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Symbolic Expert System

In artificial intelligence, symbolic expert system (likewise referred to as classical expert system or logic-based synthetic intelligence) [1] [2] is the term for the collection of all approaches in expert system research study that are based on high-level symbolic (human-readable) representations of problems, reasoning and search. [3] Symbolic AI utilized tools such as reasoning programs, production rules, semantic nets and frames, and it developed applications such as knowledge-based systems (in specific, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm caused seminal concepts in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and restrictions of official understanding and thinking systems.

Symbolic AI was the dominant paradigm of AI research study from the mid-1950s up until the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic methods would ultimately prosper in creating a device with synthetic general 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 pledges and was followed by the very first AI Winter as funding dried up. [5] [6] A 2nd boom (1969-1986) accompanied the increase of specialist systems, their pledge of recording corporate competence, and a passionate corporate welcome. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later dissatisfaction. [8] Problems with difficulties in knowledge acquisition, keeping big knowledge bases, and brittleness in dealing with out-of-domain issues arose. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists concentrated on addressing hidden problems in dealing with unpredictability and in understanding acquisition. [10] Uncertainty was resolved with formal methods such as hidden Markov designs, Bayesian reasoning, and analytical relational learning. [11] [12] Symbolic machine finding out addressed the understanding acquisition problem with contributions including Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree learning, case-based learning, and inductive reasoning shows 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 learning work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and operate in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not deemed effective till about 2012: “Until Big Data ended up being commonplace, the general agreement in the Al community was that the so-called neural-network approach was helpless. Systems simply didn’t work that well, compared to other methods. … A transformation came in 2012, when a number of people, including a team of researchers dealing with Hinton, worked out a method to use the power of GPUs to immensely increase the power of neural networks.” [16] Over the next numerous years, deep learning had magnificent success in managing vision, speech acknowledgment, speech synthesis, image generation, and device translation. However, because 2020, as fundamental problems with bias, description, comprehensibility, and robustness ended up being more obvious with deep learning methods; an increasing number of AI scientists have required combining the very best of both the symbolic and neural network approaches [17] [18] and dealing with areas that both approaches have problem with, such as common-sense thinking. [16]

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

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

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

Approaches motivated by human or animal cognition or behavior

Cybernetic approaches attempted to replicate the feedback loops between animals and their environments. A robotic turtle, with sensors, motors for driving and steering, and 7 vacuum tubes for control, based upon a preprogrammed neural web, was built as early as 1948. This work can be viewed as an early precursor to later work in neural networks, reinforcement learning, and positioned robotics. [20]

A crucial early symbolic AI program was the Logic theorist, composed by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it had the ability to show 38 primary 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 resolved issues represented with official operators via state-space search utilizing means-ends analysis. [21]

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

Herbert Simon and Allen Newell studied human analytical abilities and attempted to formalize them, and their work laid the structures of the field of expert system, along with cognitive science, operations research study and management science. Their research study team utilized the outcomes of psychological experiments to develop programs that simulated the methods that people used to resolve issues. [22] [23] This tradition, centered at Carnegie Mellon University would ultimately culminate in the advancement of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific sort of knowledge that we will see later on utilized in professional systems, early symbolic AI researchers found another more basic application of knowledge. These were called heuristics, guidelines of thumb that assist a search in appealing directions: “How can non-enumerative search be practical when the underlying problem is exponentially difficult? The technique promoted by Simon and Newell is to utilize heuristics: fast algorithms that may fail on some inputs or output suboptimal options.” [26] Another essential advance was to discover a method to use these heuristics that guarantees an option will be discovered, if there is one, not enduring the occasional fallibility of heuristics: “The A * algorithm provided a basic frame for complete and optimal heuristically assisted search. A * is used as a subroutine within virtually every AI algorithm today however is still no magic bullet; its warranty of efficiency is bought at the cost of worst-case rapid time. [26]

Early deal with knowledge representation and reasoning

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

Modeling formal reasoning with reasoning: the “neats”

Unlike Simon and Newell, John McCarthy felt that makers did not require to simulate the exact mechanisms of human thought, but might instead look for the essence of abstract reasoning and analytical with reasoning, [27] no matter whether people used the same algorithms. [a] His laboratory at Stanford (SAIL) concentrated on utilizing formal reasoning to resolve a broad range of issues, consisting of understanding representation, planning and learning. [31] Logic was also the focus of the work at the University of Edinburgh and elsewhere in Europe which caused the advancement of the shows language Prolog and the science of reasoning shows. [32] [33]

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

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that resolving difficult issues in vision and natural language processing needed ad hoc solutions-they argued that no easy and basic concept (like logic) would catch all the aspects of smart habits. Roger Schank described their “anti-logic” methods as “shabby” (instead of the “cool” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “shabby” AI, since 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 summer, lots of people believed that machine intelligence could be attained in simply a few years. The Defense Advance Research Projects Agency (DARPA) introduced programs to support AI research study to utilize AI to solve problems of national security; in specific, to automate the translation of Russian to English for intelligence operations and to produce autonomous tanks for the battleground. Researchers had started to realize that attaining AI was going to be much harder than was expected a years earlier, but a combination of hubris and disingenuousness led many university and think-tank scientists to accept funding with promises of deliverables that they should have known they might not meet. By the mid-1960s neither beneficial natural language translation systems nor self-governing tanks had been developed, and a dramatic backlash set in. New DARPA leadership canceled existing AI financing 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 a lot by dissatisfied military leaders as by competing academics who saw AI scientists as charlatans and a drain on research financing. A teacher of applied mathematics, Sir James Lighthill, was commissioned by Parliament to assess the state of AI research study in the country. The report specified that all of the issues being worked on in AI would be much better dealt with by scientists from other disciplines-such as used mathematics. The report also declared that AI successes on toy problems could never scale to real-world applications due to combinatorial explosion. [41]

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

Knowledge-based systems

As constraints with weak, domain-independent techniques became increasingly more obvious, [42] scientists from all 3 traditions started to build knowledge into AI applications. [43] [7] The understanding revolution was driven by the awareness that understanding underlies high-performance, domain-specific AI applications.

Edward Feigenbaum said:

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

( 1) The Knowledge Principle: if a program is to carry out a complicated task well, it must understand a terrific deal about the world in which it operates.
( 2) A possible extension of that concept, called the Breadth Hypothesis: there are 2 extra abilities required for smart behavior in unforeseen circumstances: falling back on progressively general knowledge, and analogizing to specific however far-flung knowledge. [45]

Success with professional systems

This “knowledge transformation” resulted in the development and release of professional systems (introduced by Edward Feigenbaum), the first commercially successful type of AI software. [46] [47] [48]

Key professional systems were:

DENDRAL, which discovered the structure of natural molecules from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and recommended further laboratory tests, when needed – by analyzing lab results, client history, and physician observations. “With about 450 guidelines, MYCIN had the ability to carry out as well as some specialists, and significantly much better than junior medical professionals.” [49] INTERNIST and CADUCEUS which took on internal medicine diagnosis. Internist attempted to capture the know-how of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS could ultimately identify as much as 1000 different diseases.
– GUIDON, which showed how an understanding base built for specialist issue fixing might be repurposed for mentor. [50] XCON, to set up VAX computers, a then tiresome process that could take up to 90 days. XCON decreased the time to about 90 minutes. [9]
DENDRAL is considered the first specialist 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:

Among the people at Stanford interested in computer-based models of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genetics. When I told him I desired an induction “sandbox”, he stated, “I have just the one for you.” His lab 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 excellent at creating the chemical problem area.

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

The generalization was: in the knowledge lies the power. That was the big idea. In my career that is the substantial, “Ah ha!,” and it wasn’t the way AI was being done previously. Sounds easy, but it’s most likely AI’s most powerful generalization. [51]

The other professional systems mentioned above followed DENDRAL. MYCIN exhibits the traditional professional system architecture of a knowledge-base of guidelines combined to a symbolic reasoning mechanism, including using certainty aspects to manage uncertainty. GUIDON reveals how an explicit understanding base can be repurposed for a 2nd application, tutoring, and is an example of an intelligent tutoring system, a specific kind of knowledge-based application. Clancey revealed that it was not enough just to utilize MYCIN’s rules for direction, but that he also required to add rules for discussion management and student modeling. [50] XCON is considerable since of the countless dollars it saved DEC, which triggered the specialist system boom where most all significant corporations in the US had professional systems groups, to capture corporate knowledge, preserve it, and automate it:

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

Chess expert 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 against the world champ at that time, Garry Kasparov. [52]

Architecture of knowledge-based and professional systems

A crucial component of the system architecture for all professional systems is the knowledge base, which shops facts and guidelines for problem-solving. [53] The most basic method for an expert system understanding base is just a collection or network of production guidelines. Production guidelines link signs in a relationship similar to an If-Then declaration. The expert system processes the rules to make reductions and to identify what additional info it needs, i.e. what concerns to ask, using human-readable signs. For instance, OPS5, CLIPS and their successors Jess and Drools run in this fashion.

Expert systems can operate in either a forward chaining – from proof to conclusions – or backwards chaining – from goals to needed data and prerequisites – way. Advanced knowledge-based systems, such as Soar can likewise perform meta-level reasoning, that is thinking about their own thinking in regards to choosing how to fix problems and keeping track of the success of analytical techniques.

Blackboard systems are a 2nd type of knowledge-based or professional system architecture. They design a community of professionals incrementally contributing, where they can, to solve an issue. The issue is represented in several levels of abstraction or alternate views. The experts (knowledge sources) offer their services whenever they recognize they can contribute. Potential analytical actions are represented on a program that is upgraded as the problem circumstance changes. A controller chooses how beneficial each contribution is, and who need to make the next analytical action. One example, the BB1 chalkboard architecture [54] was originally motivated by research studies of how humans plan to perform multiple jobs in a journey. [55] A development of BB1 was to use the same blackboard model to resolving its control problem, i.e., its controller performed meta-level thinking with knowledge sources that kept an eye on how well a strategy or the analytical was proceeding and might switch from one technique to another as conditions – such as goals or times – altered. BB1 has been applied in numerous domains: building and construction website planning, intelligent tutoring systems, and real-time patient tracking.

The second AI winter, 1988-1993

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

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

Many reasons can be offered for the arrival of the second AI winter. The hardware companies stopped working when much more cost-efficient general Unix workstations from Sun together with good compilers for LISP and Prolog came onto the marketplace. Many industrial implementations of professional systems were discontinued when they proved too costly to keep. Medical professional systems never ever captured on for numerous factors: the problem in keeping them approximately date; the challenge for medical specialists to discover how to use an overwelming variety of various expert systems for different medical conditions; and maybe most crucially, the hesitation of doctors to trust a computer-made diagnosis over their gut instinct, even for particular domains where the professional systems might exceed a typical medical professional. Equity capital cash deserted AI almost overnight. The world AI conference IJCAI hosted a huge and lavish trade show and thousands of nonacademic participants in 1987 in Vancouver; the main AI conference the following year, AAAI 1988 in St. Paul, was a small and strictly scholastic affair. [9]

Including more strenuous foundations, 1993-2011

Uncertain reasoning

Both statistical techniques and extensions to logic were tried.

One analytical approach, 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 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 expert systems. [57] Even later on, in the 1990s, statistical relational knowing, a method that integrates likelihood with sensible solutions, permitted possibility to be integrated with first-order reasoning, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order reasoning to assistance were likewise attempted. For instance, non-monotonic reasoning might be utilized with truth maintenance systems. A truth upkeep system tracked assumptions and justifications for all reasonings. It permitted inferences to be withdrawn when presumptions were discovered to be inaccurate or a contradiction was derived. Explanations might be provided for an inference by discussing which rules were applied to produce it and after that continuing through underlying inferences and guidelines all the method back to root assumptions. [58] Lofti Zadeh had actually introduced a different type of extension to manage the representation of vagueness. For example, in choosing how “heavy” or “high” a man is, there is often no clear “yes” or “no” response, and a predicate for heavy or tall would rather return worths between 0 and 1. Those worths represented to what degree the predicates were true. His fuzzy logic further supplied a method for propagating combinations of these worths through rational solutions. [59]

Artificial intelligence

Symbolic maker finding out methods were examined to resolve the understanding acquisition bottleneck. One of the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test technique to generate possible guideline hypotheses to evaluate against spectra. Domain and job understanding decreased the variety of prospects evaluated to a workable size. Feigenbaum described Meta-DENDRAL as

… the conclusion of my imagine the early to mid-1960s having to do with theory formation. The conception was that you had an issue solver like DENDRAL that took some inputs and produced an output. In doing so, it utilized layers of understanding to guide and prune the search. That understanding got in there due to the fact that we spoke with individuals. But how did individuals get the understanding? By taking a look at thousands of spectra. So we wanted a program that would take a look at countless spectra and infer the knowledge of mass spectrometry that DENDRAL might utilize to fix individual hypothesis formation problems. We did it. We were even able to release brand-new understanding of mass spectrometry in the Journal of the American Chemical Society, giving credit only in a footnote that a program, Meta-DENDRAL, actually did it. We had the ability to do something that had actually been a dream: to have a computer program created a brand-new and publishable piece of science. [51]

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

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

Symbolic device finding out included more than discovering by example. E.g., John Anderson supplied a cognitive model of human knowing 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 might discover to apply “Supplementary angles are 2 angles whose procedures sum 180 degrees” as several different procedural rules. E.g., one rule might state that if X and Y are supplementary and you know X, then Y will be 180 – X. He called his method “understanding collection”. ACT-R has actually been used effectively to model elements of human cognition, such as discovering and retention. ACT-R is likewise used in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer programming, and algebra to school kids. [64]

Inductive logic shows was another approach to discovering that allowed 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 applied genetic algorithms to program synthesis to produce genetic programs, which he utilized to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger supplied a more basic approach to program synthesis that manufactures a functional program in the course of proving its requirements to be right. [66]

As an option to logic, Roger Schank introduced case-based reasoning (CBR). The CBR method detailed in his book, Dynamic Memory, [67] focuses first on keeping in mind key problem-solving cases for future usage and generalizing them where appropriate. When faced with a new problem, CBR recovers the most comparable previous case and adjusts it to the specifics of the present problem. [68] Another option to logic, genetic algorithms and hereditary programming are based on an evolutionary design of knowing, where sets of guidelines are encoded into populations, the guidelines govern the behavior of people, and choice of the fittest prunes out sets of unsuitable rules over lots of generations. [69]

Symbolic maker learning was applied to learning concepts, rules, heuristics, and analytical. Approaches, other than those above, consist of:

1. Learning from direction or advice-i.e., taking human instruction, positioned as guidance, and figuring out how to operationalize it in specific scenarios. For instance, in a game of Hearts, finding out precisely how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving efficiency by accepting subject-matter specialist (SME) feedback throughout training. When analytical stops working, querying the specialist to either discover a brand-new exemplar for problem-solving or to learn a new explanation regarding exactly why one prototype is more appropriate than another. For instance, the program Protos discovered to identify tinnitus cases by engaging with an audiologist. [71] 3. Learning by analogy-constructing issue options based upon comparable issues seen in the past, and then customizing their options to fit a new situation or domain. [72] [73] 4. Apprentice knowing systems-learning unique services to problems by observing human analytical. Domain knowledge explains why unique options are correct and how the solution can be generalized. LEAP learned how to create VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing jobs to carry out experiments and after that finding out from the outcomes. Doug Lenat’s Eurisko, for example, learned heuristics to beat human gamers at the Traveller role-playing game for two years in a row. [75] 6. Learning macro-operators-i.e., looking for useful macro-operators to be discovered from series of fundamental problem-solving actions. Good macro-operators simplify analytical by permitting problems to be solved at a more abstract level. [76]
Deep knowing and neuro-symbolic AI 2011-now

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

Neuro-symbolic AI: integrating neural and symbolic approaches

Neuro-symbolic AI attempts to integrate neural and symbolic architectures in a way 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 numerous others, [78] the effective building of rich computational cognitive designs requires the mix of sound symbolic thinking and effective (maker) learning designs. Gary Marcus, similarly, argues that: “We can not construct rich cognitive models in a sufficient, automated method without the set of three of hybrid architecture, rich prior understanding, and advanced methods for thinking.”, [79] and in specific: “To develop a robust, knowledge-driven approach to AI we should have the machinery of symbol-manipulation in our toolkit. Too much of useful knowledge is abstract to make do without tools that represent and manipulate abstraction, and to date, the only equipment that we understand of that can manipulate such abstract understanding reliably is the apparatus of symbol adjustment. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have likewise argued for a synthesis. Their arguments are based on a requirement to address the two type of believing gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having two components, System 1 and System 2. System 1 is quick, automatic, intuitive and unconscious. System 2 is slower, detailed, and specific. System 1 is the kind used for pattern acknowledgment while System 2 is far better matched for planning, deduction, and deliberative thinking. In this view, deep knowing finest models the first sort of believing while symbolic thinking best models the 2nd kind and both are required.

Garcez and Lamb explain research study 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 actually been held every year considering that 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 combination of the symbolic and connectionist paradigms of AI has been pursued by a reasonably small research study neighborhood over the last 20 years and has actually yielded a number of significant results. Over the last decade, neural symbolic systems have actually been shown capable of getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in action 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 number of problems in the areas of bioinformatics, control engineering, software application confirmation and adaptation, visual intelligence, ontology knowing, and computer video 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 method of many neural designs in natural language processing, where words or subword tokens are both the ultimate input and output of large language models. Examples consist of BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic techniques are utilized to call neural techniques. In this case the symbolic method is Monte Carlo tree search and the neural techniques learn how to examine video game positions.
– Neural|Symbolic-uses a neural architecture to interpret perceptual data as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to create or label training data that is subsequently found out by a deep knowing design, e.g., to train a neural design for symbolic calculation by utilizing a Macsyma-like symbolic mathematics system to create or label examples.
– Neural _ Symbolic -uses a neural net that is created from symbolic guidelines. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR evidence tree produced from understanding base guidelines and terms. Logic Tensor Networks [86] likewise fall into this classification.
– Neural [Symbolic] -allows a neural design to straight call a symbolic thinking engine, e.g., to carry out an action or assess a state.

Many essential research questions remain, such as:

– What is the finest way to incorporate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and extracted from them?
– How should sensible understanding be learned and reasoned about?
– How can abstract understanding that is hard to encode realistically be managed?

Techniques and contributions

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

AI shows languages

The essential AI programs language in the US throughout the last symbolic AI boom duration was LISP. LISP is the second oldest shows language after FORTRAN and was produced in 1958 by John McCarthy. LISP provided the first read-eval-print loop to support quick program advancement. Compiled functions might be freely blended with analyzed functions. Program tracing, stepping, and breakpoints were likewise supplied, in addition to the capability 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 written in LISP and then ran interpretively to compile the compiler code.

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

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 essential AI programming language during that exact same period was Prolog. Prolog supplied an integrated store of truths and provisions that could be queried by a read-eval-print loop. The store could function as a knowledge base and the provisions could act as guidelines or a restricted form of logic. As a subset of first-order reasoning Prolog was based upon Horn stipulations with a closed-world assumption-any realities not understood were considered false-and an unique name assumption for primitive terms-e.g., the identifier barack_obama was thought about to describe precisely one object. Backtracking and marriage are built-in to Prolog.

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

Prolog is also a kind of declarative shows. The logic clauses that describe programs are directly interpreted to run the programs defined. No specific series of actions is required, as is the case with necessary programming languages.

Japan promoted Prolog for its Fifth Generation Project, meaning to construct unique hardware for high efficiency. Similarly, LISP makers were built to run LISP, but as the 2nd AI boom turned to bust these business might not take on new workstations that could now run LISP or Prolog natively at equivalent speeds. See the history section for more detail.

Smalltalk was another influential AI programs language. For example, it introduced metaclasses and, together with Flavors and CommonLoops, influenced the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the present standard Lisp dialect. CLOS is a Lisp-based object-oriented system that 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 programming languages see this list of shows languages for artificial intelligence. Currently, Python, a multi-paradigm shows language, is the most popular programming language, partially due to its comprehensive package library that supports data science, natural language processing, and deep learning. Python includes a read-eval-print loop, practical components such as higher-order functions, and object-oriented programs that includes metaclasses.

Search

Search emerges in many type of problem resolving, including preparation, restriction satisfaction, and playing games such as checkers, chess, and go. The best understood AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven stipulation knowing, and the DPLL algorithm. For adversarial search when playing games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and thinking

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

Knowledge representation

Semantic networks, conceptual charts, frames, and logic are all methods to modeling understanding such as domain knowledge, analytical understanding, and the semantic significance of language. Ontologies design key principles and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be used for any domain while WordNet is a lexical resource that can likewise be viewed as an ontology. YAGO integrates 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 used.

Description logic is a reasoning for automated classification of ontologies and for finding inconsistent classification data. OWL is a language used to represent ontologies with description reasoning. Protégé is an ontology editor that can check out in OWL ontologies and after that check 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 prove theorems in first-order logic. Horn provision logic is more restricted than first-order reasoning and is utilized in reasoning programs languages such as Prolog. Extensions to first-order reasoning include temporal logic, to handle time; epistemic reasoning, to factor about agent understanding; modal logic, to handle possibility and necessity; and probabilistic reasonings to manage logic and possibility together.

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

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

Reasoning in knowledge-based systems

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

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

A more flexible sort of problem-solving takes place when reasoning about what to do next takes place, instead of merely choosing among the available actions. This sort of meta-level thinking is utilized in Soar and in the BB1 blackboard architecture.

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

Commonsense reasoning

Marvin Minsky first proposed frames as a way of interpreting common visual scenarios, such as an office, and Roger Schank extended this concept to scripts for common routines, such as dining out. Cyc has actually attempted to capture beneficial common-sense understanding and has “micro-theories” to deal with particular sort of domain-specific reasoning.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human thinking about ignorant physics, such as what occurs when we warm a liquid in a pot on the range. We expect it to heat and potentially boil over, even though we might not know its temperature level, its boiling point, or other details, such as air 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 restraint solvers.

Constraints and constraint-based thinking

Constraint solvers perform a more minimal type of reasoning than first-order reasoning. They can streamline sets of spatiotemporal restrictions, such as those for RCC or Temporal Algebra, together with resolving other sort of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic programs can be utilized to resolve scheduling problems, for instance with restraint handling guidelines (CHR).

Automated planning

The General Problem Solver (GPS) cast preparation as problem-solving used means-ends analysis to produce plans. STRIPS took a various method, seeing planning as theorem proving. Graphplan takes a least-commitment technique to preparation, rather than sequentially picking actions from a preliminary state, working forwards, or a goal state if working backwards. Satplan is a technique to preparing where a preparation issue is minimized to a Boolean satisfiability problem.

Natural language processing

Natural language processing focuses on treating language as data to carry out jobs such as identifying topics without necessarily comprehending the designated significance. Natural language understanding, in contrast, constructs a meaning representation and utilizes that for further processing, such as addressing concerns.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all elements of natural language processing long managed by symbolic AI, but since improved by deep learning methods. In symbolic AI, discourse representation theory and first-order logic have actually been utilized to represent sentence significances. Latent semantic analysis (LSA) and explicit semantic analysis also supplied vector representations of files. In the latter case, vector elements are interpretable as ideas called by Wikipedia posts.

New deep knowing techniques based on Transformer designs have actually now eclipsed these earlier symbolic AI approaches and attained advanced performance in natural language processing. However, Transformer models are opaque and do not yet produce human-interpretable semantic representations for sentences and files. Instead, they produce task-specific vectors where the meaning of the vector elements is nontransparent.

Agents and multi-agent systems

Agents are self-governing systems embedded in an environment they view and act on in some sense. Russell and Norvig’s basic book on artificial intelligence is arranged to reflect agent architectures of increasing sophistication. [91] The sophistication of agents differs from basic reactive representatives, to those with a model of the world and automated preparation capabilities, perhaps a BDI agent, i.e., one with beliefs, desires, and objectives – or additionally a support finding out model discovered over time to choose actions – approximately a combination of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep learning for perception. [92]

In contrast, a multi-agent system consists of several agents that interact among themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The representatives require not all have the same internal architecture. Advantages of multi-agent systems consist of the capability to divide work among the representatives and to increase fault tolerance when agents are lost. Research problems consist of how agents reach agreement, distributed issue solving, multi-agent knowing, multi-agent preparation, and distributed constraint optimization.

Controversies developed from early in symbolic AI, both within the field-e.g., between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who accepted AI but rejected symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were mainly from thinkers, on intellectual grounds, but also from financing companies, especially during the 2 AI winter seasons.

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

Limitations were found in using easy first-order logic to factor about dynamic domains. Problems were discovered both with concerns to specifying the prerequisites for an action to be successful and in providing axioms for what did not alter after an action was performed.

McCarthy and Hayes presented the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Expert System.” [93] An easy example happens in “showing that a person person might get into discussion with another”, as an axiom asserting “if a person has a telephone he still has it after searching for a number in the telephone book” would be needed for the reduction to succeed. Similar axioms would be needed for other domain actions to define what did not change.

A similar issue, called the Qualification Problem, takes place in attempting to enumerate the prerequisites for an action to succeed. An unlimited variety of pathological conditions can be imagined, e.g., a banana in a tailpipe could prevent a cars and truck from running correctly.

McCarthy’s approach to fix the frame problem was circumscription, a type of non-monotonic reasoning where deductions might be made from actions that need only define what would change while not needing to explicitly specify everything that would not change. Other non-monotonic reasonings offered truth maintenance systems that modified beliefs resulting in contradictions.

Other methods of dealing with more open-ended domains consisted of probabilistic reasoning systems and artificial intelligence to find out new principles and rules. McCarthy’s Advice Taker can be considered as an inspiration here, as it could integrate new knowledge provided by a human in the kind of assertions or rules. For instance, speculative symbolic maker learning systems explored the capability to take high-level natural language guidance and to translate it into domain-specific actionable rules.

Similar to the problems in dealing with vibrant domains, sensible thinking is likewise challenging to catch in official thinking. Examples of common-sense reasoning include implicit thinking about how individuals believe or general understanding of everyday occasions, items, and living creatures. This sort of knowledge is considered given and not considered as noteworthy. Common-sense thinking is an open area of research study and challenging both for symbolic systems (e.g., Cyc has tried to catch crucial parts of this understanding over more than a years) and neural systems (e.g., self-driving automobiles 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, but his definition of sensible was various than the one above. [94] He defined a program as having sound judgment “if it automatically deduces for itself an adequately wide class of instant effects of anything it is informed and what it already understands. “

Connectionist AI: philosophical obstacles and sociological disputes

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 innovative methods, such as Transformers, GANs, and other operate in deep knowing.

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

1. Implementationism-where connectionist architectures execute the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is declined absolutely, and connectionist architectures underlie intelligence and are completely adequate to explain it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are considered as complementary and both are needed for intelligence

Olazaran, in his sociological history of the controversies within the neural network neighborhood, explained the moderate connectionism consider as basically suitable with present research in neuro-symbolic hybrids:

The 3rd and last position I wish to analyze 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 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, partly connectionist) systems. He declared 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 processes (such as serial, deductive reasoning, and generative symbol control processes) the symbolic paradigm provides appropriate designs, and not only “approximations” (contrary to what extreme connectionists would claim). [97]

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

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

And yet, for the many part, that’s how most existing AI earnings. Hinton and numerous others have actually tried hard to eradicate symbols completely. The deep learning hope-seemingly grounded not so much in science, however in a sort of historical grudge-is that intelligent habits will emerge simply from the confluence of enormous information and deep learning. Where classical computer systems and software application fix tasks by defining sets of symbol-manipulating rules devoted to specific jobs, such as editing a line in a word processor or carrying out an estimation in a spreadsheet, neural networks usually try to fix jobs by statistical approximation and gaining from examples.

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

When deep knowing reemerged in 2012, it was with a type of take-no-prisoners attitude that has actually characterized most of the last decade. By 2015, his hostility toward all things signs had actually completely taken shape. He provided a talk at an AI workshop at Stanford comparing signs to aether, among science’s greatest mistakes.

Since then, his anti-symbolic project has just increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep knowing in among science’s essential journals, Nature. It closed with a direct attack on sign control, calling not for reconciliation however for outright replacement. Later, Hinton told an event of European Union leaders that investing any additional cash in symbol-manipulating approaches was “a huge mistake,” likening it to buying internal combustion engines in the age of electrical vehicles. [98]

Part of these conflicts might be due to uncertain terminology:

Turing award winner Judea Pearl uses a review of device learning which, regrettably, conflates the terms artificial intelligence and deep learning. Similarly, when Geoffrey Hinton refers to symbolic AI, the connotation of the term tends to be that of professional systems dispossessed of any capability to find out. The use of the terms requires information. Artificial intelligence is not confined 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 sensible instead of distributed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not almost production rules composed by hand. A correct definition of AI concerns knowledge representation and thinking, autonomous multi-agent systems, preparation and argumentation, in addition to learning. [99]

Situated robotics: the world as a design

Another critique of symbolic AI is the embodied cognition approach:

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

Rodney Brooks developed behavior-based robotics, one technique to embodied cognition. Nouvelle AI, another name for this technique, is considered as an alternative to both symbolic AI and connectionist AI. His method declined representations, either symbolic or distributed, as not only unnecessary, however as destructive. Instead, he produced the subsumption architecture, a layered architecture for embodied representatives. Each layer accomplishes a different function and needs to operate in the real world. For example, the very first robotic he describes in Intelligence Without Representation, has three layers. The bottom layer interprets finder sensors to avoid items. The middle layer triggers the robotic to wander around when there are no barriers. The leading layer triggers the robotic to go to more far-off places for further exploration. Each layer can temporarily inhibit or suppress a lower-level layer. He criticized AI scientists for specifying AI problems for their systems, when: “There is no tidy department in between understanding (abstraction) and reasoning in the real life.” [101] He called his robotics “Creatures” and each layer was “composed of a fixed-topology network of simple finite state machines.” [102] In the Nouvelle AI method, “First, it is critically important to evaluate the Creatures we integrate in the genuine world; i.e., in the same world that we people populate. It is dreadful to fall under the temptation of testing them in a streamlined world first, even with the finest intents of later moving 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 the usage of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has advantages, however has been criticized by the other techniques. Symbolic AI has been criticized as disembodied, accountable to the credentials problem, and poor in dealing with the perceptual problems where deep learning excels. In turn, connectionist AI has actually been slammed as inadequately matched for deliberative detailed problem fixing, integrating understanding, and handling preparation. Finally, Nouvelle AI masters reactive and real-world robotics domains however has actually been criticized for problems in incorporating knowing and knowledge.

Hybrid AIs including several of these approaches are presently deemed the course forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw areas where AI did not have total responses and stated that Al is for that reason difficult; we now see much of these very same locations undergoing continued research and development leading to increased ability, not impossibility. [100]

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

Notes

^ McCarthy as soon as stated: “This is AI, so we don’t care if it’s emotionally real”. [4] McCarthy restated his position in 2006 at the AI@50 conference where he said “Expert system is not, by definition, simulation of human intelligence”. [28] Pamela McCorduck writes that there are “2 significant branches of expert system: one intended at producing intelligent habits no matter how it was achieved, and the other focused on modeling smart processes found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig composed “Aeronautical engineering texts do not define the objective of their field as making ‘makers that fly so precisely like pigeons that they can trick even other pigeons.'” [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). “Reconciling deep knowing with symbolic expert system: representing things and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). “Logic-Based Expert System”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep knowing with synthetic 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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