Symbolic Expert System

In expert system, symbolic expert system (also referred to as classical artificial intelligence or logic-based expert system) [1] [2] is the term for the of all methods in synthetic intelligence research that are based on high-level symbolic (human-readable) representations of issues, logic and search. [3] Symbolic AI used tools such as logic shows, production rules, semantic nets and frames, and it developed applications such as knowledge-based systems (in particular, skilled systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to critical ideas in search, symbolic programs languages, agents, multi-agent systems, the semantic web, and the strengths and restrictions of formal understanding and reasoning systems.

Symbolic AI was the dominant paradigm of AI research study from the mid-1950s up until the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic approaches would eventually succeed in developing a device with synthetic general intelligence and considered this the supreme objective of their field. [citation required] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, led to impractical expectations and pledges and was followed by the very first AI Winter as funding dried up. [5] [6] A second boom (1969-1986) took place with the rise of specialist systems, their pledge of recording corporate competence, and an enthusiastic corporate embrace. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later frustration. [8] Problems with difficulties in understanding acquisition, preserving big understanding bases, and brittleness in dealing with out-of-domain issues developed. Another, 2nd, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers focused on resolving underlying issues in managing uncertainty and in knowledge acquisition. [10] Uncertainty was resolved with official methods such as hidden Markov designs, Bayesian thinking, and statistical relational knowing. [11] [12] Symbolic device learning attended to the knowledge acquisition problem with contributions consisting of Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree knowing, case-based knowing, and inductive logic programming to find out relations. [13]

Neural networks, a subsymbolic approach, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt’s perceptron knowing work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and operate in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not viewed as successful till about 2012: “Until Big Data ended up being prevalent, the general consensus in the Al community was that the so-called neural-network approach was hopeless. Systems just didn’t work that well, compared to other approaches. … A transformation was available in 2012, when a number of individuals, consisting of a group of scientists dealing with Hinton, worked out a way to utilize the power of GPUs to immensely increase the power of neural networks.” [16] Over the next a number of years, deep knowing had magnificent success in dealing with vision, speech acknowledgment, speech synthesis, image generation, and device translation. However, given that 2020, as fundamental difficulties with bias, explanation, comprehensibility, and effectiveness became more obvious with deep knowing techniques; an increasing number of AI researchers have called for integrating the best of both the symbolic and neural network approaches [17] [18] and attending to areas that both methods have difficulty with, such as sensible thinking. [16]

A short 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 post on the History of AI, with dates and titles differing slightly for increased clearness.

The very first AI summertime: irrational spirit, 1948-1966

Success at early attempts in AI took place in 3 main locations: synthetic neural networks, knowledge representation, and heuristic search, adding to high expectations. This area summarizes Kautz’s reprise of early AI history.

Approaches motivated by human or animal cognition or behavior

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

An essential 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 prove 38 primary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later on generalized this work to create a domain-independent problem solver, GPS (General Problem Solver). GPS fixed problems represented with official operators via state-space search using means-ends analysis. [21]

During the 1960s, symbolic techniques achieved fantastic success at simulating intelligent behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was focused in 4 institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Each one developed its own style of research. Earlier techniques based on cybernetics or artificial neural networks were abandoned or pushed into the background.

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

Heuristic search

In addition to the highly specialized domain-specific sort of knowledge that we will see later on utilized in specialist systems, early symbolic AI researchers discovered another more basic application of knowledge. These were called heuristics, guidelines that direct a search in promising directions: “How can non-enumerative search be useful when the underlying issue is greatly hard? The approach promoted by Simon and Newell is to employ heuristics: quick algorithms that may fail on some inputs or output suboptimal services.” [26] Another crucial advance was to find a way to use these heuristics that guarantees a service will be discovered, if there is one, not enduring the periodic fallibility of heuristics: “The A * algorithm supplied 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 guarantee of efficiency is bought at the cost of worst-case exponential time. [26]

Early deal with knowledge representation and reasoning

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

Modeling formal thinking with logic: the “neats”

Unlike Simon and Newell, John McCarthy felt that devices did not require to replicate the precise mechanisms of human idea, however might instead search for the essence of abstract reasoning and analytical with reasoning, [27] despite whether people utilized the exact same algorithms. [a] His laboratory at Stanford (SAIL) focused on using formal logic to resolve a wide range of issues, consisting of knowledge representation, preparation and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and somewhere else in Europe which led to the development of the shows language Prolog and the science of logic programming. [32] [33]

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

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] found that solving difficult issues in vision and natural language processing required ad hoc solutions-they argued that no basic and general principle (like logic) would capture all the aspects of intelligent behavior. Roger Schank explained their “anti-logic” methods as “shabby” (as opposed to the “neat” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “scruffy” AI, given that they need to be developed by hand, one complicated idea at a time. [38] [39] [40]

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

The first AI winter season was a shock:

During the first AI summertime, lots of people believed that machine intelligence could be achieved in just a couple of years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research to utilize AI to fix problems of nationwide security; in specific, to automate the translation of Russian to English for intelligence operations and to develop autonomous tanks for the battlefield. Researchers had begun to realize that accomplishing AI was going to be much harder than was expected a decade previously, but a mix of hubris and disingenuousness led numerous university and think-tank scientists to accept funding with pledges of deliverables that they need to have understood they might not fulfill. By the mid-1960s neither beneficial natural language translation systems nor autonomous tanks had been created, and a remarkable backlash set in. New DARPA management canceled existing AI financing programs.

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

The 2nd 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] researchers from all 3 customs started to build understanding into AI applications. [43] [7] The knowledge transformation was driven by the awareness that knowledge underlies high-performance, domain-specific AI applications.

Edward Feigenbaum said:

– “In the knowledge lies the power.” [44]
to describe that high performance in a specific 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 perform an intricate task well, it needs to know a good deal about the world in which it operates.
( 2) A possible extension of that concept, called the Breadth Hypothesis: there are two extra capabilities essential for smart habits in unexpected scenarios: falling back on increasingly basic understanding, and analogizing to particular however far-flung knowledge. [45]

Success with specialist systems

This “understanding revolution” caused the advancement and implementation of professional systems (presented by Edward Feigenbaum), the very first commercially effective type of AI software. [46] [47] [48]

Key specialist systems were:

DENDRAL, which found the structure of organic molecules from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and suggested more lab tests, when essential – by translating laboratory results, client history, and doctor observations. “With about 450 rules, MYCIN had the ability to carry out as well as some experts, and significantly much better than junior medical professionals.” [49] INTERNIST and CADUCEUS which took on internal medication diagnosis. Internist tried to capture the expertise of the chairman of internal medicine at the University of Pittsburgh School of Medicine while CADUCEUS might eventually identify up to 1000 various illness.
– GUIDON, which revealed how an understanding base constructed for expert issue fixing might be repurposed for teaching. [50] XCON, to set up VAX computer systems, a then tiresome procedure that could use up to 90 days. XCON minimized the time to about 90 minutes. [9]
DENDRAL is considered the first expert system that count on knowledge-intensive problem-solving. It is described listed below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

Among individuals at Stanford interested in computer-based models 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 simply the one for you.” His lab was doing mass spectrometry of amino acids. The concern was: how do you go from taking a look at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we started the DENDRAL Project: I was proficient at heuristic search methods, and he had an algorithm that was great at creating the chemical issue space.

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

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

The other expert systems mentioned above followed DENDRAL. MYCIN exemplifies the classic professional system architecture of a knowledge-base of guidelines combined to a symbolic thinking mechanism, including making use of certainty aspects to handle unpredictability. GUIDON demonstrates how an explicit understanding base can be repurposed for a 2nd application, tutoring, and is an example of a smart tutoring system, a specific kind of knowledge-based application. Clancey showed that it was not sufficient merely to use MYCIN’s guidelines for guideline, but that he also needed to include rules for discussion management and trainee modeling. [50] XCON is significant due to the fact that of the millions of dollars it conserved DEC, which activated the specialist system boom where most all significant corporations in the US had expert systems groups, to record corporate expertise, preserve it, and automate it:

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

Chess expert knowledge was encoded in Deep Blue. In 1996, this permitted IBM’s Deep Blue, with the help 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

An essential part of the system architecture for all professional systems is the knowledge base, which stores realities and rules for problem-solving. [53] The easiest approach for an expert system knowledge base is merely a collection or network of production rules. Production rules link signs in a relationship comparable to an If-Then declaration. The expert system processes the guidelines to make reductions and to determine what additional info it needs, i.e. what questions to ask, using human-readable signs. For instance, OPS5, CLIPS and their successors Jess and Drools operate in this fashion.

Expert systems can operate in either a forward chaining – from evidence to conclusions – or backwards chaining – from goals to required data and requirements – way. Advanced knowledge-based systems, such as Soar can likewise perform meta-level thinking, that is reasoning about their own reasoning in regards to deciding how to fix issues and keeping an eye on the success of problem-solving strategies.

Blackboard systems are a 2nd type of knowledge-based or skilled system architecture. They model a community of experts incrementally contributing, where they can, to resolve an issue. The issue is represented in several levels of abstraction or alternate views. The professionals (knowledge 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 useful each contribution is, and who should make the next problem-solving action. One example, the BB1 blackboard architecture [54] was initially influenced by studies of how people prepare to perform several tasks in a trip. [55] A development of BB1 was to apply the exact same blackboard design to resolving its control problem, i.e., its controller performed meta-level reasoning with understanding sources that monitored how well a plan or the problem-solving was proceeding and could switch from one technique to another as conditions – such as goals or times – altered. BB1 has actually been used in multiple domains: building site preparation, smart tutoring systems, and real-time client monitoring.

The second AI winter season, 1988-1993

At the height of the AI boom, business such as Symbolics, LMI, and Texas Instruments were selling LISP makers specifically targeted to accelerate the development of AI applications and research. In addition, numerous artificial 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 reasons can be used for the arrival of the second AI winter season. The hardware business stopped working when far more cost-effective general Unix workstations from Sun together with great compilers for LISP and Prolog came onto the marketplace. Many industrial releases of expert systems were terminated when they showed too expensive to maintain. Medical specialist systems never captured on for several factors: the difficulty in keeping them up to date; the obstacle for medical experts to discover how to use an overwelming range of different expert systems for different medical conditions; and perhaps most crucially, the unwillingness of doctors to trust a computer-made medical diagnosis over their gut instinct, even for particular domains where the expert systems might outperform an average doctor. Equity capital money deserted AI practically over night. The world AI conference IJCAI hosted a massive and lavish trade convention and countless nonacademic participants 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 reasoning

Both statistical techniques and extensions to logic were tried.

One statistical method, hidden Markov models, had actually 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 method of handling unsure reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian techniques were applied successfully in professional systems. [57] Even later on, in the 1990s, statistical relational knowing, a technique that integrates likelihood with logical formulas, enabled probability to be integrated with first-order logic, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order logic to assistance were also tried. For instance, non-monotonic thinking might be utilized with truth maintenance systems. A fact maintenance system tracked assumptions and justifications for all inferences. It allowed reasonings to be withdrawn when presumptions were discovered to be inaccurate or a contradiction was derived. Explanations might be provided for a reasoning by discussing which guidelines were used to create it and then continuing through underlying reasonings and rules all the way back to root assumptions. [58] Lofti Zadeh had actually presented a different type of extension to manage the representation of vagueness. For example, in choosing how “heavy” or “tall” a male is, there is regularly no clear “yes” or “no” answer, and a predicate for heavy or high would rather return values in between 0 and 1. Those worths represented to what degree the predicates held true. His fuzzy logic further supplied a way for propagating mixes of these worths through sensible solutions. [59]

Machine knowing

Symbolic maker discovering methods were examined to resolve the knowledge acquisition traffic jam. One of the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test method to generate possible rule hypotheses to check against spectra. Domain and job understanding reduced the number of prospects tested to a workable size. Feigenbaum described Meta-DENDRAL as

… the conclusion of my imagine the early to mid-1960s involving 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 used layers of knowledge to guide and prune the search. That understanding acted due to the fact that we interviewed individuals. But how did individuals get the knowledge? By taking a look at thousands of spectra. So we desired a program that would look at thousands of spectra and infer the knowledge of mass spectrometry that DENDRAL might utilize to resolve specific hypothesis formation issues. We did it. We were even able to publish new understanding of mass spectrometry in the Journal of the American Chemical Society, providing credit just in a footnote that a program, Meta-DENDRAL, actually did it. We were able to do something that had actually been a dream: to have a computer program come up with a new and publishable piece of science. [51]

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

Advances were made in understanding machine learning theory, too. Tom Mitchell presented version area knowing which explains learning as an explore an area of hypotheses, with upper, more basic, and lower, more specific, boundaries incorporating all viable hypotheses constant with the examples seen up until now. [62] More formally, Valiant introduced Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of device learning. [63]

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

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

As an option to reasoning, Roger Schank introduced case-based thinking (CBR). The CBR approach laid out in his book, Dynamic Memory, [67] focuses initially on remembering key analytical cases for future usage and generalizing them where suitable. When confronted with a new issue, CBR obtains the most similar previous case and adjusts it to the specifics of the present issue. [68] Another option to logic, hereditary algorithms and genetic programs are based upon an evolutionary model of learning, where sets of rules are encoded into populations, the rules govern the habits of people, and choice of the fittest prunes out sets of inappropriate guidelines over numerous generations. [69]

Symbolic artificial intelligence was applied to learning ideas, guidelines, heuristics, and analytical. Approaches, aside from those above, include:

1. Learning from guideline or advice-i.e., taking human instruction, impersonated advice, and figuring out how to operationalize it in particular scenarios. For instance, in a game of Hearts, finding out exactly how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving performance by accepting subject-matter professional (SME) feedback during training. When problem-solving fails, querying the professional to either discover a brand-new exemplar for analytical or to discover a brand-new explanation regarding exactly why one prototype is more relevant 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 on similar problems seen in the past, and after that modifying their options to fit a new scenario or domain. [72] [73] 4. Apprentice knowing systems-learning novel services to problems by observing human analytical. Domain understanding explains why novel services are right and how the option can be generalized. LEAP learned how to create VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., developing jobs to bring out experiments and after that learning from the outcomes. Doug Lenat’s Eurisko, for example, learned heuristics to beat human gamers at the Traveller role-playing game for 2 years in a row. [75] 6. Learning macro-operators-i.e., searching for helpful macro-operators to be found out from sequences of standard problem-solving actions. Good macro-operators streamline analytical by enabling problems to be fixed at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now

With the increase of deep learning, the symbolic AI technique has actually been compared to deep knowing as complementary “… with parallels having been drawn lot of times by AI scientists between Kahneman’s research study on human thinking 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 modelled by deep learning and symbolic thinking, respectively.” In this view, symbolic reasoning is more apt for deliberative thinking, planning, and description while deep knowing is more apt for quick pattern acknowledgment in perceptual applications with loud information. [17] [18]

Neuro-symbolic AI: incorporating neural and symbolic methods

Neuro-symbolic AI efforts to integrate neural and symbolic architectures in a way that addresses strengths and weaknesses 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 efficient construction of rich computational cognitive models requires the combination of sound symbolic reasoning and efficient (machine) knowing models. Gary Marcus, likewise, argues that: “We can not build abundant cognitive designs in a sufficient, automatic method without the triune 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. Excessive 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 device of sign manipulation. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based upon a need to resolve the two kinds of thinking gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having 2 parts, System 1 and System 2. System 1 is quick, automated, instinctive and unconscious. System 2 is slower, detailed, and explicit. System 1 is the kind used for pattern acknowledgment while System 2 is far better matched for preparation, reduction, and deliberative thinking. In this view, deep knowing finest designs the first type of believing while symbolic thinking best designs the 2nd kind and both are needed.

Garcez and Lamb explain research study in this location as being continuous for a minimum of the previous twenty years, [83] dating from their 2002 book on neurosymbolic learning systems. [84] A series of workshops on neuro-symbolic reasoning has been held every year considering that 2005, see http://www.neural-symbolic.org/ for information.

In their 2015 paper, Neural-Symbolic Learning and Reasoning: Contributions and Challenges, Garcez et al. argue that:

The integration of the symbolic and connectionist paradigms of AI has been pursued by a reasonably small research community over the last twenty years and has actually yielded a number of considerable outcomes. Over the last years, neural symbolic systems have actually been revealed efficient in conquering 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 efficient in representing modal and temporal reasonings (d’Avila Garcez and Lamb, 2006) and fragments of first-order logic (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have actually been used to a variety of issues in the locations of bioinformatics, control engineering, software application verification and adjustment, visual intelligence, ontology learning, and video game. [78]

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

– Symbolic Neural symbolic-is the existing approach of many neural designs in natural language processing, where words or subword tokens are both the supreme input and output of large language models. Examples consist of BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic techniques are used to call neural methods. In this case the symbolic approach is Monte Carlo tree search and the neural strategies learn how to examine video game positions.
– Neural|Symbolic-uses a neural architecture to interpret perceptual data as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to create or label training data that is subsequently found out by a deep learning model, e.g., to train a neural model for symbolic computation by utilizing a Macsyma-like symbolic mathematics system to develop or label 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 created from understanding base guidelines and terms. Logic Tensor Networks [86] likewise fall under this classification.
– Neural [Symbolic] -enables a neural design to directly call a symbolic reasoning engine, e.g., to perform an action or evaluate a state.

Many essential research study concerns remain, such as:

– What is the finest way to integrate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and extracted from them?
– How should common-sense understanding be discovered and reasoned about?
– How can abstract understanding that is hard to encode realistically be dealt with?

Techniques and contributions

This area supplies an overview of methods and contributions in an overall context resulting in numerous other, more detailed posts in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered previously in the history area.

AI programs languages

The essential AI shows language in the US during the last symbolic AI boom duration was LISP. LISP is the second earliest programming language after FORTRAN and was created in 1958 by John McCarthy. LISP supplied the very first read-eval-print loop to support quick program advancement. Compiled functions could be easily blended with translated functions. Program tracing, stepping, and breakpoints were also provided, along with the ability to alter values or functions and continue from breakpoints or mistakes. It had the first self-hosting compiler, meaning that the compiler itself was originally composed in LISP and then ran interpretively to compile the compiler code.

Other essential innovations originated by LISP that have actually infected other programs languages include:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

Programs were themselves data structures that other programs could operate on, permitting the simple meaning of higher-level languages.

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

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

Prolog is likewise a type of declarative programming. The logic clauses that describe programs are directly analyzed to run the programs specified. No specific series of actions is required, as is the case with imperative shows languages.

Japan promoted Prolog for its Fifth Generation Project, planning to build special hardware for high efficiency. Similarly, LISP machines were constructed to run LISP, but as the 2nd AI boom turned to bust these companies could not take on new workstations that might now run LISP or Prolog natively at similar speeds. See the history section for more detail.

Smalltalk was another prominent AI shows language. For example, it introduced metaclasses and, together with Flavors and CommonLoops, affected the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the present basic Lisp dialect. CLOS is a Lisp-based object-oriented system that allows several inheritance, in addition to incremental extensions to both classes and metaclasses, hence offering a run-time meta-object protocol. [88]

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

Search

Search occurs in numerous kinds of issue solving, consisting of planning, constraint complete satisfaction, and playing games such as checkers, chess, and go. The very 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 video games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and reasoning

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

Knowledge representation

Semantic networks, conceptual charts, frames, and reasoning are all methods to modeling knowledge such as domain knowledge, 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 integrates WordNet as part of its ontology, to align realities extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology presently being used.

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

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

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

Prover9 can be used in combination 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 an explicit understanding base, generally of guidelines, to enhance reusability throughout domains by separating procedural code and domain knowledge. A separate inference engine processes rules and includes, deletes, or modifies an understanding shop.

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

A more flexible type of analytical happens when thinking about what to do next takes place, rather than merely picking one of the offered actions. This kind of meta-level thinking is used in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R may have additional capabilities, such as the capability to compile frequently utilized understanding into higher-level portions.

Commonsense thinking

Marvin Minsky first proposed frames as a way of interpreting common visual scenarios, such as a workplace, and Roger Schank extended this idea to scripts for typical routines, such as eating in restaurants. Cyc has actually tried to capture useful common-sense knowledge and has “micro-theories” to deal with particular sort of domain-specific thinking.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human reasoning about naive physics, such as what takes place when we warm a liquid in a pot on the stove. We anticipate it to heat and perhaps boil over, although we might not understand its temperature, its boiling point, or other information, such as atmospheric pressure.

Similarly, Allen’s temporal period algebra is a simplification of reasoning about time and Region Connection Calculus is a simplification of reasoning about spatial relationships. Both can be solved with restriction solvers.

Constraints and constraint-based reasoning

Constraint solvers perform a more minimal kind of inference than first-order reasoning. They can simplify sets of spatiotemporal restrictions, such as those for RCC or Temporal Algebra, together with solving other kinds of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic programs can be utilized to solve scheduling issues, for example with restraint handling rules (CHR).

Automated planning

The General Problem Solver (GPS) cast preparation as problem-solving used means-ends analysis to produce strategies. STRIPS took a different method, seeing planning as theorem proving. Graphplan takes a least-commitment approach to preparation, rather than sequentially selecting actions from an initial state, working forwards, or an objective state if working backwards. Satplan is an approach to planning where a planning problem is decreased to a Boolean satisfiability issue.

Natural language processing

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

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb phrase chunking are all aspects of natural language processing long handled by symbolic AI, however because enhanced by deep learning approaches. 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 offered vector representations of files. In the latter case, vector components are interpretable as ideas called by Wikipedia articles.

New deep learning techniques based on Transformer models have now eclipsed these earlier symbolic AI techniques and achieved cutting edge performance in natural language processing. However, Transformer designs are nontransparent 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 perceive and act upon in some sense. Russell and Norvig’s standard textbook on expert system is organized to reflect agent architectures of increasing elegance. [91] The elegance of representatives differs from basic reactive representatives, to those with a model of the world and automated preparation capabilities, potentially a BDI agent, i.e., one with beliefs, desires, and intents – or additionally a reinforcement finding out model discovered with time to select 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 multiple representatives that interact amongst themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The representatives need not all have the same internal architecture. Advantages of multi-agent systems include the capability to divide work among the representatives and to increase fault tolerance when representatives are lost. Research problems consist of how representatives reach agreement, dispersed problem resolving, multi-agent learning, multi-agent preparation, and dispersed constraint optimization.

Controversies developed from early on 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 welcomed AI however declined symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were primarily from theorists, on intellectual grounds, but likewise from funding firms, particularly during the 2 AI winters.

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

Limitations were discovered in utilizing easy first-order logic to factor about vibrant domains. Problems were discovered both with regards to identifying the prerequisites for an action to be successful and in supplying axioms for what did not alter 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] An easy example takes place in “showing that a person individual could enter 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 directory” would be needed for the reduction to prosper. Similar axioms would be required for other domain actions to specify what did not alter.

A similar problem, called the Qualification Problem, takes place in trying to specify the prerequisites for an action to succeed. An infinite variety of pathological conditions can be envisioned, e.g., a banana in a tailpipe might avoid an automobile from running properly.

McCarthy’s method to repair the frame issue was circumscription, a kind of non-monotonic logic where reductions could be made from actions that require just specify what would change while not having to explicitly specify whatever that would not change. Other non-monotonic reasonings offered fact maintenance systems that modified beliefs leading to contradictions.

Other ways of managing more open-ended domains consisted of probabilistic thinking systems and maker knowing to discover brand-new principles and rules. McCarthy’s Advice Taker can be viewed as a motivation here, as it might incorporate new knowledge provided by a human in the type of assertions or rules. For instance, speculative symbolic device finding out systems checked out the ability to take high-level natural language guidance and to translate it into domain-specific actionable guidelines.

Similar to the issues in dealing with dynamic domains, sensible thinking is also difficult to capture in official thinking. Examples of common-sense thinking include implicit thinking about how individuals believe or basic knowledge of daily events, objects, and living creatures. This type of understanding is considered granted and not deemed noteworthy. Common-sense reasoning is an open location of research study and challenging both for symbolic systems (e.g., Cyc has actually tried to catch essential parts of this understanding over more than a years) and neural systems (e.g., self-driving cars and trucks that do not understand not to drive into cones or not to strike pedestrians walking a bicycle).

McCarthy saw his Advice Taker as having sensible, but his meaning of sensible was various than the one above. [94] He specified a program as having common sense “if it instantly deduces for itself a sufficiently broad class of immediate consequences of anything it is told and what it currently knows. “

Connectionist AI: philosophical challenges and sociological disputes

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

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

1. Implementationism-where connectionist architectures implement the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected absolutely, and connectionist architectures underlie intelligence and are completely sufficient to explain it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are deemed complementary and both are required for intelligence

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

The 3rd and last position I wish to take a look at here is what I call the moderate connectionist view, a more diverse view of the current dispute in between connectionism and symbolic AI. Among the scientists who has elaborated this position most clearly is Andy Clark, a thinker from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark protected hybrid (partly symbolic, partially connectionist) systems. He declared that (at least) 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 models. But on the other hand, for other cognitive procedures (such as serial, deductive thinking, and generative symbol control procedures) the symbolic paradigm uses appropriate models, and not only “approximations” (contrary to what extreme connectionists would claim). [97]

Gary Marcus has claimed that the animus in the deep learning community against symbolic approaches now might be more sociological than philosophical:

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

And yet, for the many part, that’s how most current AI earnings. Hinton and lots of others have actually striven to eradicate symbols completely. The deep learning hope-seemingly grounded not a lot in science, however in a sort of historic grudge-is that smart habits will emerge purely from the confluence of massive information and deep learning. Where classical computers and software fix jobs by specifying sets of symbol-manipulating rules committed to particular tasks, such as editing a line in a word processor or carrying out an estimation in a spreadsheet, neural networks generally try to fix jobs by analytical approximation and learning from examples.

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

When deep knowing reemerged in 2012, it was with a type of take-no-prisoners mindset that has actually characterized the majority of the last decade. By 2015, his hostility towards all things symbols had actually fully crystallized. He lectured at an AI workshop at Stanford comparing symbols to aether, one of science’s greatest errors.

…

Since then, his anti-symbolic project has only increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep knowing in one of science’s essential journals, Nature. It closed with a direct attack on sign control, calling not for reconciliation but for outright replacement. Later, Hinton told a gathering of European Union leaders that investing any further money in symbol-manipulating methods was “a big mistake,” likening it to investing in internal combustion engines in the period of electric cars and trucks. [98]

Part of these disagreements might be because of unclear terms:

Turing award winner Judea Pearl provides a review of artificial intelligence which, unfortunately, conflates the terms artificial intelligence and deep learning. Similarly, when Geoffrey Hinton describes symbolic AI, the undertone of the term tends to be that of specialist systems dispossessed of any capability to discover. Making use of the terminology is in need of clarification. Machine learning is not confined to association rule mining, c.f. the body of work on symbolic ML and relational knowing (the differences to deep learning being the option of representation, localist sensible rather than distributed, and the non-use of gradient-based knowing algorithms). Equally, symbolic AI is not just about production guidelines written by hand. An appropriate definition of AI issues understanding representation and reasoning, self-governing multi-agent systems, planning and argumentation, along with knowing. [99]

Situated robotics: the world as a model

Another review of symbolic AI is the embodied cognition approach:

The embodied cognition technique declares that it makes no sense to consider the brain separately: cognition happens within a body, which is embedded in an environment. We need to study the system as a whole; the brain’s functioning exploits regularities in its environment, including the rest of its body. Under the embodied cognition approach, robotics, vision, and other sensors end up being central, not peripheral. [100]

Rodney Brooks created behavior-based robotics, one method to embodied cognition. Nouvelle AI, another name for this method, is deemed an alternative to both symbolic AI and connectionist AI. His method turned down representations, either symbolic or dispersed, as not just unnecessary, but as damaging. Instead, he developed the subsumption architecture, a layered architecture for embodied representatives. Each layer accomplishes a different purpose and needs to function in the real life. For instance, the very first robot he explains in Intelligence Without Representation, has 3 layers. The bottom layer interprets finder sensing units to avoid items. The middle layer causes the robotic to wander around when there are no challenges. The leading layer causes the robot to go to more distant locations for more exploration. Each layer can momentarily inhibit or reduce a lower-level layer. He slammed AI scientists for specifying AI issues for their systems, when: “There is no clean department in between perception (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 easy limited state devices.” [102] In the Nouvelle AI approach, “First, it is critically important to evaluate the Creatures we develop in the genuine world; i.e., in the same world that we human beings occupy. It is dreadful to fall under the temptation of testing them in a streamlined world initially, even with the finest intents of later transferring activity to an unsimplified world.” [103] His emphasis on real-world testing remained in contrast to “Early work in AI focused on games, geometrical issues, symbolic algebra, theorem proving, and other official systems” [104] and making use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has benefits, however has actually been criticized by the other techniques. Symbolic AI has actually been slammed as disembodied, responsible to the certification issue, and bad in dealing with the affective issues where deep finding out excels. In turn, connectionist AI has been criticized as poorly matched for deliberative detailed problem solving, including knowledge, and dealing with preparation. Finally, Nouvelle AI masters reactive and real-world robotics domains but has been slammed for problems in incorporating learning and understanding.

Hybrid AIs including one or more of these methods are currently deemed the path forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw areas where AI did not have complete answers and stated that Al is therefore impossible; we now see a lot of these exact same locations undergoing continued research study and advancement causing increased capability, not impossibility. [100]

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

Notes

^ McCarthy when stated: “This is AI, so we don’t care if it’s psychologically real”. [4] McCarthy repeated his position in 2006 at the AI@50 conference where he stated “Artificial intelligence is not, by meaning, simulation of human intelligence”. [28] Pamela McCorduck writes that there are “2 major branches of artificial intelligence: one focused on producing smart behavior no matter how it was accomplished, and the other focused on modeling smart procedures found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig composed “Aeronautical engineering texts do not specify the goal of their field as making ‘machines that fly so exactly like pigeons that they can trick even other pigeons.'” [30] Citations

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