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Symbolic Artificial Intelligence
In expert system, symbolic synthetic intelligence (likewise referred to as classical synthetic intelligence or logic-based expert system) [1] [2] is the term for the collection of all techniques in expert system research that are based upon top-level symbolic (human-readable) representations of problems, logic and search. [3] Symbolic AI used tools such as reasoning programs, production guidelines, semantic internet and frames, and it established applications such as knowledge-based systems (in specific, professional systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated preparation and scheduling systems. The Symbolic AI paradigm led to influential concepts in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of formal knowledge and thinking 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 convinced that symbolic techniques would eventually succeed in developing a machine with synthetic basic intelligence and considered this the ultimate goal of their field. [citation required] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, led to unrealistic expectations and guarantees and was followed by the first AI Winter as funding dried up. [5] [6] A 2nd boom (1969-1986) accompanied the rise of specialist systems, their promise of catching business proficiency, and an enthusiastic corporate accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later on frustration. [8] Problems with difficulties in knowledge acquisition, keeping large understanding bases, and brittleness in managing out-of-domain issues occurred. Another, 2nd, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers concentrated on resolving underlying problems in dealing with uncertainty and in understanding acquisition. [10] Uncertainty was addressed with formal techniques such as covert Markov models, Bayesian reasoning, and analytical relational knowing. [11] [12] Symbolic device learning resolved the knowledge acquisition problem with contributions including Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree knowing, case-based learning, and inductive logic programming to find out relations. [13]
Neural networks, a subsymbolic technique, 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 considered as effective up until about 2012: “Until Big Data became commonplace, the general consensus in the Al neighborhood was that the so-called neural-network method was hopeless. Systems just didn’t work that well, compared to other methods. … A transformation came in 2012, when a number of people, consisting of a group of researchers dealing with Hinton, exercised a method to utilize the power of GPUs to immensely increase the power of neural networks.” [16] Over the next numerous years, deep learning had incredible success in dealing with vision, speech recognition, speech synthesis, image generation, and maker translation. However, because 2020, as fundamental difficulties with bias, explanation, comprehensibility, and robustness became more apparent with deep knowing approaches; an increasing variety of AI researchers have actually required combining the very best of both the symbolic and neural network methods [17] [18] and resolving locations that both techniques have difficulty with, such as common-sense thinking. [16]
A brief history of symbolic AI to the present day follows listed below. Period and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture [19] and the longer Wikipedia article on the History of AI, with dates and titles differing somewhat for increased clearness.
The first AI summer: irrational enthusiasm, 1948-1966
Success at early attempts in AI occurred in three primary locations: synthetic neural networks, knowledge representation, and heuristic search, adding to high expectations. This area summarizes Kautz’s reprise of early AI history.
Approaches inspired by human or animal cognition or behavior
Cybernetic techniques attempted to duplicate the feedback loops between animals and their environments. A robotic turtle, with sensors, motors for driving and steering, and seven vacuum tubes for control, based upon 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, support knowing, and located robotics. [20]
An important early symbolic AI program was the Logic theorist, written by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it was able to show 38 elementary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later generalized this work to develop a domain-independent issue solver, GPS (General Problem Solver). GPS fixed issues represented with formal operators by means of state-space search utilizing means-ends analysis. [21]
During the 1960s, symbolic approaches achieved great success at mimicing intelligent habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was concentrated in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Every one developed its own style of research. Earlier approaches based upon cybernetics or artificial neural networks were deserted or pressed into the background.
Herbert Simon and Allen Newell studied human problem-solving skills and attempted to formalize them, and their work laid the foundations of the field of artificial intelligence, as well as cognitive science, operations research study and management science. Their research group used the results of psychological experiments to establish programs that simulated the methods that individuals used to fix problems. [22] [23] This tradition, centered at Carnegie Mellon University would ultimately culminate in the development of the Soar architecture in the middle 1980s. [24] [25]
Heuristic search
In addition to the extremely specialized domain-specific type of understanding that we will see later utilized in specialist systems, early symbolic AI scientists discovered another more basic application of understanding. These were called heuristics, general rules that guide a search in promising directions: “How can non-enumerative search be practical when the underlying issue is significantly difficult? The method advocated by Simon and Newell is to employ heuristics: quick algorithms that might fail on some inputs or output suboptimal services.” [26] Another important advance was to find a way to apply these heuristics that ensures a service will be discovered, if there is one, not enduring the occasional fallibility of heuristics: “The A * algorithm provided a general frame for total and ideal heuristically guided search. A * is used as a subroutine within virtually every AI algorithm today however is still no magic bullet; its assurance of efficiency is purchased the cost of worst-case rapid time. [26]
Early deal with knowledge representation and reasoning
Early work covered both applications of formal reasoning emphasizing first-order logic, in addition to efforts to deal with sensible thinking in a less formal way.
Modeling official thinking with logic: the “neats”
Unlike Simon and Newell, John McCarthy felt that devices did not need to imitate the precise systems of human thought, but could instead search for the essence of abstract reasoning and problem-solving with logic, [27] despite whether individuals utilized the same algorithms. [a] His laboratory at Stanford (SAIL) focused on using formal reasoning to resolve a wide array of problems, including knowledge representation, preparation and knowing. [31] Logic was also the focus of the work at the University of Edinburgh and elsewhere in Europe which led to the advancement of the shows language Prolog and the science of reasoning 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 difficult problems in vision and natural language processing needed ad hoc solutions-they argued that no basic and basic principle (like reasoning) would capture all the aspects of intelligent habits. Roger Schank explained their “anti-logic” methods as “scruffy” (as opposed to the “cool” 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 must be built by hand, one complex concept 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 first AI summertime, many individuals believed that device intelligence could be accomplished in just a few years. The Defense Advance Research Projects Agency (DARPA) released programs to support AI research study to use AI to resolve issues of national security; in particular, to automate the translation of Russian to English for intelligence operations and to create self-governing tanks for the battlefield. Researchers had actually started to recognize that achieving AI was going to be much harder than was expected a years earlier, but a mix of hubris and disingenuousness led numerous university and think-tank scientists to accept funding with pledges of deliverables that they must have known they could not satisfy. By the mid-1960s neither beneficial natural language translation systems nor autonomous tanks had actually been created, and a remarkable reaction set in. New DARPA leadership canceled existing AI funding programs.
Beyond the United States, the most fertile ground for AI research was the UK. The AI winter in the UK was stimulated on not so much by disappointed military leaders as by competing academics who viewed AI scientists as charlatans and a drain on research funding. A professor of used 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 issues being dealt with in AI would be much better dealt with by researchers from other disciplines-such as used mathematics. The report likewise declared that AI successes on toy issues might never scale to real-world applications due to combinatorial surge. [41]
The second AI summertime: understanding is power, 1978-1987
Knowledge-based systems
As limitations with weak, domain-independent approaches ended up being more and more obvious, [42] scientists from all 3 customs started to construct understanding into AI applications. [43] [7] The knowledge revolution was driven by the realization that knowledge underlies high-performance, domain-specific AI applications.
Edward Feigenbaum stated:
– “In the knowledge lies the power.” [44]
to describe that high efficiency in a specific domain needs 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 carry out a complex job well, it should know a lot about the world in which it runs.
( 2) A possible extension of that principle, called the Breadth Hypothesis: there are two extra capabilities needed for smart habits in unanticipated circumstances: drawing on increasingly basic understanding, and analogizing to specific but remote knowledge. [45]
Success with expert systems
This “understanding transformation” caused the development and implementation of specialist systems (introduced by Edward Feigenbaum), the first commercially successful form of AI software application. [46] [47] [48]
Key specialist systems were:
DENDRAL, which found the structure of organic particles from their chemical formula and mass spectrometer readings.
MYCIN, which identified bacteremia – and recommended further lab tests, when essential – by translating laboratory outcomes, client history, and physician observations. “With about 450 rules, MYCIN had the ability to perform along with some experts, and significantly better than junior physicians.” [49] INTERNIST and CADUCEUS which took on internal medication diagnosis. Internist attempted to catch the competence of the chairman of internal medicine at the University of Pittsburgh School of Medicine while CADUCEUS might eventually identify approximately 1000 different diseases.
– GUIDON, which demonstrated how a knowledge base constructed for professional problem solving might be repurposed for mentor. [50] XCON, to set up VAX computer systems, a then tiresome procedure that might take up to 90 days. XCON minimized the time to about 90 minutes. [9]
DENDRAL is thought about the very first professional system that depend on knowledge-intensive analytical. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:
Among the people at Stanford interested in computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I wanted an induction “sandbox”, he stated, “I have just the one for you.” His laboratory was doing mass spectrometry of amino acids. The question 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 techniques, and he had an algorithm that was good at generating the chemical problem space.
We did not have a grand vision. We worked bottom up. Our chemist was Carl Djerassi, creator of the chemical behind the birth control pill, and also one of the world’s most appreciated mass spectrometrists. Carl and his postdocs were first-rate experts in mass spectrometry. We began to add to their knowledge, inventing knowledge of engineering as we went along. These experiments totaled up to titrating DENDRAL more and more knowledge. The more you did that, the smarter the program ended up being. We had excellent results.
The generalization was: in the knowledge lies the power. That was the big idea. In my career that is the huge, “Ah ha!,” and it wasn’t the way AI was being done formerly. Sounds basic, however it’s most likely AI’s most powerful generalization. [51]
The other expert systems discussed above followed DENDRAL. MYCIN exemplifies the timeless professional system architecture of a knowledge-base of rules coupled to a symbolic thinking mechanism, consisting of making use of certainty elements to handle unpredictability. GUIDON demonstrates how a specific understanding base can be repurposed for a second application, tutoring, and is an example of an intelligent tutoring system, a particular sort of knowledge-based application. Clancey showed that it was not adequate simply to utilize MYCIN’s guidelines for direction, but that he likewise needed to add guidelines for discussion management and student modeling. [50] XCON is significant due to the fact that of the countless dollars it saved DEC, which set off the expert system boom where most all significant corporations in the US had skilled systems groups, to catch corporate expertise, protect it, and automate it:
By 1988, DEC’s AI group had 40 professional systems released, with more en route. DuPont had 100 in use and 500 in development. Nearly every significant U.S. corporation had its own Al group and was either utilizing or examining professional systems. [49]
Chess professional knowledge was encoded in Deep Blue. In 1996, this allowed IBM’s Deep Blue, with the aid of symbolic AI, to win in a game of chess versus the world champ at that time, Garry Kasparov. [52]
Architecture of knowledge-based and skilled systems
A key part of the system architecture for all expert systems is the knowledge base, which shops truths and guidelines for problem-solving. [53] The simplest technique for a skilled system understanding base is just a collection or network of production guidelines. Production rules connect signs in a relationship similar to an If-Then statement. The professional system processes the guidelines to make deductions and to determine what additional info it needs, i.e. what questions to ask, using human-readable symbols. For example, OPS5, CLIPS and their followers 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 required data and prerequisites – manner. More sophisticated knowledge-based systems, such as Soar can likewise carry out meta-level reasoning, that is thinking about their own thinking in terms of choosing how to solve issues and keeping an eye on the success of problem-solving techniques.
Blackboard systems are a second type of knowledge-based or expert system architecture. They design a community of experts incrementally contributing, where they can, to solve an issue. The issue is represented in multiple levels of abstraction or alternate views. The specialists (understanding sources) offer their services whenever they recognize they can contribute. Potential problem-solving actions are represented on an agenda that is upgraded as the problem scenario changes. A controller decides how helpful each contribution is, and who must make the next problem-solving action. One example, the BB1 blackboard architecture [54] was originally inspired by studies of how people plan to carry out multiple tasks in a journey. [55] A development of BB1 was to apply the exact same blackboard design to fixing its control issue, i.e., its controller performed meta-level reasoning with understanding sources that kept track of how well a plan or the analytical was continuing and could change from one method to another as conditions – such as objectives or times – changed. BB1 has been applied in multiple domains: construction website preparation, intelligent tutoring systems, and real-time client monitoring.
The second AI winter, 1988-1993
At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were selling LISP devices particularly targeted to speed up the advancement 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 describes the 2nd AI winter that followed:
Many factors can be used for the arrival of the second AI winter. The hardware business failed when far more cost-efficient basic Unix workstations from Sun together with good compilers for LISP and Prolog came onto the market. Many business deployments of professional systems were discontinued when they proved too costly to preserve. Medical professional systems never caught on for several reasons: the problem in keeping them up to date; the obstacle for physician to learn how to utilize a bewildering variety of different expert systems for different medical conditions; and possibly most crucially, the reluctance of physicians to rely on a computer-made medical diagnosis over their gut instinct, even for particular domains where the expert systems might exceed a typical physician. Equity capital money deserted AI virtually overnight. The world AI conference IJCAI hosted a huge and luxurious exhibition and countless nonacademic attendees in 1987 in Vancouver; the main AI conference the following year, AAAI 1988 in St. Paul, was a little and strictly academic affair. [9]
Adding in more rigorous structures, 1993-2011
Uncertain thinking
Both analytical methods and extensions to reasoning were attempted.
One analytical method, concealed Markov designs, had currently been promoted in the 1980s for speech acknowledgment work. [11] Subsequently, in 1988, Judea Pearl promoted the use of Bayesian Networks as a sound however efficient way of handling uncertain reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian techniques were applied successfully in specialist systems. [57] Even later, in the 1990s, statistical relational knowing, a technique that combines possibility with logical solutions, allowed likelihood to be integrated with first-order logic, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.
Other, non-probabilistic extensions to first-order reasoning to assistance were likewise tried. For instance, non-monotonic thinking could be utilized with truth upkeep systems. A truth maintenance system tracked assumptions and justifications for all reasonings. It permitted reasonings to be withdrawn when assumptions were found out to be incorrect or a contradiction was obtained. Explanations might be offered for an inference by describing which guidelines were used to produce it and after that continuing through underlying inferences and guidelines all the method back to root presumptions. [58] Lofti Zadeh had introduced a various sort of extension to handle the representation of ambiguity. For instance, in choosing how “heavy” or “tall” a guy is, there is frequently no clear “yes” or “no” answer, and a predicate for heavy or high would rather return values between 0 and 1. Those values represented to what degree the predicates held true. His fuzzy reasoning further offered a method for propagating combinations of these values through sensible formulas. [59]
Artificial intelligence
Symbolic machine learning approaches were investigated to attend to the understanding acquisition traffic jam. Among the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test technique to generate plausible guideline hypotheses to evaluate versus spectra. Domain and task understanding lowered the variety of prospects checked to a workable size. Feigenbaum described Meta-DENDRAL as
… the culmination of my dream of the early to mid-1960s relating to theory development. The conception was that you had a problem solver like DENDRAL that took some inputs and produced an output. In doing so, it utilized layers of knowledge to steer and prune the search. That understanding got in there due to the fact that we talked to people. But how did the people get the knowledge? By taking a look at countless spectra. So we desired a program that would look at thousands of spectra and presume the knowledge of mass spectrometry that DENDRAL could use to solve private hypothesis formation problems. We did it. We were even able to publish new knowledge of mass spectrometry in the Journal of the American Chemical Society, offering credit just in a footnote that a program, Meta-DENDRAL, really did it. We were able to do something that had been a dream: to have a computer program created a new and publishable piece of science. [51]
In contrast to the knowledge-intensive approach of Meta-DENDRAL, Ross Quinlan invented a domain-independent approach to statistical classification, decision tree knowing, beginning first with ID3 [60] and after that later extending its capabilities to C4.5. [61] The decision trees created are glass box, interpretable classifiers, with human-interpretable category rules.
Advances were made in comprehending device learning theory, too. Tom Mitchell presented variation area learning which explains knowing as an explore a space of hypotheses, with upper, more basic, and lower, more specific, borders encompassing all feasible 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 device knowing. [63]
Symbolic device learning encompassed more than finding out by example. E.g., John Anderson offered a cognitive model of human learning where ability practice leads to a collection of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a student may discover to use “Supplementary angles are two angles whose procedures sum 180 degrees” as numerous different procedural rules. E.g., one guideline may say that if X and Y are supplementary and you understand X, then Y will be 180 – X. He called his method “knowledge compilation”. ACT-R has been used effectively to model aspects of human cognition, such as learning and retention. ACT-R is likewise utilized in smart tutoring systems, called cognitive tutors, to successfully teach geometry, computer system shows, and algebra to school children. [64]
Inductive reasoning programming was another method to learning that permitted reasoning programs to be synthesized from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) might synthesize Prolog programs from examples. [65] John R. Koza used hereditary algorithms to program synthesis to create hereditary programming, which he used to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger provided a more general approach to program synthesis that synthesizes a practical program in the course of proving its specifications to be right. [66]
As an alternative to logic, Roger Schank presented case-based reasoning (CBR). The CBR technique detailed in his book, Dynamic Memory, [67] focuses initially on keeping in mind crucial analytical cases for future use and generalizing them where suitable. When faced with a brand-new issue, CBR recovers the most similar previous case and adapts it to the specifics of the current problem. [68] Another alternative to reasoning, genetic algorithms and hereditary programming are based upon an evolutionary design of learning, where sets of rules are encoded into populations, the guidelines govern the habits of people, and selection of the fittest prunes out sets of inappropriate guidelines over lots of generations. [69]
Symbolic artificial intelligence was used to finding out principles, guidelines, heuristics, and analytical. Approaches, other than those above, consist of:
1. Learning from instruction or advice-i.e., taking human guideline, presented as advice, and determining how to operationalize it in specific situations. For instance, in a video game of Hearts, finding out precisely how to play a hand to “prevent taking points.” [70] 2. Learning from exemplars-improving efficiency by accepting subject-matter professional (SME) feedback during training. When problem-solving stops working, querying the specialist to either discover a brand-new prototype for problem-solving or to discover a new explanation regarding precisely why one prototype is more relevant than another. For example, the program Protos found out to detect tinnitus cases by engaging with an audiologist. [71] 3. Learning by analogy-constructing issue solutions based upon similar issues seen in the past, and after that customizing their solutions to fit a new situation or domain. [72] [73] 4. Apprentice learning systems-learning novel options to problems by observing human problem-solving. Domain understanding describes why novel services are right and how the solution can be generalized. LEAP discovered how to design VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., creating jobs to carry out experiments and after that discovering from the results. Doug Lenat’s Eurisko, for instance, learned heuristics to beat human players at the Traveller role-playing video game for two years in a row. [75] 6. Learning macro-operators-i.e., looking for useful macro-operators to be found out from series of standard analytical actions. Good macro-operators streamline problem-solving by permitting issues to be resolved at a more abstract level. [76]
Deep knowing and neuro-symbolic AI 2011-now
With the rise of deep knowing, the symbolic AI approach has been compared to deep learning as complementary “… with parallels having actually been drawn numerous times by AI researchers in between Kahneman’s research study on human reasoning and decision making – shown in his book Thinking, Fast and Slow – and the so-called “AI systems 1 and 2″, which would in concept be designed by deep knowing and symbolic reasoning, respectively.” In this view, symbolic thinking is more apt for deliberative thinking, planning, and description while deep knowing is more apt for quick pattern acknowledgment in affective applications with loud data. [17] [18]
Neuro-symbolic AI: incorporating neural and symbolic approaches
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 efficient in thinking, finding out, and cognitive modeling. As argued by Valiant [77] and many others, [78] the effective building of abundant computational cognitive designs requires the mix of sound symbolic reasoning and effective (machine) knowing designs. Gary Marcus, likewise, argues that: “We can not construct rich cognitive designs in a sufficient, automated way without the set of three of hybrid architecture, rich anticipation, and advanced strategies for thinking.”, [79] and in particular: “To construct a robust, knowledge-driven method 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 know of that can manipulate such abstract knowledge reliably is the device of sign manipulation. ” [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 sort of thinking gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having two elements, System 1 and System 2. System 1 is quick, automated, instinctive and unconscious. System 2 is slower, detailed, and specific. System 1 is the kind used for pattern acknowledgment while System 2 is far much better fit for planning, reduction, and deliberative thinking. In this view, deep knowing best designs the very first kind of thinking while symbolic reasoning finest designs the second kind and both are required.
Garcez and Lamb explain research in this location as being continuous for a minimum of the past twenty years, [83] dating from their 2002 book on neurosymbolic knowing systems. [84] A series of workshops on neuro-symbolic thinking has been held every year because 2005, see http://www.neural-symbolic.org/ for details.
In their 2015 paper, Neural-Symbolic Learning and Reasoning: Contributions and Challenges, Garcez et al. argue that:
The integration of the symbolic and connectionist paradigms of AI has actually been pursued by a fairly little research community over the last 20 years and has yielded numerous significant results. Over the last decade, neural symbolic systems have been shown capable of getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in reaction to Smolensky (1988 ); see likewise (Hinton, 1990). Neural networks were shown 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 applied to a variety of issues in the areas of bioinformatics, control engineering, software application confirmation and adjustment, visual intelligence, ontology knowing, and computer system games. [78]
Approaches for integration are varied. Henry Kautz’s taxonomy of neuro-symbolic architectures, in addition to some examples, follows:
– Symbolic Neural symbolic-is the present technique of lots of neural models in natural language processing, where words or subword tokens are both the supreme input and output of large language designs. Examples consist of BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic strategies are utilized to call neural methods. In this case the symbolic technique is Monte Carlo tree search and the neural strategies find out how to evaluate game positions.
– Neural|Symbolic-uses a neural architecture to translate perceptual data as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to produce or identify training information that is consequently found out by a deep learning design, e.g., to train a neural model for symbolic calculation by utilizing a Macsyma-like symbolic mathematics system to create or identify examples.
– Neural _ Symbolic -uses a neural internet 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 knowledge base rules and terms. Logic Tensor Networks [86] also fall into this category.
– Neural [Symbolic] -allows a neural design 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 method to integrate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and drawn out from them?
– How should sensible understanding be discovered and reasoned about?
– How can abstract understanding that is hard to encode rationally be handled?
Techniques and contributions
This section supplies an overview of strategies and contributions in an overall context leading to many other, more in-depth posts in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered earlier in the history area.
AI programs languages
The key AI shows language in the US during the last symbolic AI boom duration was LISP. LISP is the second oldest shows language after FORTRAN and was created in 1958 by John McCarthy. LISP supplied the first read-eval-print loop to support fast program development. Compiled functions might be freely combined with analyzed functions. Program tracing, stepping, and breakpoints were likewise offered, together with the capability to alter values or functions and continue from breakpoints or errors. It had the first self-hosting compiler, suggesting that the compiler itself was originally composed in LISP and then ran interpretively to put together the compiler code.
Other essential innovations pioneered by LISP that have spread to other programming languages include:
Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals
Programs were themselves information structures that other programs might operate on, permitting the easy meaning of higher-level languages.
In contrast to the US, in Europe the crucial AI programming language during that same duration was Prolog. Prolog offered an integrated shop of facts and stipulations that could be queried by a read-eval-print loop. The shop might serve as an understanding base and the clauses might function as guidelines or a limited type of logic. As a subset of first-order reasoning Prolog was based on Horn clauses with a closed-world assumption-any realities not understood were considered false-and a distinct name assumption for primitive terms-e.g., the identifier barack_obama was thought about to refer to precisely one object. Backtracking and marriage are built-in to Prolog.
Alain Colmerauer and Philippe Roussel are credited as the creators of Prolog. Prolog is a kind of reasoning shows, which was invented by Robert Kowalski. Its history was likewise influenced by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of approaches. For more information see the section on the origins of Prolog in the PLANNER post.
Prolog is also a kind of declarative shows. The logic clauses that explain programs are straight interpreted to run the programs defined. No explicit series of actions is required, as is the case with vital programs languages.
Japan promoted Prolog for its Fifth Generation Project, intending to build special hardware for high performance. Similarly, LISP makers were built to run LISP, however as the second AI boom turned to bust these companies might not take on brand-new workstations that might now run LISP or Prolog natively at equivalent speeds. See the history section for more information.
Smalltalk was another influential AI shows language. For instance, it presented metaclasses and, along with Flavors and CommonLoops, affected the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the current standard Lisp dialect. CLOS is a Lisp-based object-oriented system that permits 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 programming languages for expert system. Currently, Python, a multi-paradigm shows language, is the most popular programming language, partially due to its substantial package library that supports information science, natural language processing, and deep learning. Python consists of a read-eval-print loop, practical elements such as higher-order functions, and object-oriented programming that consists of metaclasses.
Search
Search arises in lots of type of problem resolving, including preparation, restriction fulfillment, and playing video games such as checkers, chess, and go. The finest understood AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven clause learning, 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 knowledge and after that factor with those representations have actually been investigated. Below is a fast introduction of techniques to understanding representation and automated thinking.
Knowledge representation
Semantic networks, conceptual graphs, frames, and reasoning are all methods to modeling understanding such as domain understanding, analytical understanding, 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 utilized for any domain while WordNet is a lexical resource that can likewise be considered as an ontology. YAGO incorporates WordNet as part of its ontology, to align truths extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being utilized.
Description logic is a logic for automated classification of ontologies and for detecting inconsistent category information. OWL is a language utilized to represent ontologies with description reasoning. Protégé is an ontology editor that can check out in OWL ontologies and after that inspect consistency with deductive classifiers such as such as HermiT. [89]
First-order logic is more general than description reasoning. The automated theorem provers gone over listed below can prove theorems in first-order reasoning. Horn clause reasoning is more limited than first-order logic and is used in logic programs languages such as Prolog. Extensions to first-order reasoning consist of temporal logic, to handle time; epistemic reasoning, to factor about agent knowledge; modal reasoning, to deal with possibility and need; and probabilistic reasonings to handle logic and likelihood together.
Automatic theorem proving
Examples of automated theorem provers for first-order reasoning are:
Prover9.
ACL2.
Vampire.
Prover9 can be utilized in combination with the Mace4 design checker. ACL2 is a theorem prover that can manage proofs by induction and is a descendant of the Boyer-Moore Theorem Prover, likewise referred to as Nqthm.
Reasoning in knowledge-based systems
Knowledge-based systems have an explicit understanding base, normally of guidelines, to enhance reusability across domains by separating procedural code and domain knowledge. A different inference engine procedures rules and adds, deletes, or customizes an understanding store.
Forward chaining inference engines are the most common, and are seen in CLIPS and OPS5. Backward chaining takes place in Prolog, where a more minimal rational representation is utilized, Horn Clauses. Pattern-matching, specifically marriage, is used in Prolog.
A more flexible sort of problem-solving happens when thinking about what to do next takes place, instead of simply selecting among the available actions. This type of meta-level thinking is utilized in Soar and in the BB1 chalkboard architecture.
Cognitive architectures such as ACT-R may have extra capabilities, such as the capability to compile regularly used knowledge into higher-level chunks.
Commonsense reasoning
Marvin Minsky first proposed frames as a way of interpreting typical visual scenarios, such as an office, and Roger Schank extended this concept to scripts for common routines, such as eating in restaurants. Cyc has attempted to capture useful sensible understanding and has “micro-theories” to handle particular sort of domain-specific reasoning.
Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] estimates human reasoning about ignorant physics, such as what happens when we heat a liquid in a pot on the stove. We anticipate it to heat and possibly boil over, even though we may not know 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 reasoning about spatial relationships. Both can be solved with constraint solvers.
Constraints and constraint-based thinking
Constraint solvers perform a more restricted type of inference than first-order reasoning. They can simplify sets of spatiotemporal constraints, such as those for RCC or Temporal Algebra, along with solving other type of puzzle problems, such as Wordle, Sudoku, cryptarithmetic issues, and so on. Constraint logic programming can be used to fix scheduling problems, for instance with restraint handling rules (CHR).
Automated preparation
The General Problem Solver (GPS) cast planning as problem-solving used means-ends analysis to create plans. STRIPS took a different method, seeing planning as theorem proving. Graphplan takes a least-commitment technique to planning, rather than sequentially picking actions from a preliminary state, working forwards, or an objective state if working in reverse. Satplan is a method to preparing where a preparation issue is lowered to a Boolean satisfiability problem.
Natural language processing
Natural language processing focuses on treating language as data to perform jobs such as identifying subjects without necessarily comprehending the intended significance. Natural language understanding, on the other hand, constructs a meaning representation and uses that for further processing, such as answering 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, but since enhanced by deep learning methods. In symbolic AI, discourse representation theory and first-order logic have been used to represent sentence significances. Latent semantic analysis (LSA) and explicit semantic analysis likewise provided vector representations of documents. In the latter case, vector elements are interpretable as principles called by Wikipedia articles.
New deep knowing methods based upon Transformer designs have actually now eclipsed these earlier symbolic AI approaches 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 documents. Instead, they produce task-specific vectors where the significance of the vector components 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 book on expert system is organized to reflect agent architectures of increasing elegance. [91] The sophistication of agents varies from basic reactive agents, to those with a design of the world and automated preparation capabilities, possibly a BDI agent, i.e., one with beliefs, desires, and intents – or additionally a reinforcement finding out model learned in time to pick actions – approximately a mix of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep learning for understanding. [92]
In contrast, a multi-agent system consists of several representatives that communicate amongst themselves with some inter-agent interaction language such as Knowledge Query and Manipulation Language (KQML). The agents need not all have the same internal architecture. Advantages of multi-agent systems include the capability to divide work amongst the representatives and to increase fault tolerance when agents are lost. Research issues include how representatives reach agreement, dispersed issue resolving, multi-agent learning, multi-agent planning, and dispersed restriction optimization.
Controversies arose from at an early stage in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and between those who accepted AI but rejected symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were mostly from philosophers, on intellectual premises, however also from funding firms, specifically during the two AI winter seasons.
The Frame Problem: understanding representation challenges for first-order reasoning
Limitations were found in using simple first-order logic to factor about vibrant domains. Problems were found both with regards to mentioning the prerequisites for an action to be successful and in supplying 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 simple example takes place in “showing that a person person could enter into conversation with another”, as an axiom asserting “if an individual has a telephone he still has it after looking up a number in the telephone directory” would be required for the reduction to be successful. Similar axioms would be needed for other domain actions to specify what did not change.
A comparable problem, called the Qualification Problem, occurs in trying to enumerate the preconditions for an action to succeed. An infinite variety of pathological conditions can be thought of, e.g., a banana in a tailpipe could prevent a cars and truck from running correctly.
McCarthy’s method to repair the frame problem was circumscription, a kind of non-monotonic reasoning where deductions could be made from actions that require just specify what would alter while not needing to clearly specify whatever that would not alter. Other non-monotonic logics offered fact maintenance systems that modified beliefs resulting in contradictions.
Other methods of handling more open-ended domains included probabilistic thinking systems and artificial intelligence to find out brand-new ideas and guidelines. McCarthy’s Advice Taker can be considered as an inspiration here, as it might include new understanding offered by a human in the form of assertions or rules. For instance, speculative symbolic device learning systems checked out the ability to take top-level natural language recommendations and to translate it into domain-specific actionable guidelines.
Similar to the issues in dealing with dynamic domains, sensible thinking is also difficult to catch in official reasoning. Examples of common-sense thinking include implicit thinking about how people believe or general knowledge of everyday events, things, and living animals. This sort of knowledge is taken for granted and not considered as noteworthy. Common-sense thinking is an open area of research and challenging both for symbolic systems (e.g., Cyc has attempted to record crucial parts of this understanding over more than a years) and neural systems (e.g., self-driving cars and trucks that do not know not to drive into cones or not to strike pedestrians strolling a bicycle).
McCarthy viewed his Advice Taker as having common-sense, however his meaning of common-sense was different than the one above. [94] He defined a program as having typical sense “if it automatically deduces for itself an adequately wide class of immediate effects of anything it is told and what it already knows. “
Connectionist AI: philosophical difficulties and sociological conflicts
Connectionist approaches consist of earlier deal with neural networks, [95] such as perceptrons; work in the mid to late 80s, such as Danny Hillis’s Connection Machine and Yann LeCun’s advances in convolutional neural networks; to today’s more advanced approaches, such as Transformers, GANs, and other operate in deep knowing.
Three philosophical positions [96] have actually been outlined amongst connectionists:
1. Implementationism-where connectionist architectures implement the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected totally, and connectionist architectures underlie intelligence and are fully enough to describe it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are seen as complementary and both are needed for intelligence
Olazaran, in his sociological history of the debates within the neural network community, explained the moderate connectionism view as essentially suitable with current research study in neuro-symbolic hybrids:
The 3rd and last position I want to examine here is what I call the moderate connectionist view, a more diverse view of the present dispute in between connectionism and symbolic AI. Among the researchers who has actually elaborated this position most clearly is Andy Clark, a philosopher from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark protected hybrid (partly symbolic, partly connectionist) systems. He claimed 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 acknowledgment) connectionism has benefits over symbolic models. But on the other hand, for other cognitive procedures (such as serial, deductive thinking, and generative sign adjustment processes) the symbolic paradigm offers appropriate models, and not just “approximations” (contrary to what extreme connectionists would declare). [97]
Gary Marcus has declared that the animus in the deep learning neighborhood versus symbolic approaches now might be more sociological than philosophical:
To think that we can merely abandon symbol-manipulation is to suspend disbelief.
And yet, for the most part, that’s how most present AI proceeds. Hinton and numerous others have actually attempted tough to banish signs altogether. The deep learning hope-seemingly grounded not a lot in science, but in a sort of historical grudge-is that smart behavior will emerge simply from the confluence of huge information and deep knowing. Where classical computer systems and software application fix jobs by specifying sets of symbol-manipulating guidelines devoted to specific tasks, such as editing a line in a word processor or carrying out a calculation in a spreadsheet, neural networks normally attempt to solve tasks by statistical approximation and finding out from examples.
According to Marcus, Geoffrey Hinton and his associates have been vehemently “anti-symbolic”:
When deep learning reemerged in 2012, it was with a kind of take-no-prisoners attitude that has actually defined the majority of the last years. By 2015, his hostility toward all things signs had actually totally crystallized. He lectured at an AI workshop at Stanford comparing symbols to aether, one of science’s greatest errors.
…
Ever since, his anti-symbolic project has just increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep knowing in among science’s crucial journals, Nature. It closed with a direct attack on sign manipulation, calling not for reconciliation however for outright replacement. Later, Hinton informed a gathering of European Union leaders that investing any more cash in symbol-manipulating methods was “a substantial mistake,” likening it to investing in internal combustion engines in the period of electric vehicles. [98]
Part of these disagreements may be because of unclear terms:
Turing award winner Judea Pearl offers a critique of artificial intelligence which, unfortunately, conflates the terms machine learning and deep learning. Similarly, when Geoffrey Hinton describes symbolic AI, the connotation of the term tends to be that of specialist systems dispossessed of any capability to learn. The use of the terminology needs information. Machine knowing is not restricted to association guideline mining, c.f. the body of work on symbolic ML and relational learning (the differences to deep knowing being the option of representation, localist rational rather than dispersed, and the non-use of gradient-based knowing algorithms). Equally, symbolic AI is not almost production guidelines composed by hand. A correct definition of AI concerns knowledge representation and reasoning, autonomous multi-agent systems, planning and argumentation, in addition to learning. [99]
Situated robotics: the world as a model
Another review of symbolic AI is the embodied cognition technique:
The embodied cognition approach declares that it makes no sense to consider the brain individually: cognition takes place 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, consisting of the rest of its body. Under the embodied cognition method, robotics, vision, and other sensing units become central, not peripheral. [100]
Rodney Brooks invented behavior-based robotics, one approach to embodied cognition. Nouvelle AI, another name for this approach, is deemed an alternative to both symbolic AI and connectionist AI. His approach declined representations, either symbolic or dispersed, as not only unnecessary, however as detrimental. Instead, he produced the subsumption architecture, a layered architecture for embodied agents. Each layer achieves a different function and must function in the real life. For example, the very first robotic he describes in Intelligence Without Representation, has three layers. The bottom layer translates sonar sensing units to prevent items. The middle layer triggers the robotic to wander around when there are no barriers. The top layer causes the robotic to go to more remote places for further exploration. Each layer can temporarily hinder or suppress a lower-level layer. He criticized AI scientists for defining AI problems for their systems, when: “There is no tidy division between understanding (abstraction) and reasoning in the real life.” [101] He called his robotics “Creatures” and each layer was “made up of a fixed-topology network of basic finite state devices.” [102] In the Nouvelle AI approach, “First, it is critically important to evaluate the Creatures we integrate in the real life; i.e., in the same world that we people populate. It is disastrous to fall into the temptation of checking them in a simplified world initially, even with the best objectives of later transferring activity to an unsimplified world.” [103] His focus on real-world screening was in contrast to “Early operate in AI concentrated on video games, geometrical problems, symbolic algebra, theorem proving, and other official systems” [104] and using the blocks world in symbolic AI systems such as SHRDLU.
Current views
Each approach-symbolic, connectionist, and behavior-based-has advantages, however has actually been criticized by the other techniques. Symbolic AI has been slammed as disembodied, accountable to the credentials problem, and bad in dealing with the affective problems where deep learning excels. In turn, connectionist AI has been slammed as inadequately matched for deliberative detailed issue solving, including understanding, and dealing with preparation. Finally, Nouvelle AI excels in reactive and real-world robotics domains but has been criticized for troubles in integrating knowing and knowledge.
Hybrid AIs including one or more of these techniques are currently seen as the path forward. [19] [81] [82] Russell and Norvig conclude that:
Overall, Dreyfus saw locations where AI did not have total responses and said that Al is for that reason impossible; we now see a number of these same locations going through ongoing research and advancement leading to increased ability, not impossibility. [100]
Expert system.
Automated planning and scheduling
Automated theorem proving
Belief revision
Case-based reasoning
Cognitive architecture
Cognitive science
Connectionism
Constraint shows
Deep knowing
First-order reasoning
GOFAI
History of expert system
Inductive logic programs
Knowledge-based systems
Knowledge representation and thinking
Logic shows
Machine learning
Model monitoring
Model-based thinking
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of expert system
Physical symbol systems hypothesis
Semantic Web
Sequential pattern mining
Statistical relational 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 reiterated 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 writes that there are “2 significant branches of expert system: one focused on producing intelligent behavior despite how it was accomplished, and the other intended at modeling intelligent procedures 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 ‘devices that fly so exactly like pigeons that they can deceive even other pigeons.'” [30] Citations
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^ 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 expert system: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating mistakes”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
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^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. “Thinking Fast and Slow in AI“. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. “AAAI Presidential Address: The State of AI”. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
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^ Russell & Norvig 2021, pp. 22-24.
^ McCorduck 2004, pp. 327-335, 434-435.
^ Crevier 1993, pp. 145-62, 197-203.
^ a b Russell & Norvig 2021, p. 23.
^ a b Clancey 1987.
^ a b Shustek, Len (2010 ). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-08-05.
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