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Symbolic Artificial Intelligence

In artificial intelligence, symbolic expert system (likewise called classical expert system or logic-based synthetic intelligence) [1] [2] is the term for the collection of all approaches in expert system research that are based on top-level symbolic (human-readable) representations of problems, logic and search. [3] Symbolic AI used tools such as logic programs, production rules, semantic nets and frames, and it established applications such as knowledge-based systems (in particular, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to influential concepts in search, symbolic shows languages, representatives, multi-agent systems, the semantic web, and the strengths and constraints of official knowledge and reasoning systems.

Symbolic AI was the dominant paradigm of AI research from the mid-1950s till the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic techniques would ultimately be successful in producing a maker with artificial general intelligence and considered this the supreme goal 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 promises and was followed by the very first AI Winter as funding dried up. [5] [6] A 2nd boom (1969-1986) accompanied the rise of professional systems, their pledge of recording corporate competence, and a passionate business welcome. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later on dissatisfaction. [8] Problems with problems in understanding acquisition, maintaining large knowledge bases, and brittleness in dealing with out-of-domain issues occurred. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists concentrated on addressing hidden problems in managing unpredictability and in understanding acquisition. [10] Uncertainty was addressed with formal methods such as surprise Markov designs, Bayesian thinking, and analytical relational learning. [11] [12] Symbolic device discovering resolved the knowledge acquisition problem with contributions including Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree learning, case-based knowing, and inductive reasoning shows to discover relations. [13]

Neural networks, a subsymbolic method, had been pursued from early days and reemerged highly 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 seen as successful up until about 2012: “Until Big Data ended up being prevalent, 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 transformation came in 2012, when a variety of people, consisting of a team of scientists working with Hinton, exercised a method to use the power of GPUs to tremendously increase the power of neural networks.” [16] Over the next numerous years, deep learning had spectacular success in dealing with vision, speech acknowledgment, speech synthesis, image generation, and maker translation. However, given that 2020, as inherent problems with bias, description, coherence, and robustness ended up being more obvious with deep learning methods; an increasing variety of AI researchers have actually called for integrating the very best of both the symbolic and neural network approaches [17] [18] and resolving areas that both techniques have trouble with, such as sensible reasoning. [16]

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

The first AI summer: irrational vitality, 1948-1966

Success at early efforts in AI took place in three primary areas: synthetic neural networks, understanding representation, and heuristic search, contributing to high expectations. This section sums up Kautz’s reprise of early AI history.

Approaches influenced by human or animal cognition or behavior

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

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

During the 1960s, symbolic methods achieved excellent success at mimicing smart behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was focused in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Every one developed its own style of research. Earlier techniques based upon cybernetics or synthetic neural networks were abandoned or pushed into the background.

Herbert Simon and Allen Newell studied human analytical abilities and tried to formalize them, and their work laid the foundations of the field of synthetic intelligence, in addition to cognitive science, operations research study and management science. Their research study group used the outcomes of psychological experiments to develop programs that simulated the strategies that people used to resolve issues. [22] [23] This tradition, centered at Carnegie Mellon University would eventually culminate in the advancement of the Soar architecture in the middle 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific kinds of understanding that we will see later on used in expert systems, early symbolic AI scientists found another more basic application of knowledge. These were called heuristics, general rules that assist a search in appealing directions: “How can non-enumerative search be practical when the underlying issue is significantly difficult? The method promoted by Simon and Newell is to employ heuristics: fast algorithms that might stop working on some inputs or output suboptimal services.” [26] Another important advance was to find a way to use these heuristics that ensures a solution will be discovered, if there is one, not holding up against the periodic fallibility of heuristics: “The A * algorithm offered 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 purchased the expense of worst-case rapid time. [26]

Early work on understanding representation and thinking

Early work covered both applications of official reasoning stressing first-order reasoning, along with efforts to manage sensible thinking in a less formal manner.

Modeling formal reasoning with reasoning: the “neats”

Unlike Simon and Newell, John McCarthy felt that machines did not require to replicate the specific systems of human thought, but could rather attempt to discover the essence of abstract reasoning and analytical with logic, [27] despite whether individuals used the same algorithms. [a] His lab at Stanford (SAIL) concentrated on utilizing official logic to resolve a variety of problems, including understanding representation, preparation and knowing. [31] Logic was also the focus of the work at the University of Edinburgh and in other places in Europe which caused the advancement of the programs language Prolog and the science of logic programming. [32] [33]

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

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that solving challenging issues in vision and natural language processing needed ad hoc solutions-they argued that no simple and general principle (like logic) would record all the aspects of intelligent habits. Roger Schank described their “anti-logic” approaches 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 “shabby” AI, because they must be developed by hand, one complicated idea at a time. [38] [39] [40]

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

The first AI winter season was a shock:

During the first AI summer season, lots of people believed that device intelligence could be achieved in just a few years. The Defense Advance Research Projects Agency (DARPA) introduced programs to support AI research to use AI to solve issues of nationwide security; in particular, to automate the translation of Russian to English for intelligence operations and to produce autonomous tanks for the battlefield. Researchers had actually begun to understand that accomplishing AI was going to be much harder than was expected a years previously, however a combination of hubris and disingenuousness led numerous university and think-tank researchers to accept financing with pledges of deliverables that they need to have understood they might not meet. By the mid-1960s neither helpful natural language translation systems nor self-governing tanks had been produced, and a remarkable reaction embeded in. New DARPA management canceled existing AI financing programs.

Outside of the United States, the most fertile ground for AI research study was the UK. The AI winter season in the UK was stimulated on not so much by disappointed military leaders as by rival academics who saw AI scientists as charlatans and a drain on research study funding. A professor of used mathematics, Sir James Lighthill, was commissioned by Parliament to assess the state of AI research study in the nation. The report stated that all of the issues being worked on in AI would be much better managed by researchers from other disciplines-such as used mathematics. The report likewise claimed that AI successes on toy problems might never scale to real-world applications due to combinatorial explosion. [41]

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

Knowledge-based systems

As limitations with weak, domain-independent techniques ended up being a growing number of evident, [42] researchers from all 3 traditions began to construct understanding into AI applications. [43] [7] The understanding revolution was driven by the awareness that understanding underlies high-performance, domain-specific AI applications.

Edward Feigenbaum stated:

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

( 1) The Knowledge Principle: if a program is to perform an intricate job well, it must know a good deal about the world in which it runs.
( 2) A possible extension of that concept, called the Breadth Hypothesis: there are 2 extra capabilities essential for intelligent behavior in unanticipated situations: falling back on increasingly basic knowledge, and analogizing to particular but far-flung knowledge. [45]

Success with specialist systems

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

Key professional systems were:

DENDRAL, which discovered the structure of natural particles from their chemical formula and mass spectrometer readings.
MYCIN, which detected bacteremia – and recommended further laboratory tests, when essential – by interpreting lab results, client history, and doctor observations. “With about 450 rules, MYCIN had the ability to carry out as well as some experts, and significantly better than junior physicians.” [49] INTERNIST and CADUCEUS which dealt with internal medicine diagnosis. Internist attempted to record the competence of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS could eventually detect approximately 1000 various illness.
– GUIDON, which showed how an understanding base constructed for expert problem resolving might be repurposed for teaching. [50] XCON, to set up VAX computers, a then laborious procedure that might take up to 90 days. XCON lowered the time to about 90 minutes. [9]
DENDRAL is considered the very first expert system that count on knowledge-intensive analytical. It is described listed below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

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

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, inventor of the chemical behind the birth control tablet, and likewise one of the world’s most respected mass spectrometrists. Carl and his postdocs were first-rate experts in mass spectrometry. We began to add to their knowledge, inventing understanding of engineering as we went along. These experiments totaled up to titrating DENDRAL increasingly 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 career that is the substantial, “Ah ha!,” and it wasn’t the method AI was being done formerly. Sounds easy, however it’s most likely AI’s most effective generalization. [51]

The other expert systems pointed out above came after DENDRAL. MYCIN exhibits the traditional expert system architecture of a knowledge-base of rules paired to a symbolic reasoning mechanism, including the usage of certainty factors to deal with uncertainty. GUIDON demonstrates how an explicit understanding base can be repurposed for a 2nd application, tutoring, and is an example of a smart tutoring system, a specific type of knowledge-based application. Clancey revealed that it was not sufficient simply to use MYCIN’s guidelines for instruction, but that he also needed to include guidelines for dialogue management and student modeling. [50] XCON is substantial since of the countless dollars it conserved DEC, which set off the expert system boom where most all significant corporations in the US had professional systems groups, to catch business expertise, maintain it, and automate it:

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

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

Architecture of knowledge-based and expert systems

An essential element of the system architecture for all professional systems is the knowledge base, which shops facts and rules for problem-solving. [53] The most basic method for an expert system knowledge base is simply a collection or network of production guidelines. Production rules connect signs in a relationship comparable to an If-Then statement. The specialist system processes the guidelines to make deductions and to determine what additional information it requires, i.e. what questions to ask, utilizing human-readable signs. For instance, OPS5, CLIPS and their successors Jess and Drools operate in this style.

Expert systems can operate in either a forward chaining – from evidence to conclusions – or backwards chaining – from objectives to needed data and requirements – way. Advanced knowledge-based systems, such as Soar can likewise perform meta-level thinking, that is thinking about their own reasoning in terms of deciding how to fix problems and monitoring the success of analytical strategies.

Blackboard systems are a 2nd sort of knowledge-based or professional system architecture. They design a community of experts incrementally contributing, where they can, to resolve an issue. The issue is represented in several levels of abstraction or alternate views. The experts (understanding sources) offer their services whenever they acknowledge they can contribute. Potential problem-solving actions are represented on a program that is updated as the issue scenario modifications. A controller decides how beneficial each contribution is, and who must make the next problem-solving action. One example, the BB1 blackboard architecture [54] was originally motivated by research studies of how human beings plan to perform numerous tasks in a journey. [55] A development of BB1 was to use the same chalkboard model to resolving its control problem, i.e., its controller carried out meta-level thinking with understanding sources that kept an eye on how well a plan or the problem-solving was continuing and could change from one technique to another as conditions – such as objectives or times – changed. BB1 has been used in numerous domains: building site preparation, smart tutoring systems, and real-time patient tracking.

The second AI winter, 1988-1993

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

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

Many reasons can be offered for the arrival of the second AI winter. The hardware business failed when far more economical basic Unix workstations from Sun together with great compilers for LISP and Prolog came onto the market. Many business implementations of specialist systems were stopped when they proved too pricey to maintain. Medical specialist systems never caught on for several reasons: the difficulty in keeping them up to date; the difficulty for medical experts to find out how to utilize a bewildering variety of various specialist systems for different medical conditions; and perhaps most crucially, the reluctance of medical professionals to trust a computer-made diagnosis over their gut instinct, even for specific domains where the professional systems could surpass an average medical professional. Venture capital cash deserted AI virtually over night. The world AI conference IJCAI hosted an enormous and extravagant trade convention and thousands of nonacademic attendees in 1987 in Vancouver; the main AI conference the list below year, AAAI 1988 in St. Paul, was a small and strictly scholastic affair. [9]

Adding in more rigorous structures, 1993-2011

Uncertain thinking

Both analytical approaches and extensions to logic were attempted.

One statistical technique, hidden Markov models, had currently been promoted in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl promoted making use of Bayesian Networks as a noise but effective method of handling unpredictable thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian approaches were applied effectively in expert systems. [57] Even later, in the 1990s, statistical relational learning, an approach that combines probability with sensible solutions, enabled likelihood to be integrated with first-order logic, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order logic to assistance were also attempted. For example, non-monotonic reasoning could be used with fact upkeep systems. A reality upkeep system tracked presumptions and reasons for all inferences. It enabled inferences to be withdrawn when presumptions were found out to be inaccurate or a contradiction was obtained. Explanations might be attended to an inference by explaining which rules were applied to produce it and after that continuing through underlying inferences and guidelines all the way back to root assumptions. [58] Lofti Zadeh had introduced a different sort of extension to handle the representation of vagueness. For instance, in deciding how “heavy” or “high” a guy is, there is frequently no clear “yes” or “no” answer, and a predicate for heavy or high would rather return worths between 0 and 1. Those worths represented to what degree the predicates held true. His fuzzy logic even more provided a method for propagating combinations of these values through logical solutions. [59]

Artificial intelligence

Symbolic device finding out methods were examined to address the knowledge acquisition bottleneck. Among the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test method to create plausible guideline hypotheses to test versus spectra. Domain and job understanding reduced the number of prospects evaluated to a workable size. Feigenbaum described Meta-DENDRAL as

… the culmination of my dream of the early to mid-1960s involving 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 guide and prune the search. That understanding got in there due to the fact that we spoke with individuals. But how did the people get the knowledge? By looking at countless spectra. So we wanted a program that would take a look at thousands of spectra and infer the knowledge of mass spectrometry that DENDRAL might utilize to fix specific hypothesis formation problems. We did it. We were even able to release new understanding of mass spectrometry in the Journal of the American Chemical Society, offering credit only 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 system program created a new and publishable piece of science. [51]

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

Advances were made in understanding machine learning theory, too. Tom Mitchell introduced version area learning which describes learning as an explore an area of hypotheses, with upper, more basic, and lower, more particular, boundaries including 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 device discovering included more than discovering by example. E.g., John Anderson offered a cognitive model of human learning where skill practice results in a compilation of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a trainee might discover to apply “Supplementary angles are two angles whose procedures sum 180 degrees” as numerous different procedural rules. E.g., one guideline might state 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 been used successfully to model elements of human cognition, such as learning and retention. ACT-R is likewise utilized in intelligent tutoring systems, called cognitive tutors, to successfully teach geometry, computer programs, and algebra to school kids. [64]

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

As an option to reasoning, Roger Schank presented case-based thinking (CBR). The CBR approach detailed in his book, Dynamic Memory, [67] focuses first on keeping in mind essential problem-solving cases for future usage and generalizing them where appropriate. When faced with a brand-new problem, CBR obtains the most similar previous case and adjusts it to the specifics of the existing issue. [68] Another option to reasoning, hereditary algorithms and genetic programming are based on an evolutionary design of learning, where sets of rules are encoded into populations, the rules govern the behavior of individuals, and selection of the fittest prunes out sets of inappropriate rules over lots of generations. [69]

Symbolic maker knowing was used to learning principles, rules, heuristics, and problem-solving. Approaches, other than those above, include:

1. Learning from direction or advice-i.e., taking human direction, presented as suggestions, and identifying how to operationalize it in particular 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 performance by accepting subject-matter expert (SME) feedback throughout training. When analytical stops working, querying the professional to either find out a new prototype for problem-solving or to learn a new description as to exactly why one exemplar is more relevant than another. For example, the program Protos found out to diagnose ringing in the ears cases by communicating with an audiologist. [71] 3. Learning by analogy-constructing problem options based upon similar problems seen in the past, and after that modifying their options to fit a brand-new circumstance or domain. [72] [73] 4. Apprentice knowing systems-learning unique services to problems by observing human problem-solving. Domain understanding discusses why novel services are appropriate and how the service can be generalized. LEAP discovered how to create VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing jobs to carry out experiments and then finding out from the results. Doug Lenat’s Eurisko, for example, 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., browsing for beneficial macro-operators to be found out from series of standard analytical actions. Good macro-operators streamline analytical by enabling problems to be resolved at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now

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

Neuro-symbolic AI: integrating neural and symbolic techniques

Neuro-symbolic AI efforts to incorporate neural and symbolic architectures in a manner that addresses strengths and weak points of each, in a complementary style, in order to support robust AI efficient in thinking, discovering, and cognitive modeling. As argued by Valiant [77] and many others, [78] the efficient building and construction of abundant computational cognitive designs demands the mix of sound symbolic thinking and effective (machine) learning designs. Gary Marcus, likewise, argues that: “We can not build rich cognitive designs in an appropriate, automatic method without the triumvirate of hybrid architecture, abundant prior understanding, and sophisticated methods for reasoning.”, [79] and in particular: “To build a robust, knowledge-driven method to AI we need to have the machinery of symbol-manipulation in our toolkit. Excessive of helpful knowledge is abstract to make do without tools that represent and control abstraction, and to date, the only machinery that we understand of that can manipulate such abstract understanding reliably is the apparatus of sign control. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based upon a need to deal with the two kinds of believing discussed in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having two elements, System 1 and System 2. System 1 is quickly, automated, intuitive and unconscious. System 2 is slower, detailed, and explicit. System 1 is the kind utilized for pattern acknowledgment while System 2 is far much better fit for preparation, reduction, and deliberative thinking. In this view, deep knowing finest designs the very first type of believing while symbolic reasoning best models the 2nd kind and both are needed.

Garcez and Lamb explain research in this area 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 thinking 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 integration of the symbolic and connectionist paradigms of AI has actually been pursued by a fairly small research study community over the last 20 years and has yielded a number of significant outcomes. Over the last years, neural symbolic systems have actually been revealed capable of getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in response to Smolensky (1988 ); see also (Hinton, 1990). Neural networks were revealed capable of representing modal and temporal reasonings (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 actually been used to a variety of problems in the areas of bioinformatics, control engineering, software application confirmation and adjustment, visual intelligence, ontology learning, and computer system games. [78]

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

– Symbolic Neural symbolic-is the present approach of many neural models in natural language processing, where words or subword tokens are both the ultimate input and output of big language designs. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic techniques are utilized to call neural methods. In this case the symbolic technique is Monte Carlo tree search and the neural methods find out how to examine video game positions.
– Neural|Symbolic-uses a neural architecture to analyze affective data as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to generate or label training information that is subsequently found out by a deep learning model, e.g., to train a neural design for symbolic computation by utilizing a Macsyma-like symbolic mathematics system to create or label examples.
– Neural _ Symbolic -utilizes a neural net that is generated from symbolic guidelines. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR proof tree produced from understanding base rules and terms. Logic Tensor Networks [86] likewise fall under this classification.
– Neural [Symbolic] -permits a neural model to straight call a symbolic thinking engine, e.g., to carry out an action or evaluate a state.

Many crucial research study concerns remain, such as:

– What is the 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 common-sense knowledge be found out and reasoned about?
– How can abstract understanding that is difficult to encode rationally be managed?

Techniques and contributions

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

AI programming languages

The crucial AI programs language in the US throughout the last symbolic AI boom duration was LISP. LISP is the second oldest programming language after FORTRAN and was created in 1958 by John McCarthy. LISP provided the very first read-eval-print loop to support rapid program advancement. Compiled functions might be freely combined with analyzed functions. Program tracing, stepping, and breakpoints were also supplied, in addition to the ability to alter values or functions and continue from breakpoints or errors. It had the very first self-hosting compiler, implying that the compiler itself was originally composed in LISP and then ran interpretively to compile the compiler code.

Other key developments originated by LISP that have infected other programming languages include:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

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

In contrast to the US, in Europe the essential AI programs language throughout that same period was Prolog. Prolog provided a built-in shop of facts and stipulations that might be queried by a read-eval-print loop. The store might serve as a knowledge base and the clauses might function as rules or a limited form of reasoning. As a subset of first-order logic Prolog was based on Horn stipulations with a closed-world assumption-any truths not known were thought about false-and an unique name presumption for primitive terms-e.g., the identifier barack_obama was thought about to describe precisely one things. Backtracking and marriage are integrated to Prolog.

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

Prolog is likewise a sort of declarative shows. The logic clauses that explain programs are directly interpreted to run the programs defined. No specific series of actions is required, as holds true with important shows languages.

Japan championed Prolog for its Fifth Generation Project, intending to develop special hardware for high efficiency. Similarly, LISP machines were developed to run LISP, however as the 2nd AI boom turned to bust these companies could not contend with new workstations that could now run LISP or Prolog natively at comparable speeds. See the history section for more information.

Smalltalk was another prominent AI programs language. For example, it introduced 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 enables several inheritance, in addition to incremental extensions to both classes and metaclasses, therefore supplying a run-time meta-object protocol. [88]

For other AI shows languages see this list of programming languages for artificial intelligence. Currently, Python, a multi-paradigm shows language, is the most popular programming language, partly due to its substantial plan library that supports information 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 consists of metaclasses.

Search

Search occurs in lots of type of issue 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 stipulation 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 thinking

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

Knowledge representation

Semantic networks, conceptual graphs, frames, and logic are all approaches to modeling understanding such as domain knowledge, problem-solving understanding, and the semantic significance of language. Ontologies model crucial 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 utilized for any domain while WordNet is a lexical resource that can also be deemed an ontology. YAGO incorporates WordNet as part of its ontology, to line up realities extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being used.

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

First-order reasoning is more general than description reasoning. The automated theorem provers talked about below can show theorems in first-order reasoning. Horn clause reasoning is more limited than first-order logic and is used in logic shows languages such as Prolog. Extensions to first-order reasoning include temporal reasoning, to manage time; epistemic reasoning, to reason about representative knowledge; modal reasoning, to manage possibility and need; and probabilistic logics to manage reasoning and likelihood together.

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

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

Reasoning in knowledge-based systems

Knowledge-based systems have a specific knowledge base, usually of rules, to boost reusability across domains by separating procedural code and domain understanding. A separate reasoning engine procedures rules and includes, deletes, or customizes a knowledge shop.

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

A more flexible sort of problem-solving happens when reasoning about what to do next takes place, rather than simply selecting one of the offered actions. This type of meta-level thinking is used in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R may have extra abilities, such as the capability to compile frequently used knowledge into higher-level pieces.

Commonsense thinking

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

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] estimates human thinking about naive physics, such as what happens when we heat up a liquid in a pot on the range. We expect it to heat and perhaps boil over, despite the fact that we may not understand its temperature, its boiling point, or other details, such as climatic pressure.

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

Constraints and constraint-based reasoning

Constraint solvers perform a more limited kind 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 reasoning programs can be utilized to resolve scheduling issues, for instance with restraint handling guidelines (CHR).

Automated planning

The General Problem Solver (GPS) cast planning as problem-solving utilized means-ends analysis to produce plans. STRIPS took a different method, viewing planning 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 backwards. Satplan is a method to preparing where a planning problem is reduced to a Boolean satisfiability problem.

Natural language processing

Natural language processing concentrates on dealing with language as data to carry out tasks such as recognizing subjects without necessarily comprehending the desired significance. Natural language understanding, on the other hand, constructs a meaning representation and uses that for additional processing, such as addressing concerns.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all aspects of natural language processing long handled by symbolic AI, however since enhanced by deep knowing techniques. In symbolic AI, discourse representation theory and first-order reasoning have actually been used to represent sentence meanings. Latent semantic analysis (LSA) and explicit semantic analysis also provided vector representations of documents. In the latter case, vector parts are interpretable as concepts named by Wikipedia posts.

New deep learning approaches based upon Transformer designs have actually now eclipsed these earlier symbolic AI techniques and achieved cutting edge 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 significance of the vector elements is nontransparent.

Agents and multi-agent systems

Agents are autonomous systems embedded in an environment they view and act upon in some sense. Russell and Norvig’s basic textbook on synthetic intelligence is organized to reflect agent architectures of increasing sophistication. [91] The elegance of representatives differs from basic reactive representatives, to those with a design of the world and automated preparation abilities, potentially a BDI representative, i.e., one with beliefs, desires, and objectives – or additionally a reinforcement finding out design found out gradually to choose actions – approximately 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 consists of multiple representatives that communicate among themselves with some inter-agent interaction language such as Knowledge Query and Manipulation Language (KQML). The agents need not all have the exact same internal architecture. Advantages of multi-agent systems include the capability to divide work amongst the agents and to increase fault tolerance when representatives are lost. Research issues include how agents reach consensus, dispersed problem solving, multi-agent learning, multi-agent planning, and dispersed constraint optimization.

Controversies occurred from early in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who accepted AI however declined symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were primarily from philosophers, on intellectual premises, however also from financing agencies, specifically during the two AI winters.

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

Limitations were found in utilizing basic first-order logic to reason about dynamic domains. Problems were found both with concerns to enumerating the preconditions for an action to be successful and in offering axioms for what did not change after an action was carried out.

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

A similar problem, called the Qualification Problem, takes place in trying to identify the prerequisites for an action to succeed. A limitless variety of pathological conditions can be pictured, e.g., a banana in a tailpipe might avoid a car from running properly.

McCarthy’s technique to fix the frame problem was circumscription, a kind of non-monotonic logic where deductions might be made from actions that require only specify what would alter while not needing to clearly define whatever that would not alter. Other non-monotonic reasonings offered truth upkeep systems that modified beliefs causing contradictions.

Other ways of managing more open-ended domains consisted of probabilistic reasoning systems and device learning to find out brand-new concepts and rules. McCarthy’s Advice Taker can be viewed as an inspiration here, as it might include new understanding supplied by a human in the form of assertions or rules. For example, speculative symbolic maker learning systems explored the capability to take top-level natural language recommendations and to analyze it into domain-specific actionable guidelines.

Similar to the problems in handling vibrant domains, common-sense thinking is likewise difficult to capture in official thinking. Examples of common-sense thinking include implicit reasoning about how individuals think or general knowledge of everyday occasions, objects, and living animals. This kind of understanding is considered approved and not considered as noteworthy. Common-sense reasoning is an open location of research study and challenging both for symbolic systems (e.g., Cyc has actually tried to capture key parts of this knowledge over more than a decade) and neural systems (e.g., self-driving cars and trucks that do not understand not to drive into cones or not to strike pedestrians strolling a bicycle).

McCarthy viewed his Advice Taker as having sensible, however his definition of sensible was different than the one above. [94] He defined a program as having sound judgment “if it automatically deduces for itself an adequately large class of instant effects of anything it is informed and what it currently understands. “

Connectionist AI: philosophical difficulties and sociological disputes

Connectionist techniques 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 approaches, such as Transformers, GANs, and other work in deep learning.

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

1. Implementationism-where connectionist architectures carry out the abilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected completely, and connectionist architectures underlie intelligence and are fully enough to describe it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are considered as complementary and both are required for intelligence

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

The 3rd and last position I wish to take a look at here is what I call the moderate connectionist view, a more diverse view of the current dispute between connectionism and symbolic AI. Among the researchers who has elaborated this position most clearly is Andy Clark, a thinker from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark protected hybrid (partly symbolic, partially connectionist) systems. He claimed that (a minimum of) 2 kinds of theories are required in order to study and design cognition. On the one hand, for some information-processing tasks (such as pattern acknowledgment) connectionism has advantages over symbolic designs. But on the other hand, for other cognitive procedures (such as serial, deductive thinking, and generative sign adjustment procedures) the symbolic paradigm offers adequate models, and not only “approximations” (contrary to what extreme connectionists would declare). [97]

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

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

And yet, for the many part, that’s how most existing AI proceeds. Hinton and lots of others have actually striven to get rid of signs entirely. The deep knowing hope-seemingly grounded not a lot in science, however in a sort of historical grudge-is that intelligent behavior will emerge purely from the confluence of massive data and deep learning. Where classical computers and software application fix jobs by specifying sets of symbol-manipulating guidelines dedicated to particular tasks, such as editing a line in a word processor or carrying out a calculation in a spreadsheet, neural networks generally try to resolve jobs by analytical approximation and finding out from examples.

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

When deep learning reemerged in 2012, it was with a type of take-no-prisoners attitude that has actually identified many of the last decade. By 2015, his hostility toward all things symbols had actually completely crystallized. He gave a talk at an AI workshop at Stanford comparing symbols to aether, among science’s biggest mistakes.

Ever since, his anti-symbolic project has actually just increased in strength. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep knowing in among science’s most essential journals, Nature. It closed with a direct attack on sign control, calling not for reconciliation but for outright replacement. Later, Hinton informed a gathering of European Union leaders that investing any more money in symbol-manipulating methods was “a big mistake,” comparing it to buying internal combustion engines in the era of electrical cars. [98]

Part of these conflicts may be due to uncertain terminology:

Turing award winner Judea Pearl offers a critique of maker learning which, unfortunately, 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 learn. Using the terminology needs clarification. Artificial intelligence is not restricted to association rule mining, c.f. the body of work on symbolic ML and relational learning (the differences to deep learning being the choice of representation, localist rational instead of dispersed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not practically production rules written by hand. A proper meaning of AI issues knowledge representation and reasoning, autonomous multi-agent systems, planning and argumentation, in addition to learning. [99]

Situated robotics: the world as a design

Another review of symbolic AI is the embodied cognition technique:

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

Rodney Brooks invented behavior-based robotics, one technique to embodied cognition. Nouvelle AI, another name for this technique, is seen as 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 created the subsumption architecture, a layered architecture for embodied agents. Each layer attains a different purpose and must function in the real world. For example, the very first robot he explains in Intelligence Without Representation, has 3 layers. The bottom layer analyzes sonar sensors to prevent things. The middle layer causes the robotic to roam around when there are no challenges. The leading layer triggers the robotic to go to more distant places for additional exploration. Each layer can briefly hinder or reduce a lower-level layer. He criticized AI scientists for defining AI issues for their systems, when: “There is no tidy department in between understanding (abstraction) and reasoning in the real world.” [101] He called his robotics “Creatures” and each layer was “composed of a fixed-topology network of basic limited state makers.” [102] In the Nouvelle AI technique, “First, it is critically important to evaluate the Creatures we construct in the real world; i.e., in the same world that we humans inhabit. It is disastrous to fall under the temptation of testing them in a streamlined world initially, even with the very best intents of later transferring activity to an unsimplified world.” [103] His emphasis on real-world screening was in contrast to “Early work in AI concentrated on games, geometrical problems, symbolic algebra, theorem proving, and other formal systems” [104] and making use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has benefits, but has been criticized by the other techniques. Symbolic AI has actually been slammed as disembodied, responsible to the certification problem, and poor in managing the affective issues where deep learning excels. In turn, connectionist AI has actually been criticized as poorly suited for deliberative detailed problem solving, incorporating knowledge, and handling preparation. Finally, Nouvelle AI stands out in reactive and real-world robotics domains but has actually been slammed for troubles in incorporating learning and understanding.

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

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

Artificial intelligence.
Automated planning 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 synthetic intelligence
Inductive logic shows
Knowledge-based systems
Knowledge representation and reasoning
Logic programs
Machine knowing
Model checking
Model-based thinking
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 once stated: “This is AI, so we do not care if it’s real”. [4] McCarthy restated his position in 2006 at the AI@50 conference where he said “Artificial intelligence is not, by meaning, simulation of human intelligence”. [28] Pamela McCorduck composes that there are “2 significant branches of artificial intelligence: one targeted at producing intelligent behavior despite how it was achieved, and the other aimed at modeling smart processes discovered in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig composed “Aeronautical engineering texts do not define the goal 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 artificial intelligence: representing objects and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). “Logic-Based Artificial Intelligence”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep knowing with symbolic artificial intelligence: representing objects and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating errors”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten Zip Code Recognition”. Neural Computation. 1 (4 ): 541-551. doi:10.1162/ neco.1989.1.4.541. S2CID 41312633.
^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. “Thinking Fast and Slow in AI”. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. “AAAI Presidential Address: The State of AI”. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
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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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