfortunately, conflates the terms machine knowing and deep knowing. Similarly, when Geoffrey Hinton refers to symbolic AI, the connotation of the term tends to be that of specialist systems dispossessed of any ability to find out. Making use of the terms is in requirement of information. Machine learning is not restricted to association rule mining, c.f. the body of work on symbolic ML and relational learning (the distinctions to deep knowing being the option of representation, localist rational instead of distributed, and the non-use of gradient-based knowing algorithms). Equally, symbolic AI is not just about production guidelines written by hand. A proper meaning of AI issues knowledge representation and reasoning, autonomous multi-agent systems, preparation and argumentation, along with knowing. [99]

Situated robotics: the world as a model

Another critique of symbolic AI is the embodied cognition technique:

The embodied cognition approach declares that it makes no sense to think about the brain individually: cognition happens within a body, which is embedded in an environment. We need to study the system as a whole; the brain’s working exploits regularities in its environment, consisting of the rest of its body. Under the embodied cognition approach, robotics, vision, and other sensing units become main, not peripheral. [100]

Rodney Brooks created behavior-based robotics, one approach to embodied cognition. Nouvelle AI, another name for this method, is deemed an alternative to both symbolic AI and connectionist AI. His method declined representations, either symbolic or dispersed, as not just unneeded, but as harmful. Instead, he developed the subsumption architecture, a layered architecture for embodied agents. Each layer attains a various function and needs to operate in the real life. For instance, the first robotic he explains in Intelligence Without Representation, has three layers. The bottom layer translates finder sensing units to prevent things. The middle layer triggers the robotic to wander around when there are no barriers. The top layer triggers the robotic to go to more far-off places for further expedition. Each layer can momentarily hinder or suppress a lower-level layer. He criticized AI researchers for defining AI issues for their systems, when: “There is no tidy division between perception (abstraction) and thinking in the real life.” [101] He called his robotics “Creatures” and each layer was “made up of a fixed-topology network of simple finite state devices.” [102] In the Nouvelle AI approach, “First, it is vitally essential to test the Creatures we integrate in the real life; i.e., in the same world that we human beings inhabit. It is disastrous to fall under the temptation of testing them in a streamlined world initially, even with the very best intentions of later moving activity to an unsimplified world.” [103] His emphasis on real-world screening was in contrast to “Early work in AI focused on video games, geometrical issues, symbolic algebra, theorem proving, and other formal systems” [104] and using the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has advantages, however has been slammed by the other methods. Symbolic AI has been criticized as disembodied, accountable to the qualification issue, and bad in managing the perceptual problems where deep learning excels. In turn, connectionist AI has been criticized as improperly matched for deliberative detailed problem resolving, integrating understanding, and managing preparation. Finally, Nouvelle AI stands out in reactive and real-world robotics domains but has been criticized for troubles in incorporating knowing and understanding.

Hybrid AIs integrating several of these methods are currently considered as the course forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw locations where AI did not have complete answers and stated that Al is therefore impossible; we now see a lot of these very same locations going through ongoing research and advancement resulting in increased ability, 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 reasoning programming
Knowledge-based systems
Knowledge representation and reasoning
Logic programming
Machine learning
Model checking
Model-based reasoning
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of expert system
Physical symbol systems hypothesis
Semantic Web
Sequential pattern mining
Statistical relational learning
Symbolic mathematics
YAGO ontology
WordNet

Notes

^ McCarthy once stated: “This is AI, so we do not care if it’s mentally real”. [4] McCarthy reiterated his position in 2006 at the AI@50 conference where he stated “Expert system is not, by definition, simulation of human intelligence”. [28] Pamela McCorduck writes that there are “2 significant branches of expert system: one focused on producing smart behavior regardless of how it was achieved, and the other targeted at modeling smart processes found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig composed “Aeronautical engineering texts do not specify the objective of their field as making ‘devices that fly so exactly like pigeons that they can deceive even other pigeons.'” [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). “Reconciling deep learning 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.
^ 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 things and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating errors”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten Zip Code Recognition”. Neural Computation. 1 (4 ): 541-551. doi:10.1162/ neco.1989.1.4.541. S2CID 41312633.
^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. “Thinking Fast and Slow in AI”. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. “AAAI Presidential Address: The State of AI”. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
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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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