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Symbolic Expert System

In synthetic intelligence, symbolic artificial intelligence (likewise understood as classical expert system or logic-based expert system) [1] [2] is the term for the collection of all methods in artificial intelligence research study that are based upon high-level symbolic (human-readable) representations of issues, logic and search. [3] Symbolic AI used tools such as logic programming, production guidelines, semantic webs and frames, and it established applications such as knowledge-based systems (in specific, skilled systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated preparation and scheduling systems. The Symbolic AI paradigm caused influential ideas in search, symbolic shows languages, agents, multi-agent systems, the semantic web, and the strengths and restrictions of formal understanding and reasoning systems.

Symbolic AI was the dominant paradigm of AI research from the mid-1950s until the mid-1990s. [4] Researchers in the 1960s and the 1970s were encouraged that symbolic methods would ultimately succeed in developing a machine with artificial basic 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, resulted in impractical expectations and pledges and was followed by the very first AI Winter as moneying dried up. [5] [6] A second boom (1969-1986) accompanied the increase of expert systems, their pledge of recording business expertise, and a passionate corporate welcome. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later on dissatisfaction. [8] Problems with problems in knowledge acquisition, maintaining large understanding bases, and brittleness in managing out-of-domain problems occurred. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists focused on addressing hidden issues in handling uncertainty and in understanding acquisition. [10] Uncertainty was addressed with formal techniques such as surprise Markov models, Bayesian thinking, and statistical relational knowing. [11] [12] Symbolic device learning addressed the knowledge acquisition issue with contributions consisting of Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree knowing, case-based knowing, and inductive logic programs to discover relations. [13]

Neural networks, a subsymbolic method, had actually 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 operate in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not deemed effective up until about 2012: “Until Big Data became commonplace, the basic consensus in the Al neighborhood was that the so-called neural-network method was helpless. Systems just didn’t work that well, compared to other methods. … A revolution was available in 2012, when a variety of individuals, including a group of scientists dealing with Hinton, worked out a way to utilize the power of GPUs to tremendously increase the power of neural networks.” [16] Over the next numerous years, deep learning had amazing success in handling vision, speech recognition, speech synthesis, image generation, and device translation. However, since 2020, as fundamental troubles with predisposition, explanation, comprehensibility, and toughness ended up being more evident with deep knowing approaches; an increasing number of AI researchers have required integrating the very best of both the symbolic and neural network techniques [17] [18] and addressing locations that both methods have difficulty with, such as common-sense thinking. [16]

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

The very first AI summertime: illogical vitality, 1948-1966

Success at early efforts in AI took place in three main areas: synthetic 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 attempted to replicate the feedback loops in between animals and their environments. A robotic turtle, with sensors, motors for driving and guiding, and seven vacuum tubes for control, based upon a preprogrammed neural web, was developed as early as 1948. This work can be seen as an early precursor to later work in neural networks, support learning, and situated robotics. [20]

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

During the 1960s, symbolic techniques attained great success at replicating intelligent habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was concentrated in 4 institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Each one developed its own style of research study. Earlier approaches based on cybernetics or synthetic neural networks were deserted or pressed into the background.

Herbert Simon and Allen Newell studied human analytical skills and tried to formalize them, and their work laid the structures of the field of expert system, as well as cognitive science, operations research study and management science. Their research team used the outcomes of mental experiments to develop programs that simulated the techniques that individuals used to solve issues. [22] [23] This tradition, focused at Carnegie Mellon University would eventually culminate in the development of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific kinds of understanding that we will see later used in specialist systems, early symbolic AI scientists discovered another more general application of understanding. These were called heuristics, general rules that guide a search in appealing directions: “How can non-enumerative search be useful when the underlying issue is significantly tough? The technique advocated by Simon and Newell is to utilize heuristics: fast algorithms that may fail on some inputs or output suboptimal solutions.” [26] Another important 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 occasional fallibility of heuristics: “The A * algorithm supplied a basic frame for complete and optimum heuristically assisted search. A * is used as a subroutine within almost every AI algorithm today however is still no magic bullet; its assurance of efficiency is bought at the expense of worst-case rapid time. [26]

Early deal with understanding representation and reasoning

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

Modeling official thinking with logic: the “neats”

Unlike Simon and Newell, John McCarthy felt that makers did not require to imitate the specific systems of human thought, however could instead search for the essence of abstract thinking and problem-solving with reasoning, [27] despite whether people utilized the very same algorithms. [a] His lab at Stanford (SAIL) focused on utilizing official reasoning to solve a large variety of issues, including knowledge representation, preparation and knowing. [31] Logic was also the focus of the work at the University of Edinburgh and somewhere else in Europe which caused the development of the programs language Prolog and the science of reasoning programs. [32] [33]

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

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that resolving challenging issues in vision and natural language processing needed ad hoc solutions-they argued that no basic and basic concept (like logic) would catch all the aspects of smart habits. Roger Schank explained their “anti-logic” approaches as “shabby” (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, given that they need to be developed by hand, one complex principle at a time. [38] [39] [40]

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

The first AI winter season was a shock:

During the very first AI summertime, many individuals thought that maker intelligence might be attained in just a couple of years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research study to use AI to fix problems of nationwide security; in specific, to automate the translation of Russian to English for intelligence operations and to produce self-governing tanks for the battlefield. Researchers had actually begun to recognize that accomplishing AI was going to be much harder than was expected a decade previously, but a combination of hubris and disingenuousness led many university and think-tank researchers to accept funding with promises of deliverables that they must have known they might not satisfy. By the mid-1960s neither beneficial natural language translation systems nor autonomous tanks had actually been created, and a dramatic reaction set in. New DARPA leadership canceled existing AI funding programs.

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

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

Knowledge-based systems

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

Edward Feigenbaum stated:

– “In the knowledge lies the power.” [44]
to describe that high performance in a specific domain requires both general 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 a complicated task well, it needs to know a lot about the world in which it runs.
( 2) A possible extension of that principle, called the Breadth Hypothesis: there are 2 additional abilities necessary for intelligent behavior in unanticipated scenarios: falling back on significantly general knowledge, and analogizing to specific but far-flung understanding. [45]

Success with professional systems

This “knowledge revolution” caused the development and deployment of expert systems (presented by Edward Feigenbaum), the very first commercially effective form of AI software. [46] [47] [48]

Key specialist systems were:

DENDRAL, which found the structure of natural particles from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and suggested additional laboratory tests, when necessary – by translating laboratory results, client history, and physician observations. “With about 450 rules, MYCIN had the ability to perform along with some specialists, and considerably much better than junior medical professionals.” [49] INTERNIST and CADUCEUS which took on internal medicine medical diagnosis. Internist attempted to record the expertise of the chairman of internal medicine at the University of Pittsburgh School of Medicine while CADUCEUS could eventually detect up to 1000 different illness.
– GUIDON, which demonstrated how an understanding base constructed for specialist problem resolving might be repurposed for mentor. [50] XCON, to set up VAX computer systems, a then laborious procedure that could use up to 90 days. XCON lowered the time to about 90 minutes. [9]
DENDRAL is considered the first professional system that count on knowledge-intensive problem-solving. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

One of the individuals at Stanford interested in computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I desired an induction “sandbox”, he said, “I have simply the one for you.” His laboratory was doing mass spectrometry of amino acids. The concern was: how do you go from 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 great at heuristic search methods, and he had an algorithm that was great at creating the chemical issue area.

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, developer of the chemical behind the contraceptive pill, and also one of the world’s most respected mass spectrometrists. Carl and his postdocs were first-rate professionals in mass spectrometry. We started to contribute to their knowledge, creating understanding of engineering as we went along. These experiments amounted 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 understanding lies the power. That was the big concept. In my profession that is the big, “Ah ha!,” and it wasn’t the way AI was being done formerly. Sounds simple, but it’s most likely AI‘s most effective generalization. [51]

The other expert systems mentioned above came after DENDRAL. MYCIN exhibits the traditional professional system architecture of a knowledge-base of rules combined to a symbolic thinking system, including using certainty factors to handle unpredictability. GUIDON reveals how an explicit knowledge base can be repurposed for a 2nd application, tutoring, and is an example of a smart tutoring system, a specific kind of knowledge-based application. Clancey revealed that it was not enough simply to utilize MYCIN’s rules for direction, however that he likewise needed to include rules for discussion management and student modeling. [50] XCON is substantial because of the millions of dollars it saved DEC, which set off the professional system boom where most all major corporations in the US had expert systems groups, to record corporate proficiency, protect it, and automate it:

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

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

Architecture of knowledge-based and professional systems

A key component of the system architecture for all professional systems is the understanding base, which shops facts and guidelines for problem-solving. [53] The easiest method for a professional system knowledge base is just 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 extra information it needs, i.e. what concerns to ask, utilizing human-readable symbols. 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 required information and requirements – manner. More innovative knowledge-based systems, such as Soar can also carry out meta-level reasoning, that is reasoning about their own thinking in regards to deciding how to resolve issues and keeping an eye on the success of analytical strategies.

Blackboard systems are a second sort of knowledge-based or skilled system architecture. They design a neighborhood of experts incrementally contributing, where they can, to fix a problem. The problem is represented in several 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 an agenda that is updated as the issue situation modifications. A controller chooses how beneficial 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 humans prepare to carry out several jobs in a trip. [55] A development of BB1 was to apply the exact same chalkboard model to fixing its control problem, i.e., its controller carried out meta-level thinking with understanding sources that kept track of how well a strategy or the problem-solving was continuing and could change from one technique to another as conditions – such as goals or times – altered. BB1 has actually been used in numerous domains: building website preparation, intelligent tutoring systems, and real-time patient monitoring.

The second AI winter, 1988-1993

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

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

Many reasons can be used for the arrival of the 2nd AI winter. The hardware business failed when far more cost-effective basic Unix workstations from Sun together with excellent compilers for LISP and Prolog came onto the marketplace. Many business implementations of expert systems were ceased when they proved too costly to preserve. Medical specialist systems never ever captured on for numerous reasons: the problem in keeping them approximately date; the challenge for physician to learn how to use a bewildering variety of different professional systems for different medical conditions; and possibly most crucially, the unwillingness of medical professionals to rely on a computer-made diagnosis over their gut instinct, even for specific domains where the professional systems might exceed an average doctor. Equity capital cash deserted AI almost over night. The world AI conference IJCAI hosted a massive and lavish exhibition and countless nonacademic participants in 1987 in Vancouver; the primary AI conference the following year, AAAI 1988 in St. Paul, was a small and strictly scholastic affair. [9]

Adding in more rigorous structures, 1993-2011

Uncertain reasoning

Both statistical techniques and extensions to reasoning were tried.

One analytical method, hidden Markov models, had currently been popularized in the 1980s for speech acknowledgment work. [11] Subsequently, in 1988, Judea Pearl popularized the usage of Bayesian Networks as a sound but effective method of handling unsure thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian techniques were used successfully in professional systems. [57] Even later on, in the 1990s, analytical relational knowing, a method that integrates possibility with sensible formulas, enabled probability to be integrated with first-order reasoning, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order reasoning to assistance were also tried. For instance, non-monotonic thinking could be used with reality maintenance systems. A fact upkeep system tracked assumptions and validations for all reasonings. It allowed inferences to be withdrawn when presumptions were discovered to be incorrect or a contradiction was obtained. Explanations might be offered an inference by describing which guidelines were applied to create it and then continuing through underlying inferences and rules all the way back to root assumptions. [58] Lofti Zadeh had introduced a various sort of extension to deal with the representation of uncertainty. For instance, in choosing how “heavy” or “high” a man is, there is regularly no clear “yes” or “no” answer, and a predicate for heavy or tall would rather return worths between 0 and 1. Those values represented to what degree the predicates held true. His fuzzy logic even more offered a means for propagating combinations of these values through logical formulas. [59]

Machine learning

Symbolic machine discovering approaches were investigated to resolve the understanding acquisition bottleneck. Among the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test strategy to create possible guideline hypotheses to evaluate against spectra. Domain and task understanding minimized the variety of prospects evaluated to a workable size. Feigenbaum described Meta-DENDRAL as

… the culmination of my dream of 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 utilized layers of understanding to steer and prune the search. That knowledge got in there since we talked to people. But how did individuals get the understanding? By looking at thousands of spectra. So we wanted a program that would look at countless spectra and presume the knowledge of mass spectrometry that DENDRAL could use to fix individual hypothesis development issues. We did it. We were even able to release new knowledge of mass spectrometry in the Journal of the American Chemical Society, providing credit just in a footnote that a program, Meta-DENDRAL, really did it. We were able to do something that had actually been a dream: to have a computer program developed a new and publishable piece of science. [51]

In contrast to the knowledge-intensive approach of Meta-DENDRAL, Ross Quinlan created a domain-independent method to analytical classification, choice tree learning, beginning initially with ID3 [60] and then later on extending its abilities to C4.5. [61] The choice trees created are glass box, interpretable classifiers, with human-interpretable classification rules.

Advances were made in comprehending maker knowing theory, too. Tom Mitchell presented variation area knowing which describes knowing as a search through a space of hypotheses, with upper, more basic, and lower, more specific, limits encompassing all viable hypotheses constant with the examples seen so far. [62] More formally, Valiant presented Probably Approximately Correct Learning (PAC Learning), a framework for the mathematical analysis of artificial intelligence. [63]

Symbolic machine discovering encompassed more than discovering by example. E.g., John Anderson provided a cognitive model of human knowing where skill practice leads to a compilation of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For example, a student might find out to use “Supplementary angles are two angles whose procedures sum 180 degrees” as a number of different procedural rules. E.g., one guideline might say that if X and Y are extra and you understand X, then Y will be 180 – X. He called his approach “understanding compilation”. ACT-R has actually been used successfully to model aspects of human cognition, such as learning and retention. ACT-R is also utilized in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer system programming, and algebra to school children. [64]

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

As an option to reasoning, Roger Schank introduced case-based thinking (CBR). The CBR approach detailed in his book, Dynamic Memory, [67] focuses first on remembering crucial analytical cases for future usage and generalizing them where suitable. When faced with a brand-new problem, CBR obtains the most similar previous case and adjusts it to the specifics of the current problem. [68] Another alternative to logic, genetic algorithms and hereditary shows are based upon an evolutionary design of learning, where sets of guidelines are encoded into populations, the guidelines govern the behavior of people, and choice of the fittest prunes out sets of unsuitable guidelines over lots of generations. [69]

Symbolic machine learning was used to finding out concepts, guidelines, heuristics, and analytical. Approaches, besides those above, consist of:

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

With the increase of deep learning, the symbolic AI technique has been compared to deep knowing as complementary “… with parallels having been drawn lots of times by AI researchers in between Kahneman’s research 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 thinking, respectively.” In this view, symbolic thinking is more apt for deliberative thinking, preparation, and explanation while deep knowing is more apt for fast pattern recognition in perceptual applications with noisy data. [17] [18]

Neuro-symbolic AI: incorporating neural and symbolic methods

Neuro-symbolic AI attempts to incorporate neural and symbolic architectures in a way that addresses strengths and weak points of each, in a complementary fashion, in order to support robust AI capable of thinking, discovering, and cognitive modeling. As argued by Valiant [77] and many others, [78] the efficient construction of rich computational cognitive designs requires the mix of sound symbolic reasoning and effective (machine) learning designs. Gary Marcus, likewise, argues that: “We can not build rich cognitive designs in a sufficient, automatic way without the triumvirate of hybrid architecture, abundant prior understanding, and sophisticated strategies for thinking.”, [79] and in specific: “To build a robust, knowledge-driven approach to AI we need to have the machinery of symbol-manipulation in our toolkit. Too much of beneficial understanding is abstract to make do without tools that represent and manipulate abstraction, and to date, the only machinery that we understand of that can manipulate such abstract understanding dependably is the device of sign control. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have likewise argued for a synthesis. Their arguments are based on a requirement to attend to the 2 kinds of thinking gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having 2 elements, System 1 and System 2. System 1 is quickly, automatic, intuitive and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is the kind utilized for pattern acknowledgment while System 2 is far better matched for planning, reduction, and deliberative thinking. In this view, deep knowing best designs the very first kind of believing while symbolic thinking finest designs the 2nd kind and both are needed.

Garcez and Lamb explain research study in this area as being ongoing for at least the past twenty years, [83] dating from their 2002 book on neurosymbolic knowing systems. [84] A series of workshops on neuro-symbolic reasoning has been held every year considering 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 integration of the symbolic and connectionist paradigms of AI has actually been pursued by a relatively small research study neighborhood over the last 20 years and has yielded numerous significant outcomes. Over the last decade, neural symbolic systems have been shown capable of overcoming 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 shown efficient in representing modal and temporal logics (d’Avila Garcez and Lamb, 2006) and pieces of first-order logic (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have been used to a variety of problems in the areas of bioinformatics, control engineering, software verification and adjustment, visual intelligence, ontology learning, and video game. [78]

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

– Symbolic Neural symbolic-is the existing approach of numerous neural models in natural language processing, where words or subword tokens are both the ultimate input and output of large language designs. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic techniques are utilized to call neural techniques. In this case the symbolic method is Monte Carlo tree search and the neural techniques find out how to examine video game positions.
– Neural|Symbolic-uses a neural architecture to analyze affective information as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to produce or label training information that is subsequently discovered by a deep knowing model, e.g., to train a neural design for symbolic calculation 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 evidence tree produced from understanding base rules and terms. Logic Tensor Networks [86] also fall under this category.
– Neural [Symbolic] -allows a neural design to straight call a symbolic thinking engine, e.g., to carry out an action or assess a state.

Many key research concerns stay, such as:

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

Techniques and contributions

This section provides a summary of strategies and contributions in a total context resulting in many other, more comprehensive articles in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered previously in the history section.

AI programs languages

The crucial AI programming language in the US throughout the last symbolic AI boom period was LISP. LISP is the second oldest shows language after FORTRAN and was created in 1958 by John McCarthy. LISP offered the first read-eval-print loop to support fast program advancement. Compiled functions might be easily mixed with interpreted functions. Program tracing, stepping, and breakpoints were also offered, in addition to the capability to alter values or functions and continue from breakpoints or errors. It had the first self-hosting compiler, meaning that the compiler itself was originally written in LISP and after that ran interpretively to assemble the compiler code.

Other key developments pioneered by LISP that have infected other programs languages consist of:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

Programs were themselves information structures that other programs could operate on, permitting the easy definition of higher-level languages.

In contrast to the US, in Europe the crucial AI shows language during that very same period was Prolog. Prolog offered an integrated shop of truths and stipulations that might be queried by a read-eval-print loop. The store might function as a knowledge base and the stipulations could act as rules or a restricted type of logic. As a subset of first-order reasoning Prolog was based upon Horn provisions with a closed-world assumption-any realities not known were thought about false-and a distinct name presumption for primitive terms-e.g., the identifier barack_obama was considered to refer to precisely one object. Backtracking and unification are integrated to Prolog.

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

Prolog is likewise a kind of declarative programs. The reasoning clauses that explain programs are straight analyzed to run the programs specified. No specific series of actions is required, as is the case with vital shows languages.

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

Smalltalk was another influential AI programming language. For instance, it presented metaclasses and, in addition to 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 allows several inheritance, in addition to incremental extensions to both classes and metaclasses, therefore providing a run-time meta-object protocol. [88]

For other AI programming languages see this list of programs languages for expert system. Currently, Python, a multi-paradigm programs language, is the most popular programs 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 elements such as higher-order functions, and object-oriented programs that includes metaclasses.

Search

Search arises in lots of type of issue solving, consisting of planning, restraint fulfillment, and playing games such as checkers, chess, and go. The very best known AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven 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 methods to represent understanding and then reason with those representations have actually been examined. Below is a fast summary of approaches to understanding representation and automated reasoning.

Knowledge representation

Semantic networks, conceptual charts, frames, and logic are all methods to modeling understanding such as domain knowledge, problem-solving knowledge, and the semantic meaning 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 also be deemed an ontology. YAGO incorporates WordNet as part of its ontology, to line up truths drawn out from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology presently being used.

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

First-order reasoning is more basic than description reasoning. The automated theorem provers gone over below can prove theorems in first-order reasoning. Horn stipulation reasoning is more restricted than first-order logic and is used in reasoning programs languages such as Prolog. Extensions to first-order logic consist of temporal logic, to manage time; epistemic reasoning, to reason about agent knowledge; modal logic, to manage possibility and requirement; and probabilistic reasonings to deal with reasoning and probability together.

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

Prover9 can be utilized in conjunction with the Mace4 design checker. ACL2 is a theorem prover that can handle evidence by induction and is a descendant of the Boyer-Moore Theorem Prover, also known as Nqthm.

Reasoning in knowledge-based systems

Knowledge-based systems have an explicit understanding base, normally of guidelines, to boost reusability throughout domains by separating procedural code and domain understanding. A separate inference engine processes guidelines and adds, deletes, or customizes 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 rational representation is used, Horn Clauses. Pattern-matching, particularly marriage, is used in Prolog.

A more versatile kind of analytical happens when reasoning about what to do next occurs, instead of just choosing one of the available actions. This sort of meta-level thinking is utilized in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R might have extra abilities, such as the capability to put together regularly used understanding into higher-level pieces.

Commonsense reasoning

Marvin Minsky first proposed frames as a way of analyzing typical visual situations, such as an office, and Roger Schank extended this concept to scripts for common regimens, such as eating in restaurants. Cyc has attempted to capture useful sensible knowledge and has “micro-theories” to manage specific type of domain-specific thinking.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human thinking about ignorant physics, such as what takes place when we heat up a liquid in a pot on the range. We anticipate it to heat and possibly boil over, although we may not understand its temperature level, its boiling point, or other details, such as climatic pressure.

Similarly, Allen’s temporal interval algebra is a simplification of thinking 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 reasoning

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

Automated preparation

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

Natural language processing

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

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, however since improved by deep knowing methods. In symbolic AI, discourse representation theory and first-order reasoning have actually been utilized to represent sentence significances. Latent semantic analysis (LSA) and explicit semantic analysis likewise supplied vector representations of documents. In the latter case, vector parts are interpretable as principles called by Wikipedia articles.

New deep learning approaches based upon Transformer designs have actually now eclipsed these earlier symbolic AI techniques and obtained advanced efficiency in natural language processing. However, Transformer models are opaque and do not yet produce human-interpretable semantic representations for sentences and files. Instead, they produce task-specific vectors where the meaning of the vector elements 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 standard textbook on synthetic intelligence is arranged to reflect representative architectures of increasing elegance. [91] The elegance of agents varies from simple reactive agents, to those with a design of the world and automated planning capabilities, potentially a BDI agent, i.e., one with beliefs, desires, and intentions – or additionally a support discovering model found out with time to select actions – up to a combination of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep learning for understanding. [92]

In contrast, a multi-agent system includes multiple agents that communicate among themselves with some inter-agent interaction language such as Knowledge Query and Manipulation Language (KQML). The representatives need not all have the very same internal architecture. Advantages of multi-agent systems consist of the ability to divide work amongst the representatives and to increase fault tolerance when representatives are lost. Research problems include how agents reach agreement, dispersed issue solving, multi-agent knowing, multi-agent planning, and dispersed constraint optimization.

Controversies occurred from early in symbolic AI, both within the field-e.g., between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and between those who accepted AI but turned down symbolic approaches-primarily connectionists-and those outside the field. Critiques from beyond the field were primarily from thinkers, on intellectual grounds, but also from financing companies, particularly during the 2 AI winters.

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

Limitations were found in utilizing simple first-order reasoning to reason about vibrant domains. Problems were found both with concerns to specifying the prerequisites for an action to succeed and in offering axioms for what did not change after an action was performed.

McCarthy and Hayes introduced the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Artificial Intelligence.” [93] A basic example takes place in “proving that a person person might 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 directory” would be needed for the deduction to be successful. Similar axioms would be required for other domain actions to specify what did not alter.

A similar issue, called the Qualification Problem, happens in trying to identify the preconditions for an action to succeed. A boundless number of pathological conditions can be imagined, e.g., a banana in a tailpipe might prevent a vehicle from operating correctly.

McCarthy’s technique to repair the frame issue was circumscription, a type of non-monotonic reasoning where reductions could be made from actions that require only specify what would alter while not having to explicitly specify everything that would not change. Other non-monotonic logics provided fact upkeep systems that revised beliefs leading to contradictions.

Other methods of managing more open-ended domains consisted of probabilistic thinking systems and device learning to find out brand-new concepts and rules. McCarthy’s Advice Taker can be considered as an inspiration here, as it might incorporate new knowledge supplied by a human in the kind of assertions or rules. For example, experimental symbolic machine discovering systems checked out the capability to take high-level natural language suggestions and to interpret it into domain-specific actionable rules.

Similar to the problems in managing dynamic domains, common-sense thinking is also tough to record in official thinking. Examples of sensible reasoning include implicit reasoning about how people believe or general knowledge of everyday events, objects, and living creatures. This kind of understanding is considered approved and not deemed noteworthy. Common-sense thinking is an open area of research and challenging both for symbolic systems (e.g., Cyc has actually tried to record essential parts of this knowledge over more than a decade) and neural systems (e.g., self-driving automobiles that do not know not to drive into cones or not to strike pedestrians walking a bike).

McCarthy saw his Advice Taker as having common-sense, but his definition of common-sense was different than the one above. [94] He defined a program as having common sense “if it immediately deduces for itself a sufficiently broad class of immediate effects of anything it is told and what it currently knows. “

Connectionist AI: philosophical challenges and sociological disputes

Connectionist approaches 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 techniques, such as Transformers, GANs, and other operate in deep knowing.

Three philosophical positions [96] have been laid out among connectionists:

1. Implementationism-where connectionist architectures implement the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is declined absolutely, and connectionist architectures underlie intelligence and are completely adequate to explain 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 consider as basically suitable with present research study in neuro-symbolic hybrids:

The third and last position I would like to examine here is what I call the moderate connectionist view, a more diverse view of the current argument between connectionism and symbolic AI. One of the scientists who has actually elaborated this position most explicitly is Andy Clark, a thinker from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark defended hybrid (partly symbolic, partly connectionist) systems. He declared that (a minimum of) 2 kinds of theories are needed in order to study and design cognition. On the one hand, for some information-processing tasks (such as pattern recognition) connectionism has advantages over symbolic designs. But on the other hand, for other cognitive procedures (such as serial, deductive reasoning, and generative symbol control procedures) the symbolic paradigm provides sufficient models, and not just “approximations” (contrary to what radical connectionists would claim). [97]

Gary Marcus has actually claimed that the animus in the deep knowing community versus symbolic techniques now might be more sociological than philosophical:

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

And yet, for the a lot of part, that’s how most current AI proceeds. Hinton and many others have actually tried tough to get rid of symbols completely. The deep knowing hope-seemingly grounded not a lot in science, however in a sort of historical grudge-is that smart habits will emerge simply from the confluence of huge information and deep learning. Where classical computer systems and software solve tasks by specifying sets of symbol-manipulating rules committed to specific jobs, such as modifying a line in a word processor or performing a computation in a spreadsheet, neural networks typically try to resolve jobs by statistical approximation and gaining from examples.

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

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

Since then, his anti-symbolic campaign has only increased in strength. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep knowing in one of science’s crucial journals, Nature. It closed with a direct attack on sign adjustment, calling not for reconciliation however for straight-out replacement. Later, Hinton informed a gathering of European Union leaders that investing any further cash in symbol-manipulating techniques was “a huge mistake,” comparing it to investing in internal combustion engines in the era of electric automobiles. [98]

Part of these disputes may be due to uncertain terms:

Turing award winner Judea Pearl uses a critique of artificial intelligence which, regrettably, conflates the terms artificial intelligence and deep knowing. Similarly, when Geoffrey Hinton describes symbolic AI, the undertone of the term tends to be that of specialist systems dispossessed of any capability to discover. Making use of the terminology needs explanation. Machine learning 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 rational instead of distributed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not practically production guidelines written by hand. An appropriate meaning of AI concerns understanding representation and thinking, autonomous multi-agent systems, planning and argumentation, in addition to learning. [99]

Situated robotics: the world as a design

Another critique of symbolic AI is the embodied cognition approach:

The embodied cognition approach claims that it makes no sense to consider the brain separately: 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 consistencies in its environment, consisting of the rest of its body. Under the embodied cognition method, robotics, vision, and other sensors end up being main, not peripheral. [100]

Rodney Brooks invented behavior-based robotics, one method to embodied cognition. Nouvelle AI, another name for this method, is considered as an alternative to both symbolic AI and connectionist AI. His method turned down representations, either symbolic or distributed, as not only unnecessary, however as detrimental. Instead, he developed the subsumption architecture, a layered architecture for embodied agents. Each layer achieves a different purpose and must work in the genuine world. For instance, the first robot he describes in Intelligence Without Representation, has 3 layers. The bottom layer analyzes sonar sensing units to prevent items. The middle layer triggers the robot to roam around when there are no obstacles. The top layer causes the robot to go to more distant places for more expedition. Each layer can momentarily inhibit or suppress a lower-level layer. He slammed AI researchers for defining AI problems for their systems, when: “There is no clean department in between understanding (abstraction) and reasoning in the real life.” [101] He called his robots “Creatures” and each layer was “made up of a fixed-topology network of basic finite state devices.” [102] In the Nouvelle AI method, “First, it is critically important to evaluate the Creatures we integrate in the genuine world; i.e., in the same world that we human beings populate. It is devastating to fall into the temptation of evaluating them in a streamlined world initially, even with the best intentions of later transferring activity to an unsimplified world.” [103] His emphasis on real-world testing was in contrast to “Early operate in AI concentrated on video games, geometrical issues, symbolic algebra, theorem proving, and other official systems” [104] and the use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has advantages, but has actually been criticized by the other approaches. Symbolic AI has actually been criticized as disembodied, responsible to the credentials problem, and bad in dealing with the affective issues where deep finding out excels. In turn, connectionist AI has actually been criticized as improperly fit for deliberative step-by-step problem fixing, including understanding, and handling planning. Finally, Nouvelle AI stands out in reactive and real-world robotics domains but has been criticized for difficulties in incorporating knowing and knowledge.

Hybrid AIs integrating one or more of these approaches are currently considered as the path 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 difficult; we now see much of these very same areas undergoing ongoing research study and advancement causing increased capability, not impossibility. [100]

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

Notes

^ McCarthy when stated: “This is AI, so we do not care if it’s psychologically real”. [4] McCarthy repeated 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 significant branches of expert system: one targeted at producing intelligent habits regardless of how it was accomplished, and the other targeted at modeling intelligent procedures discovered in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not specify the objective of their field as making ‘makers that fly so precisely 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 objects and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating mistakes”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten Postal 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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