Symbolic Expert System

In expert system, symbolic artificial intelligence (also referred to as classical synthetic intelligence or logic-based artificial 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 logic programming, production rules, semantic internet and frames, and it developed applications such as knowledge-based systems (in particular, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm resulted in seminal ideas in search, symbolic programs languages, representatives, 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 encouraged that symbolic techniques would eventually succeed in developing a machine with artificial basic intelligence and considered this the supreme goal of their field. [citation needed] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, led to impractical expectations and guarantees and was followed by the first AI Winter as funding dried up. [5] [6] A 2nd boom (1969-1986) accompanied the rise of specialist systems, their promise of recording business competence, and a passionate corporate welcome. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later on frustration. [8] Problems with troubles in understanding acquisition, maintaining big understanding bases, and brittleness in managing out-of-domain problems arose. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists concentrated on attending to hidden issues in dealing with uncertainty and in understanding acquisition. [10] Uncertainty was addressed with official methods such as hidden Markov designs, Bayesian reasoning, and analytical relational learning. [11] [12] Symbolic machine out addressed the knowledge acquisition problem with contributions including Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree knowing, case-based learning, and inductive logic programming to discover relations. [13]

Neural networks, a subsymbolic technique, had actually been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt’s perceptron knowing work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and work in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not deemed effective till about 2012: “Until Big Data became commonplace, the basic agreement in the Al neighborhood was that the so-called neural-network technique was helpless. Systems just didn’t work that well, compared to other approaches. … A revolution can be found in 2012, when a number of individuals, including a group of researchers dealing with Hinton, exercised a method to use the power of GPUs to tremendously increase the power of neural networks.” [16] Over the next a number of years, deep learning had spectacular success in dealing with vision, speech recognition, speech synthesis, image generation, and maker translation. However, since 2020, as inherent difficulties with predisposition, explanation, coherence, and robustness ended up being more evident with deep learning approaches; an increasing variety of AI researchers have required combining the very best of both the symbolic and neural network methods [17] [18] and dealing with locations that both techniques have difficulty with, such as sensible reasoning. [16]

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

The first AI summer: unreasonable liveliness, 1948-1966

Success at early attempts in AI took place in three primary locations: artificial neural networks, understanding representation, and heuristic search, contributing to high expectations. This area summarizes Kautz’s reprise of early AI history.

Approaches influenced by human or animal cognition or behavior

Cybernetic approaches tried to replicate the feedback loops in between animals and their environments. A robotic turtle, with sensing units, motors for driving and steering, and seven vacuum tubes for control, based upon a preprogrammed neural net, was constructed as early as 1948. This work can be viewed as an early precursor to later operate in neural networks, reinforcement learning, and located robotics. [20]

An important early symbolic AI program was the Logic theorist, composed by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it was able to show 38 elementary 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 solved issues represented with formal operators through state-space search using means-ends analysis. [21]

During the 1960s, symbolic techniques achieved terrific success at imitating smart behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was concentrated in four organizations in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Every one developed its own design of research study. Earlier methods based upon cybernetics or synthetic 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 study and management science. Their research study team utilized the results of mental experiments to develop programs that simulated the techniques that individuals utilized to solve problems. [22] [23] This custom, focused at Carnegie Mellon University would ultimately culminate in the advancement of the Soar architecture in the middle 1980s. [24] [25]

Heuristic search

In addition to the highly specialized domain-specific type of understanding that we will see later on utilized in specialist systems, early symbolic AI scientists discovered another more general application of knowledge. These were called heuristics, rules of thumb that guide a search in appealing directions: “How can non-enumerative search be practical when the underlying issue is greatly difficult? The approach advocated by Simon and Newell is to employ heuristics: fast algorithms that may fail on some inputs or output suboptimal services.” [26] Another essential advance was to find a way to use these heuristics that ensures a service will be found, if there is one, not enduring the occasional fallibility of heuristics: “The A * algorithm supplied a general frame for complete and optimum heuristically guided search. A * is utilized as a subroutine within almost every AI algorithm today but is still no magic bullet; its guarantee of completeness is bought at the expense of worst-case exponential time. [26]

Early work on understanding representation and thinking

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

Modeling formal reasoning with reasoning: the “neats”

Unlike Simon and Newell, John McCarthy felt that devices did not require to imitate the specific systems of human idea, but might instead attempt to find the essence of abstract thinking and problem-solving with reasoning, [27] no matter whether individuals used the exact same algorithms. [a] His laboratory at Stanford (SAIL) concentrated on utilizing official reasoning to fix a wide array of problems, including knowledge representation, preparation and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and elsewhere in Europe which led to the development of the programming language Prolog and the science of reasoning shows. [32] [33]

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

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] found that fixing challenging issues in vision and natural language processing needed ad hoc solutions-they argued that no simple and general concept (like reasoning) would record all the aspects of smart habits. Roger Schank explained their “anti-logic” approaches as “shabby” (rather than the “cool” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “scruffy” AI, because they should be constructed by hand, one complicated idea at a time. [38] [39] [40]

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

The very first AI winter season was a shock:

During the first AI summer, numerous people believed that machine intelligence could be achieved in simply a few years. The Defense Advance Research Projects Agency (DARPA) released programs to support AI research to utilize AI to solve issues of national security; in specific, to automate the translation of Russian to English for intelligence operations and to produce self-governing tanks for the battlefield. Researchers had begun to realize that accomplishing AI was going to be much more difficult than was supposed a decade earlier, but a mix of hubris and disingenuousness led many university and think-tank researchers to accept financing with pledges of deliverables that they must have understood they might not satisfy. By the mid-1960s neither beneficial natural language translation systems nor autonomous tanks had been developed, and a dramatic backlash embeded in. New DARPA leadership canceled existing AI funding programs.

Outside of the United States, the most fertile ground for AI research was the UK. The AI winter in the United Kingdom was stimulated on not a lot by disappointed military leaders as by rival academics who viewed AI researchers as charlatans and a drain on research financing. A teacher of applied mathematics, Sir James Lighthill, was commissioned by Parliament to evaluate the state of AI research in the country. The report mentioned that all of the problems being worked on in AI would be better dealt with 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 explosion. [41]

The 2nd AI summertime: understanding is power, 1978-1987

Knowledge-based systems

As restrictions with weak, domain-independent techniques ended up being more and more evident, [42] researchers from all three traditions began to develop 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 stated:

– “In the understanding lies the power.” [44]
to explain that high efficiency in a specific domain needs both general 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 complex job well, it needs to know a terrific offer about the world in which it operates.
( 2) A plausible extension of that concept, called the Breadth Hypothesis: there are 2 extra capabilities essential for intelligent behavior in unexpected circumstances: falling back on significantly general knowledge, and analogizing to specific but far-flung understanding. [45]

Success with expert systems

This “understanding revolution” resulted in the advancement and implementation of expert systems (presented by Edward Feigenbaum), the very first commercially effective kind of AI software application. [46] [47] [48]

Key specialist systems were:

DENDRAL, which discovered the structure of natural molecules from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and suggested additional laboratory tests, when essential – by analyzing lab outcomes, client history, and medical professional observations. “With about 450 guidelines, MYCIN had the ability to carry out along with some specialists, and substantially better than junior physicians.” [49] INTERNIST and CADUCEUS which took on internal medicine medical 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 eventually identify approximately 1000 different illness.
– GUIDON, which demonstrated how a knowledge base developed for specialist problem resolving could be repurposed for mentor. [50] XCON, to configure VAX computer systems, a then laborious process that could take up to 90 days. XCON minimized the time to about 90 minutes. [9]
DENDRAL is thought about the first expert system that relied 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 individuals at Stanford interested in computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I told him I wanted an induction “sandbox”, he said, “I have just the one for you.” His laboratory was doing mass spectrometry of amino acids. The concern was: how do you go from taking a look at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we started the DENDRAL Project: I was great at heuristic search approaches, and he had an algorithm that was good at producing the chemical problem area.

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, creator of the chemical behind the birth control pill, and likewise among the world’s most respected mass spectrometrists. Carl and his postdocs were world-class professionals in mass spectrometry. We began to add to their knowledge, developing understanding of engineering as we went along. These experiments totaled up to titrating DENDRAL increasingly more knowledge. The more you did that, the smarter the program ended up being. We had very great outcomes.

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

The other expert systems pointed out above came after DENDRAL. MYCIN exemplifies the classic specialist system architecture of a knowledge-base of rules coupled to a symbolic reasoning mechanism, consisting of using certainty elements to handle uncertainty. GUIDON demonstrates how an explicit understanding base can be repurposed for a second application, tutoring, and is an example of an intelligent tutoring system, a specific sort of knowledge-based application. Clancey showed that it was not enough simply to utilize MYCIN’s guidelines for direction, but that he also required to add guidelines for dialogue management and student modeling. [50] XCON is substantial due to the fact that of the countless dollars it conserved DEC, which triggered the expert system boom where most all major corporations in the US had expert systems groups, to capture corporate proficiency, maintain 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 utilizing or examining professional systems. [49]

Chess specialist understanding was encoded in Deep Blue. In 1996, this permitted IBM’s Deep Blue, with the assistance of symbolic AI, to win in a video 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 expert systems is the understanding base, which stores truths and rules for problem-solving. [53] The simplest approach for an expert system understanding base is merely a collection or network of production guidelines. Production guidelines link signs in a relationship comparable to an If-Then statement. The professional system processes the rules to make deductions and to determine what extra details it needs, i.e. what concerns to ask, utilizing human-readable symbols. 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 objectives to required data and prerequisites – way. Advanced knowledge-based systems, such as Soar can likewise perform meta-level thinking, that is thinking about their own reasoning in regards to choosing how to fix problems and keeping track of the success of problem-solving techniques.

Blackboard systems are a 2nd sort of knowledge-based or skilled system architecture. They design a neighborhood of experts incrementally contributing, where they can, to fix an issue. The problem is represented in multiple levels of abstraction or alternate views. The experts (understanding sources) volunteer their services whenever they recognize they can contribute. Potential analytical actions are represented on an agenda that is upgraded as the issue situation changes. A controller decides how helpful each contribution is, and who need to make the next analytical action. One example, the BB1 blackboard architecture [54] was initially motivated by studies of how human beings prepare to carry out numerous jobs in a journey. [55] An innovation of BB1 was to apply the same blackboard model to resolving its control problem, i.e., its controller carried out meta-level reasoning with knowledge sources that kept track of how well a strategy or the problem-solving was continuing and could switch from one technique to another as conditions – such as goals or times – changed. BB1 has actually been applied in several domains: construction site planning, smart tutoring systems, and real-time patient monitoring.

The second AI winter, 1988-1993

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

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

Many factors can be offered for the arrival of the second AI winter. The hardware business stopped working when much more cost-effective general Unix workstations from Sun together with great compilers for LISP and Prolog came onto the market. Many business releases of professional systems were discontinued when they proved too costly to maintain. Medical specialist systems never ever caught on for a number of reasons: the difficulty in keeping them approximately date; the challenge for physician to discover how to utilize a bewildering variety of different specialist systems for different medical conditions; and perhaps most crucially, the hesitation of physicians to rely on a computer-made diagnosis over their gut impulse, even for specific domains where the specialist systems could surpass a typical physician. Equity capital money deserted AI virtually overnight. The world AI conference IJCAI hosted a huge and extravagant exhibition and countless nonacademic guests in 1987 in Vancouver; the primary AI conference the list below year, AAAI 1988 in St. Paul, was a little and strictly academic affair. [9]

Adding in more extensive structures, 1993-2011

Uncertain thinking

Both statistical methods and extensions to logic were tried.

One statistical method, concealed Markov models, had actually already been popularized in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl promoted making use of Bayesian Networks as a noise but efficient method of dealing with uncertain thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian techniques were used successfully in expert systems. [57] Even later on, in the 1990s, statistical relational learning, an approach that combines possibility with rational formulas, 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 logic to support were likewise tried. For example, non-monotonic reasoning could be used with fact upkeep systems. A fact upkeep system tracked presumptions and validations for all inferences. It permitted reasonings to be withdrawn when assumptions were found out to be incorrect or a contradiction was obtained. Explanations might be attended to a reasoning by explaining which rules were applied to produce it and then continuing through underlying inferences and rules all the method back to root assumptions. [58] Lofti Zadeh had introduced a various type of extension to deal with the representation of uncertainty. For instance, in deciding how “heavy” or “high” a guy is, there is regularly no clear “yes” or “no” response, and a predicate for heavy or tall would instead return values between 0 and 1. Those values represented to what degree the predicates held true. His fuzzy logic further offered a way for propagating combinations of these worths through rational formulas. [59]

Machine knowing

Symbolic machine learning approaches were investigated to address the understanding acquisition traffic jam. Among the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test strategy to produce possible rule hypotheses to test against spectra. Domain and job understanding decreased the number of candidates checked to a manageable size. Feigenbaum explained Meta-DENDRAL as

… the culmination of my dream of the early to mid-1960s involving theory development. 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 understanding to guide and prune the search. That understanding got in there due to the fact that we talked to individuals. But how did individuals get the knowledge? By looking at countless spectra. So we desired a program that would look at countless spectra and presume the understanding of mass spectrometry that DENDRAL might utilize to resolve 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, providing credit only in a footnote that a program, Meta-DENDRAL, really did it. We had the ability to do something that had been a dream: to have a computer program come up with a brand-new and publishable piece of science. [51]

In contrast to the knowledge-intensive technique of Meta-DENDRAL, Ross Quinlan invented a domain-independent method to analytical classification, decision tree learning, beginning initially 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 guidelines.

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

Symbolic device discovering encompassed more than finding out by example. E.g., John Anderson provided a cognitive design of human knowing where ability practice leads to a collection of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For example, a student may learn to use “Supplementary angles are 2 angles whose measures sum 180 degrees” as a number of various procedural rules. E.g., one guideline may say that if X and Y are supplementary and you understand X, then Y will be 180 – X. He called his approach “knowledge collection”. ACT-R has actually been utilized effectively to design elements of human cognition, such as learning and retention. ACT-R is also utilized in smart tutoring systems, called cognitive tutors, to successfully teach geometry, computer programs, and algebra to school kids. [64]

Inductive logic shows was another method to finding out that permitted reasoning programs to be synthesized from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) might synthesize Prolog programs from examples. [65] John R. Koza applied genetic algorithms to program synthesis to produce hereditary shows, which he used to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger offered a more general approach to program synthesis that synthesizes a functional program in the course of proving its specs to be correct. [66]

As an option to logic, Roger Schank introduced case-based reasoning (CBR). The CBR approach outlined in his book, Dynamic Memory, [67] focuses initially on remembering crucial analytical cases for future usage and generalizing them where proper. When faced with a brand-new problem, CBR retrieves the most comparable previous case and adapts it to the specifics of the current problem. [68] Another alternative to reasoning, hereditary algorithms and hereditary programs are based upon an evolutionary model of learning, where sets of guidelines are encoded into populations, the rules govern the habits of individuals, and choice of the fittest prunes out sets of inappropriate rules over numerous generations. [69]

Symbolic artificial intelligence was applied to discovering ideas, rules, heuristics, and problem-solving. Approaches, other than those above, consist of:

1. Learning from direction or advice-i.e., taking human guideline, impersonated advice, and determining how to operationalize it in particular situations. For instance, in a game of Hearts, discovering exactly 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 problem-solving fails, querying the specialist to either learn a new exemplar for problem-solving or to learn a new explanation regarding exactly why one prototype is more appropriate than another. For example, the program Protos discovered to detect tinnitus cases by connecting with an audiologist. [71] 3. Learning by analogy-constructing problem services based upon comparable problems seen in the past, and after that modifying their solutions to fit a brand-new circumstance or domain. [72] [73] 4. Apprentice learning systems-learning novel solutions to problems by observing human analytical. Domain understanding describes why novel solutions are proper and how the service can be generalized. LEAP discovered how to develop VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., creating tasks to perform experiments and then gaining from the outcomes. Doug Lenat’s Eurisko, for example, discovered heuristics to beat human players at the Traveller role-playing game for 2 years in a row. [75] 6. Learning macro-operators-i.e., searching for useful macro-operators to be learned from series of standard problem-solving actions. Good macro-operators simplify analytical by enabling issues to be resolved at a more abstract level. [76]
Deep knowing and neuro-symbolic AI 2011-now

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

Neuro-symbolic AI: integrating neural and symbolic techniques

Neuro-symbolic AI attempts to integrate neural and symbolic architectures in a manner that addresses strengths and weaknesses of each, in a complementary style, in order to support robust AI capable of reasoning, discovering, and cognitive modeling. As argued by Valiant [77] and numerous others, [78] the effective building and construction of rich computational cognitive models demands the combination of sound symbolic reasoning and efficient (device) knowing models. Gary Marcus, similarly, argues that: “We can not build rich cognitive designs in an adequate, automatic method without the triumvirate of hybrid architecture, rich anticipation, and advanced techniques for thinking.”, [79] and in specific: “To develop a robust, knowledge-driven technique to AI we should have the equipment of symbol-manipulation in our toolkit. Excessive of useful understanding is abstract to make do without tools that represent and manipulate abstraction, and to date, the only machinery that we understand of that can control such abstract understanding dependably is the apparatus of symbol manipulation. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have likewise argued for a synthesis. Their arguments are based on a requirement to resolve the two type of thinking gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having 2 components, System 1 and System 2. System 1 is quickly, automatic, user-friendly and unconscious. System 2 is slower, step-by-step, and specific. System 1 is the kind used for pattern recognition while System 2 is far better suited for planning, deduction, and deliberative thinking. In this view, deep knowing finest designs the first sort of believing while symbolic reasoning best designs the 2nd kind and both are needed.

Garcez and Lamb describe research study in this location as being continuous for a minimum of the past twenty years, [83] dating from their 2002 book on neurosymbolic learning systems. [84] A series of workshops on neuro-symbolic thinking has been held every year 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 integration of the symbolic and connectionist paradigms of AI has been pursued by a reasonably small research study community over the last 20 years and has yielded several substantial outcomes. Over the last decade, neural symbolic systems have been shown efficient in conquering the so-called propositional fixation of neural networks, as McCarthy (1988) put it in reaction to Smolensky (1988 ); see likewise (Hinton, 1990). Neural networks were shown efficient in representing modal and temporal logics (d’Avila Garcez and Lamb, 2006) and pieces of first-order reasoning (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have been applied to a number of problems in the areas of bioinformatics, control engineering, software application verification and adaptation, visual intelligence, ontology knowing, and video game. [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 existing technique of many neural designs in natural language processing, where words or subword tokens are both the ultimate input and output of large language designs. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic techniques are utilized to call neural techniques. In this case the symbolic approach is Monte Carlo tree search and the neural strategies learn how to assess video game positions.
– Neural|Symbolic-uses a neural architecture to interpret perceptual information as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to generate or label training information that is subsequently learned by a deep knowing design, e.g., to train a neural model for symbolic computation by using a Macsyma-like symbolic mathematics system to create or identify examples.
– Neural _ Symbolic -uses a neural net that is created from symbolic rules. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR evidence tree generated from understanding base guidelines and terms. Logic Tensor Networks [86] also fall under this classification.
– Neural [Symbolic] -allows a neural design to directly call a symbolic thinking engine, e.g., to perform an action or examine a state.

Many crucial research concerns stay, such as:

– What is the very best way to incorporate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and drawn out from them?
– How should common-sense knowledge be discovered and reasoned about?
– How can abstract understanding that is difficult to encode realistically be managed?

Techniques and contributions

This area offers an introduction of methods and contributions in a general context resulting in lots of other, more detailed articles in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered previously in the history section.

AI shows languages

The crucial AI shows language in the US throughout the last symbolic AI boom period was LISP. LISP is the second earliest programs language after FORTRAN and was created in 1958 by John McCarthy. LISP provided the first read-eval-print loop to support quick program development. Compiled functions might be freely blended with analyzed functions. Program tracing, stepping, and breakpoints were also supplied, together with the ability to change values or functions and continue from breakpoints or errors. It had the very first self-hosting compiler, meaning that the compiler itself was initially written in LISP and after that ran interpretively to assemble the compiler code.

Other essential developments pioneered by LISP that have infected other programming languages consist of:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

Programs were themselves data structures that other programs might operate on, allowing the easy meaning of higher-level languages.

In contrast to the US, in Europe the crucial AI programs language during that same period was Prolog. Prolog provided an integrated store of facts and provisions that might be queried by a read-eval-print loop. The store could serve as an understanding base and the stipulations might function as rules or a restricted type of reasoning. As a subset of first-order reasoning Prolog was based upon Horn provisions with a closed-world assumption-any realities not understood were thought about false-and an unique name presumption for primitive terms-e.g., the identifier barack_obama was considered to describe exactly one item. Backtracking and marriage are built-in to Prolog.

Alain Colmerauer and Philippe Roussel are credited as the developers of Prolog. Prolog is a kind of reasoning shows, which was developed by Robert Kowalski. Its history was likewise influenced by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of techniques. For more information see the section on the origins of Prolog in the PLANNER post.

Prolog is also a sort of declarative programs. The reasoning stipulations that describe programs are directly analyzed to run the programs defined. No specific series of actions is required, as is the case with imperative shows languages.

Japan championed Prolog for its Fifth Generation Project, meaning to build unique hardware for high performance. Similarly, LISP devices were built to run LISP, however as the 2nd AI boom turned to bust these companies could not contend with brand-new workstations that might now run LISP or Prolog natively at equivalent speeds. See the history section for more detail.

Smalltalk was another prominent AI programs language. For instance, it introduced metaclasses and, in addition to Flavors and CommonLoops, influenced the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the current 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, thus offering a run-time meta-object procedure. [88]

For other AI programming languages see this list of programming languages for expert system. Currently, Python, a multi-paradigm programs language, is the most popular programs language, partly due to its extensive plan library that supports information science, natural language processing, and deep knowing. Python includes a read-eval-print loop, functional elements such as higher-order functions, and object-oriented programming that includes metaclasses.

Search

Search emerges in numerous kinds of problem fixing, consisting of preparation, constraint complete satisfaction, and playing video games such as checkers, chess, and go. The best known AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven clause knowing, and the DPLL algorithm. For adversarial search when playing video games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and reasoning

Multiple different techniques to represent understanding and then reason with those representations have been examined. Below is a fast introduction of methods to knowledge representation and automated reasoning.

Knowledge representation

Semantic networks, conceptual charts, frames, and logic are all techniques 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 considered as an ontology. YAGO includes WordNet as part of its ontology, to align facts extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being used.

Description reasoning is a reasoning for automated category of ontologies and for spotting inconsistent 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 then examine consistency with deductive classifiers such as such as HermiT. [89]

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

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

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

Reasoning in knowledge-based systems

Knowledge-based systems have an explicit understanding base, generally of rules, to enhance reusability throughout domains by separating procedural code and domain knowledge. A separate inference engine procedures guidelines and adds, deletes, or customizes an understanding shop.

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

A more flexible type of problem-solving takes place when reasoning about what to do next occurs, instead of simply choosing one of the available actions. This type of meta-level thinking is used in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R may have extra abilities, such as the ability to compile often used understanding into higher-level portions.

Commonsense reasoning

Marvin Minsky initially proposed frames as a method of analyzing typical visual scenarios, such as a workplace, and Roger Schank extended this idea to scripts for typical routines, such as dining out. Cyc has attempted to capture helpful common-sense understanding and has “micro-theories” to manage particular kinds of domain-specific thinking.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human thinking about ignorant physics, such as what happens when we heat up a liquid in a pot on the stove. We anticipate it to heat and possibly boil over, despite the fact that we may not know its temperature level, its boiling point, or other details, such as air pressure.

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

Constraints and constraint-based reasoning

Constraint solvers perform a more minimal sort of inference than first-order logic. They can streamline sets of spatiotemporal restraints, such as those for RCC or Temporal Algebra, in addition to resolving other kinds of puzzle issues, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic programming can be utilized to fix scheduling problems, for instance with restraint dealing with guidelines (CHR).

Automated planning

The General Problem Solver (GPS) cast preparation as analytical utilized means-ends analysis to create plans. STRIPS took a various approach, seeing preparation as theorem proving. Graphplan takes a least-commitment approach to preparation, rather than sequentially choosing actions from a preliminary state, working forwards, or an objective state if working backwards. Satplan is an approach to planning where a preparation issue is decreased to a Boolean satisfiability issue.

Natural language processing

Natural language processing focuses on dealing with language as information to carry out tasks such as recognizing subjects without always comprehending the intended meaning. Natural language understanding, in contrast, constructs a significance representation and utilizes that for further processing, such as responding to concerns.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all aspects of natural language processing long handled by symbolic AI, however because enhanced by deep learning approaches. In symbolic AI, discourse representation theory and first-order logic have been utilized to represent sentence meanings. Latent semantic analysis (LSA) and explicit semantic analysis also supplied vector representations of files. In the latter case, vector parts are interpretable as principles called by Wikipedia posts.

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

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 expert system is arranged to show agent architectures of increasing sophistication. [91] The sophistication of agents varies from easy reactive representatives, to those with a design of the world and automated planning capabilities, possibly a BDI representative, i.e., one with beliefs, desires, and objectives – or additionally a support discovering model learned in time to pick actions – approximately a mix of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep learning for understanding. [92]

On the other hand, a multi-agent system includes several representatives that communicate amongst themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The representatives require not all have the exact same internal architecture. Advantages of multi-agent systems include the ability to divide work amongst the representatives and to increase fault tolerance when representatives are lost. Research issues consist of how representatives reach consensus, distributed issue resolving, multi-agent knowing, multi-agent preparation, and dispersed restriction optimization.

Controversies emerged from at an early stage in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and between those who welcomed AI but turned down symbolic approaches-primarily connectionists-and those outside the field. Critiques from beyond the field were mainly from philosophers, on intellectual premises, however likewise from financing agencies, specifically throughout the two AI winter seasons.

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

Limitations were found in utilizing simple first-order logic to reason about dynamic domains. Problems were found both with concerns to enumerating the preconditions for an action to prosper and in providing axioms for what did not alter after an action was carried out.

McCarthy and Hayes introduced the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Artificial Intelligence.” [93] A simple example occurs in “proving that a person person might get into discussion with another”, as an axiom asserting “if an individual has a telephone he still has it after looking up a number in the telephone book” would be needed for the reduction to prosper. Similar axioms would be needed for other domain actions to specify what did not change.

A comparable problem, called the Qualification Problem, takes place in attempting to enumerate the prerequisites for an action to be successful. A limitless variety of pathological conditions can be thought of, e.g., a banana in a tailpipe might avoid an automobile from operating properly.

McCarthy’s method to repair the frame problem was circumscription, a sort of non-monotonic reasoning where deductions might be made from actions that require just define what would change while not having to explicitly specify whatever that would not alter. Other non-monotonic reasonings supplied reality upkeep systems that revised beliefs leading to contradictions.

Other methods of handling more open-ended domains included probabilistic thinking systems and machine learning to find out brand-new ideas and guidelines. McCarthy’s Advice Taker can be considered as an inspiration here, as it might include brand-new knowledge supplied by a human in the kind of assertions or rules. For instance, experimental symbolic maker learning systems checked out the capability to take top-level natural language suggestions and to analyze it into domain-specific actionable guidelines.

Similar to the problems in dealing with vibrant domains, common-sense thinking is also difficult to capture in official reasoning. Examples of sensible reasoning consist of implicit reasoning about how people believe or basic understanding of day-to-day events, objects, and living animals. This sort of understanding is considered given and not deemed noteworthy. Common-sense reasoning is an open area of research study and challenging both for symbolic systems (e.g., Cyc has actually attempted to record crucial parts of this knowledge over more than a years) and neural systems (e.g., self-driving automobiles that do not know not to drive into cones or not to strike pedestrians strolling a bike).

McCarthy saw his Advice Taker as having sensible, however his meaning of common-sense was different than the one above. [94] He defined a program as having sound judgment “if it instantly deduces for itself an adequately large class of immediate repercussions of anything it is informed and what it already knows. “

Connectionist AI: philosophical difficulties and sociological disputes

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

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

1. Implementationism-where connectionist architectures implement the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected totally, and connectionist architectures underlie intelligence and are fully sufficient to discuss it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are considered as complementary and both are required for intelligence

Olazaran, in his sociological history of the debates within the neural network community, explained the moderate connectionism view as essentially suitable with current research in neuro-symbolic hybrids:

The third and last position I would like to examine here is what I call the moderate connectionist view, a more diverse view of the current debate in between connectionism and symbolic AI. Among the scientists who has elaborated this position most explicitly is Andy Clark, a philosopher from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark defended hybrid (partially symbolic, partially connectionist) systems. He claimed that (a minimum of) 2 sort of theories are needed in order to study and model cognition. On the one hand, for some information-processing jobs (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 sign manipulation procedures) the symbolic paradigm provides appropriate designs, and not just “approximations” (contrary to what radical connectionists would declare). [97]

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

To believe that we can just abandon symbol-manipulation is to suspend shock.

And yet, for the most part, that’s how most current AI earnings. Hinton and numerous others have actually striven to get rid of symbols completely. The deep knowing hope-seemingly grounded not so much in science, however in a sort of historical grudge-is that intelligent behavior will emerge simply from the confluence of huge 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 generally try to resolve jobs by statistical approximation and learning from examples.

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

When deep learning reemerged in 2012, it was with a sort of take-no-prisoners mindset that has actually identified the majority of the last decade. By 2015, his hostility towards all things symbols had actually completely taken shape. He provided a talk at an AI workshop at Stanford comparing signs to aether, one of science’s biggest mistakes.

…

Ever since, his anti-symbolic project has actually only increased in strength. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep learning in among science’s crucial journals, Nature. It closed with a direct attack on symbol manipulation, calling not for reconciliation however for straight-out replacement. Later, Hinton informed a gathering of European Union leaders that investing any more money in symbol-manipulating methods was “a huge mistake,” likening it to purchasing internal combustion engines in the era of electrical automobiles. [98]

Part of these disagreements might be because of uncertain terms:

Turing award winner Judea Pearl uses a critique of artificial intelligence which, unfortunately, conflates the terms maker knowing and deep knowing. Similarly, when Geoffrey Hinton describes symbolic AI, the connotation of the term tends to be that of expert systems dispossessed of any capability to discover. Using the terms needs information. Machine learning is not confined to association rule mining, c.f. the body of work on symbolic ML and relational knowing (the distinctions to deep knowing being the choice of representation, localist rational rather than distributed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not almost production rules written by hand. A correct definition of AI issues knowledge representation and thinking, self-governing multi-agent systems, planning and argumentation, in addition to knowing. [99]

Situated robotics: the world as a model

Another critique of symbolic AI is the embodied cognition approach:

The embodied cognition technique claims that it makes no sense to think about 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 operating 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 invented 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 approach declined representations, either symbolic or dispersed, as not just unneeded, but as destructive. Instead, he created the subsumption architecture, a layered architecture for embodied agents. Each layer accomplishes a various purpose and needs to function in the real life. For instance, the first robot he explains in Intelligence Without Representation, has 3 layers. The bottom layer translates sonar sensors to prevent things. The middle layer triggers the robotic to wander around when there are no obstacles. The top layer causes the robotic to go to more far-off locations for further exploration. Each layer can temporarily hinder or suppress a lower-level layer. He slammed AI scientists for specifying AI problems for their systems, when: “There is no tidy department between understanding (abstraction) and thinking in the real life.” [101] He called his robotics “Creatures” and each layer was “made up of a fixed-topology network of easy finite state machines.” [102] In the Nouvelle AI method, “First, it is essential to test the Creatures we build in the real world; i.e., in the same world that we humans populate. It is devastating to fall into the temptation of evaluating them in a streamlined world initially, even with the best intentions of later transferring activity to an unsimplified world.” [103] His focus on real-world testing was in contrast to “Early work in AI focused on games, geometrical issues, symbolic algebra, theorem proving, and other official systems” [104] and the use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has benefits, however has been slammed by the other approaches. Symbolic AI has actually been slammed as disembodied, liable to the credentials problem, and bad in managing the perceptual issues where deep learning excels. In turn, connectionist AI has been slammed as improperly fit for deliberative detailed issue resolving, incorporating understanding, and handling planning. Finally, Nouvelle AI stands out in reactive and real-world robotics domains but has actually been slammed for troubles in incorporating learning and understanding.

Hybrid AIs integrating several of these approaches are presently considered as the path forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw locations where AI did not have total answers and said that Al is for that reason difficult; we now see many of these same areas going through ongoing research and advancement 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 programs
Deep knowing
First-order reasoning
GOFAI
History of expert system
Inductive reasoning shows
Knowledge-based systems
Knowledge representation and thinking
Logic shows
Machine knowing
Model checking
Model-based reasoning
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of expert system
Physical symbol systems hypothesis
Semantic Web
Sequential pattern mining
Statistical relational learning
Symbolic mathematics
YAGO ontology
WordNet

Notes

^ McCarthy as soon as said: “This is AI, so we don’t care if it’s emotionally genuine”. [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 significant branches of expert system: one aimed at producing intelligent behavior no matter how it was achieved, and the other intended at modeling intelligent procedures found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig composed “Aeronautical engineering texts do not define the goal of their field as making ‘makers that fly so precisely like pigeons that they can trick even other pigeons.'” [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). “Reconciling deep learning with symbolic expert system: representing objects and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). “Logic-Based Expert System”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep learning with symbolic synthetic intelligence: representing things and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating mistakes”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten 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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^ Carbonell, Jaime. “Chapter 5: Learning by Analogy: Formulating and Generalizing Plans from Past Experience”. In Michalski, Carbonell & Mitchell (1983 ), pp. 137-162.
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