Symbolic Artificial Intelligence

In expert system, symbolic expert system (also called classical artificial intelligence or logic-based artificial intelligence) [1] [2] is the term for the collection of all techniques in synthetic intelligence research that are based upon high-level symbolic (human-readable) representations of problems, reasoning and search. [3] Symbolic AI utilized tools such as logic shows, production rules, semantic webs and frames, and it established applications such as knowledge-based systems (in specific, professional systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated preparation and scheduling systems. The Symbolic AI paradigm resulted in influential ideas in search, symbolic shows languages, agents, multi-agent systems, the semantic web, and the strengths and constraints of official knowledge and reasoning systems.

Symbolic AI was the dominant paradigm of AI research from the mid-1950s until the mid-1990s. [4] Researchers in the 1960s and the 1970s were convinced that symbolic techniques would eventually succeed in developing a maker with synthetic 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 unrealistic expectations and guarantees and was followed by the very first AI Winter as moneying dried up. [5] [6] A second boom (1969-1986) took place with the rise of specialist systems, their guarantee of catching business expertise, and a passionate corporate accept. [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 large understanding bases, and brittleness in dealing with out-of-domain issues emerged. Another, 2nd, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists concentrated on attending to hidden issues in dealing with unpredictability and in understanding acquisition. [10] Uncertainty was resolved with formal methods such as concealed Markov models, Bayesian thinking, and analytical relational learning. [11] [12] Symbolic machine learning resolved the knowledge acquisition issue with contributions consisting of Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree knowing, case-based knowing, and inductive logic programming to learn relations. [13]

Neural networks, a subsymbolic technique, had actually been pursued from early days and reemerged highly in 2012. Early examples are Rosenblatt’s perceptron knowing work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and operate in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not deemed successful till about 2012: “Until Big Data ended up being commonplace, the general agreement in the Al community was that the so-called neural-network technique was helpless. Systems just didn’t work that well, compared to other techniques. … A transformation can be found in 2012, when a variety of people, including a team of researchers working with Hinton, exercised a method to use the power of GPUs to tremendously increase the power of neural networks.” [16] Over the next numerous years, deep knowing had amazing success in dealing with vision, speech acknowledgment, speech synthesis, image generation, and machine translation. However, since 2020, as inherent difficulties with predisposition, description, coherence, and robustness ended up being more obvious with deep learning techniques; an increasing number of AI researchers have actually called for combining the finest of both the symbolic and neural network methods [17] [18] and attending to that both techniques have difficulty with, such as common-sense thinking. [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 very first AI summer: illogical liveliness, 1948-1966

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

Approaches influenced by human or animal cognition or habits

Cybernetic techniques tried to replicate the feedback loops in between animals and their environments. A robotic turtle, with sensing units, motors for driving and steering, and 7 vacuum tubes for control, based upon a preprogrammed neural web, was constructed as early as 1948. This work can be viewed as an early precursor to later work in neural networks, support knowing, and located robotics. [20]

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

During the 1960s, symbolic approaches attained terrific success at simulating smart habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was focused in 4 institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Each one established its own design of research. Earlier approaches based on cybernetics or synthetic neural networks were deserted or pushed into the background.

Herbert Simon and Allen Newell studied human analytical abilities and attempted 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 utilized the outcomes of psychological experiments to establish programs that simulated the techniques that people utilized to solve issues. [22] [23] This tradition, focused at Carnegie Mellon University would eventually culminate in the advancement of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the highly specialized domain-specific kinds of knowledge that we will see later on used in specialist systems, early symbolic AI researchers discovered another more basic application of knowledge. These were called heuristics, rules of thumb that direct a search in appealing instructions: “How can non-enumerative search be practical when the underlying issue is exponentially difficult? The approach promoted by Simon and Newell is to utilize heuristics: fast algorithms that may fail on some inputs or output suboptimal services.” [26] Another crucial advance was to find a method to use these heuristics that ensures a solution will be found, if there is one, not enduring the occasional fallibility of heuristics: “The A * algorithm supplied a general frame for complete and ideal heuristically guided search. A * is utilized as a subroutine within almost every AI algorithm today but is still no magic bullet; its warranty of efficiency is purchased the cost of worst-case rapid time. [26]

Early work on knowledge representation and reasoning

Early work covered both applications of formal reasoning emphasizing first-order logic, in addition to efforts to handle common-sense reasoning in a less formal manner.

Modeling formal thinking with reasoning: the “neats”

Unlike Simon and Newell, John McCarthy felt that makers did not require to simulate the precise systems of human thought, but might rather attempt to find the essence of abstract reasoning and problem-solving with logic, [27] despite whether people utilized the very same algorithms. [a] His lab at Stanford (SAIL) focused on using formal reasoning to solve a wide range of issues, consisting of understanding representation, planning and knowing. [31] Logic was likewise the focus of the work at the University of Edinburgh and elsewhere in Europe which resulted in the advancement of the programs language Prolog and the science of reasoning programs. [32] [33]

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

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] found that resolving challenging problems in vision and natural language processing needed advertisement hoc solutions-they argued that no basic and general concept (like reasoning) would record all the aspects of intelligent habits. Roger Schank explained their “anti-logic” approaches as “scruffy” (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 “shabby” AI, because they must be constructed by hand, one complex 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 very first AI summer season, lots of people thought that device intelligence could be attained in just a few years. The Defense Advance Research Projects Agency (DARPA) introduced programs to support AI research to utilize AI to solve issues of national security; in particular, to automate the translation of Russian to English for intelligence operations and to create self-governing tanks for the battlefield. Researchers had started to realize that attaining AI was going to be much harder than was supposed a decade previously, but a mix of hubris and disingenuousness led numerous university and think-tank researchers to accept financing with pledges of deliverables that they must have known they could not satisfy. By the mid-1960s neither useful natural language translation systems nor autonomous tanks had been created, and a significant backlash set in. New DARPA management canceled existing AI funding programs.

Outside of the United States, the most fertile ground for AI research study was the United Kingdom. The AI winter in the United Kingdom was spurred on not so much by dissatisfied military leaders as by rival academics who saw AI researchers as charlatans and a drain on research financing. A professor of applied mathematics, Sir James Lighthill, was commissioned by Parliament to evaluate the state of AI research study in the nation. The report stated that all of the problems being dealt with in AI would be much better managed by scientists from other disciplines-such as applied mathematics. The report likewise claimed that AI successes on toy problems could never scale to real-world applications due to combinatorial surge. [41]

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

Knowledge-based systems

As restrictions with weak, domain-independent methods became more and more obvious, [42] researchers from all 3 traditions began to construct knowledge into AI applications. [43] [7] The understanding revolution was driven by the awareness that understanding underlies high-performance, domain-specific AI applications.

Edward Feigenbaum said:

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

( 1) The Knowledge Principle: if a program is to carry out a complicated job well, it needs to know a good deal about the world in which it operates.
( 2) A possible extension of that principle, called the Breadth Hypothesis: there are two extra capabilities required for smart behavior in unexpected scenarios: falling back on increasingly basic knowledge, and analogizing to specific however remote knowledge. [45]

Success with professional systems

This “understanding transformation” caused the advancement and implementation of specialist systems (presented by Edward Feigenbaum), the first commercially successful form of AI software application. [46] [47] [48]

Key specialist systems were:

DENDRAL, which discovered the structure of natural particles from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and suggested more laboratory tests, when necessary – by translating lab results, client history, and medical professional observations. “With about 450 rules, MYCIN had the ability to perform as well as some specialists, and substantially better than junior doctors.” [49] INTERNIST and CADUCEUS which dealt with internal medicine diagnosis. Internist attempted to capture the knowledge of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS could eventually identify up to 1000 various illness.
– GUIDON, which demonstrated how an understanding base built for expert problem resolving might be repurposed for teaching. [50] XCON, to configure VAX computers, a then tiresome process that could take up to 90 days. XCON lowered the time to about 90 minutes. [9]
DENDRAL is thought about the first expert system that depend on knowledge-intensive analytical. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

Among the individuals at Stanford thinking about computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genetics. When I informed him I wanted an induction “sandbox”, he said, “I have just the one for you.” His lab was doing mass spectrometry of amino acids. The question was: how do you go from looking at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we began the DENDRAL Project: I was great at heuristic search methods, and he had an algorithm that was proficient at creating the chemical problem area.

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

The generalization was: in the knowledge lies the power. That was the big idea. In my career that is the substantial, “Ah ha!,” and it wasn’t the way AI was being done previously. Sounds basic, 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 expert system architecture of a knowledge-base of guidelines coupled to a symbolic thinking mechanism, consisting of using certainty elements to deal with uncertainty. GUIDON shows how an explicit understanding base can be repurposed for a second application, tutoring, and is an example of an intelligent tutoring system, a particular kind of knowledge-based application. Clancey revealed that it was not adequate simply to use MYCIN’s guidelines for instruction, but that he also required to add rules for dialogue management and student modeling. [50] XCON is substantial because of the millions of dollars it conserved DEC, which triggered the professional system boom where most all significant corporations in the US had skilled systems groups, to record business know-how, 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 advancement. Nearly every significant U.S. corporation had its own Al group and was either utilizing or examining professional systems. [49]

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

Architecture of knowledge-based and expert systems

An essential component of the system architecture for all specialist systems is the understanding base, which stores truths and guidelines for problem-solving. [53] The most basic method for a professional system knowledge base is simply a collection or network of production rules. Production rules connect symbols in a relationship similar to an If-Then declaration. The specialist system processes the rules to make reductions and to determine what extra info it requires, i.e. what concerns to ask, utilizing human-readable symbols. For example, OPS5, CLIPS and their successors Jess and Drools run in this fashion.

Expert systems can run in either a forward chaining – from proof to conclusions – or backward chaining – from goals to needed data and prerequisites – way. Advanced knowledge-based systems, such as Soar can also perform meta-level reasoning, that is thinking about their own thinking in terms of deciding how to fix problems and monitoring the success of problem-solving strategies.

Blackboard systems are a 2nd kind of knowledge-based or expert system architecture. They design a neighborhood of specialists incrementally contributing, where they can, to resolve an issue. The issue is represented in several levels of abstraction or alternate views. The professionals (understanding sources) volunteer their services whenever they acknowledge they can contribute. Potential analytical actions are represented on a program that is updated as the issue situation changes. A controller decides how beneficial each contribution is, and who must make the next problem-solving action. One example, the BB1 blackboard architecture [54] was originally motivated by studies of how humans plan to carry out several tasks in a trip. [55] A development of BB1 was to apply the very same blackboard model to fixing its control problem, i.e., its controller carried out meta-level thinking with understanding sources that kept an eye on how well a strategy or the problem-solving was continuing and might change from one method to another as conditions – such as goals or times – altered. BB1 has actually been used in numerous domains: building website planning, intelligent tutoring systems, and real-time client tracking.

The 2nd AI winter, 1988-1993

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

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

Many factors can be provided for the arrival of the second AI winter season. The hardware business stopped working when much more cost-efficient general Unix workstations from Sun together with good compilers for LISP and Prolog came onto the marketplace. Many industrial deployments of expert systems were ceased when they showed too pricey to keep. Medical specialist systems never ever captured on for a number of reasons: the problem in keeping them as much as date; the difficulty for medical professionals to find out how to utilize an overwelming range of different professional systems for different medical conditions; and maybe most crucially, the hesitation of doctors to rely on a computer-made medical diagnosis over their gut instinct, even for specific domains where the expert systems might surpass a typical physician. Equity capital money deserted AI almost over night. The world AI conference IJCAI hosted a huge and extravagant trade convention and thousands of nonacademic guests in 1987 in Vancouver; the primary AI conference the following year, AAAI 1988 in St. Paul, was a little and strictly academic affair. [9]

Including more strenuous foundations, 1993-2011

Uncertain reasoning

Both statistical techniques and extensions to reasoning were tried.

One analytical method, hidden Markov models, had already been promoted in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized making use of Bayesian Networks as a sound but effective method of dealing with unsure reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian methods were used effectively in professional systems. [57] Even later on, in the 1990s, statistical relational knowing, an approach that combines probability with rational formulas, permitted probability to be combined 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 likewise tried. For example, non-monotonic reasoning could be utilized with fact upkeep systems. A fact maintenance system tracked presumptions and validations for all reasonings. It permitted reasonings to be withdrawn when assumptions were learnt to be incorrect or a contradiction was obtained. Explanations might be supplied for a reasoning by describing which rules were used to produce it and then continuing through underlying inferences and guidelines all the way back to root assumptions. [58] Lofti Zadeh had presented a different kind of extension to deal with the representation of ambiguity. For instance, in choosing how “heavy” or “tall” a man is, there is frequently no clear “yes” or “no” answer, and a predicate for heavy or tall would instead return worths in between 0 and 1. Those worths represented to what degree the predicates were true. His fuzzy logic even more supplied a way for propagating combinations of these worths through sensible formulas. [59]

Machine learning

Symbolic device learning techniques were investigated to attend to the knowledge acquisition traffic jam. One of the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test strategy to create possible rule hypotheses to check against spectra. Domain and job understanding minimized the number of candidates evaluated to a manageable size. Feigenbaum explained Meta-DENDRAL as

… the culmination of my dream of the early to mid-1960s relating to theory development. The conception was that you had a problem solver like DENDRAL that took some inputs and produced an output. In doing so, it used layers of knowledge to guide and prune the search. That understanding acted due to the fact that we spoke with people. But how did the people 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 understanding of mass spectrometry that DENDRAL might utilize to fix specific hypothesis development problems. We did it. We were even able to publish new understanding of mass spectrometry in the Journal of the American Chemical Society, giving credit just in a footnote that a program, Meta-DENDRAL, actually did it. We had the ability to do something that had actually been a dream: to have a computer program developed a brand-new and publishable piece of science. [51]

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

Advances were made in comprehending artificial intelligence theory, too. Tom Mitchell introduced variation space learning which explains knowing as an explore a space of hypotheses, with upper, more basic, and lower, more particular, boundaries including all viable hypotheses constant with the examples seen up until now. [62] More officially, Valiant presented Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of machine learning. [63]

Symbolic machine finding out incorporated more than finding out by example. E.g., John Anderson offered a cognitive model of human knowing where ability practice leads to a compilation of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a trainee may discover to apply “Supplementary angles are 2 angles whose measures sum 180 degrees” as a number of different procedural guidelines. E.g., one rule may say that if X and Y are supplementary and you understand X, then Y will be 180 – X. He called his approach “understanding compilation”. ACT-R has actually been used effectively to model aspects of human cognition, such as finding out and retention. ACT-R is likewise utilized in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer system shows, and algebra to school children. [64]

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

As an option to reasoning, Roger Schank introduced case-based reasoning (CBR). The CBR technique described in his book, Dynamic Memory, [67] focuses first on keeping in mind essential analytical cases for future usage and generalizing them where appropriate. When faced with a new problem, CBR recovers the most comparable previous case and adjusts it to the specifics of the present issue. [68] Another alternative to logic, hereditary algorithms and hereditary shows are based upon an evolutionary design of knowing, where sets of rules are encoded into populations, the rules govern the behavior of individuals, and selection of the fittest prunes out sets of unsuitable guidelines over numerous generations. [69]

Symbolic maker knowing was used to finding out concepts, rules, heuristics, and problem-solving. Approaches, besides those above, consist of:

1. Learning from direction or advice-i.e., taking human direction, posed as advice, and identifying how to operationalize it in particular circumstances. For instance, in a video game of Hearts, learning precisely how to play a hand to “prevent taking points.” [70] 2. Learning from exemplars-improving performance by accepting subject-matter professional (SME) feedback during training. When problem-solving fails, querying the expert to either discover a brand-new prototype for analytical or to find out a brand-new explanation regarding precisely why one exemplar is more relevant than another. For instance, the program Protos learned to diagnose tinnitus cases by communicating with an audiologist. [71] 3. Learning by analogy-constructing issue solutions based upon similar issues seen in the past, and after that modifying their options to fit a new circumstance or domain. [72] [73] 4. Apprentice knowing systems-learning novel options to issues by observing human analytical. Domain understanding discusses why unique solutions are proper and how the service can be generalized. LEAP found out how to create VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing jobs to perform experiments and then learning from the results. Doug Lenat’s Eurisko, for example, found out heuristics to beat human gamers at the Traveller role-playing video game for two years in a row. [75] 6. Learning macro-operators-i.e., looking for helpful macro-operators to be gained from sequences of standard analytical actions. Good macro-operators streamline analytical by permitting 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 approach has actually been compared to deep knowing as complementary “… with parallels having actually been drawn often times by AI scientists between Kahneman’s research study on human reasoning and decision making – 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 reasoning, planning, and explanation while deep learning is more apt for fast pattern acknowledgment in perceptual applications with noisy data. [17] [18]

Neuro-symbolic AI: incorporating neural and symbolic approaches

Neuro-symbolic AI attempts to incorporate neural and symbolic architectures in a manner that addresses strengths and weak points of each, in a complementary fashion, in order to support robust AI efficient in thinking, finding out, and cognitive modeling. As argued by Valiant [77] and lots of others, [78] the effective building and construction of abundant computational cognitive models requires the mix of sound symbolic reasoning and effective (device) learning designs. Gary Marcus, likewise, argues that: “We can not construct abundant cognitive designs in an appropriate, automatic method without the triumvirate of hybrid architecture, rich prior understanding, and sophisticated techniques for reasoning.”, [79] and in specific: “To construct a robust, knowledge-driven method to AI we need to have the equipment of symbol-manipulation in our toolkit. Too much of beneficial understanding is abstract to make do without tools that represent and manipulate abstraction, and to date, the only equipment that we understand of that can manipulate such abstract knowledge dependably is the device of sign control. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based on a need to address the 2 type of believing gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having two elements, System 1 and System 2. System 1 is quick, automated, instinctive and unconscious. System 2 is slower, detailed, and specific. System 1 is the kind used for pattern recognition while System 2 is far much better suited for planning, deduction, and deliberative thinking. In this view, deep knowing finest models the very first sort of believing while symbolic reasoning finest designs the second kind and both are required.

Garcez and Lamb explain research in this location as being ongoing for a minimum of the previous twenty years, [83] dating from their 2002 book on neurosymbolic knowing systems. [84] A series of workshops on neuro-symbolic thinking has actually been held every year because 2005, see http://www.neural-symbolic.org/ for details.

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

The integration of the symbolic and connectionist paradigms of AI has been pursued by a fairly small research neighborhood over the last 2 decades and has yielded a number of substantial outcomes. Over the last years, neural symbolic systems have been shown efficient in getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in reaction to Smolensky (1988 ); see also (Hinton, 1990). Neural networks were shown capable of representing modal and temporal reasonings (d’Avila Garcez and Lamb, 2006) and fragments of first-order reasoning (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have actually been applied to a variety of problems in the locations 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 current method of numerous neural models in natural language processing, where words or subword tokens are both the ultimate input and output of big language models. Examples consist of BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic methods are utilized to call neural techniques. In this case the symbolic approach is Monte Carlo tree search and the neural techniques learn how to evaluate video game positions.
– Neural|Symbolic-uses a neural architecture to interpret affective data as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to create or identify training data that is subsequently learned by a deep knowing model, e.g., to train a neural model for symbolic calculation by using a Macsyma-like symbolic mathematics system to create or identify examples.
– Neural _ Symbolic -uses a neural net that is generated from symbolic rules. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR evidence tree generated from knowledge base rules and terms. Logic Tensor Networks [86] likewise fall under this category.
– Neural [Symbolic] -enables a neural design to straight call a symbolic thinking engine, e.g., to carry out an action or evaluate a state.

Many key research study questions stay, such as:

– What is the very best method to incorporate 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 knowledge that is difficult to encode logically be managed?

Techniques and contributions

This section offers an overview of strategies and contributions in a general context causing many other, more comprehensive posts in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered earlier in the history section.

AI shows languages

The crucial AI programming language in the US during the last symbolic AI boom duration was LISP. LISP is the 2nd earliest shows language after FORTRAN and was developed in 1958 by John McCarthy. LISP provided the first read-eval-print loop to support rapid program development. Compiled functions might be freely combined with interpreted functions. Program tracing, stepping, and breakpoints were likewise supplied, in addition to the capability to alter values or functions and continue from breakpoints or errors. It had the very first self-hosting compiler, implying that the compiler itself was originally composed in LISP and after that ran interpretively to put together the compiler code.

Other key innovations pioneered by LISP that have actually spread out to other programs languages include:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

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

In contrast to the US, in Europe the essential AI programs language throughout that same duration was Prolog. Prolog provided a built-in store of truths and stipulations that might be queried by a read-eval-print loop. The shop could act as a knowledge base and the stipulations might function as guidelines or a limited type of reasoning. As a subset of first-order reasoning Prolog was based upon Horn provisions with a closed-world assumption-any truths not known were considered false-and a distinct 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 innovators of Prolog. Prolog is a form of logic programming, which was invented by Robert Kowalski. Its history was also influenced by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of techniques. For more information see the area on the origins of Prolog in the PLANNER post.

Prolog is also a type of declarative programs. The logic stipulations that describe programs are directly analyzed to run the programs specified. No specific series of actions is needed, as holds true with imperative programs languages.

Japan promoted Prolog for its Fifth Generation Project, meaning to build special hardware for high performance. Similarly, LISP machines were built to run LISP, however as the 2nd AI boom turned to bust these business might not contend with new workstations that could now run LISP or Prolog natively at similar speeds. See the history section for more information.

Smalltalk was another prominent AI shows language. For instance, it presented 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 standard Lisp dialect. CLOS is a Lisp-based object-oriented system that permits several inheritance, in addition to incremental extensions to both classes and metaclasses, thus offering a run-time meta-object procedure. [88]

For other AI programming languages see this list of shows languages for synthetic intelligence. Currently, Python, a multi-paradigm shows language, is the most popular shows language, partly due to its comprehensive bundle library that supports data science, natural language processing, and deep learning. Python includes a read-eval-print loop, functional components such as higher-order functions, and object-oriented programs that includes metaclasses.

Search

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

Knowledge representation and thinking

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

Knowledge representation

Semantic networks, conceptual charts, frames, and reasoning are all techniques to modeling knowledge such as domain knowledge, problem-solving knowledge, and the semantic significance of language. Ontologies design essential ideas 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 deemed an ontology. YAGO incorporates WordNet as part of its ontology, to line up facts extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being utilized.

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

First-order reasoning is more basic than description logic. The automated theorem provers gone over listed below can show theorems in first-order logic. Horn provision logic is more restricted than first-order logic and is used in reasoning programs languages such as Prolog. Extensions to first-order reasoning include temporal logic, to manage time; epistemic reasoning, to reason about representative understanding; modal logic, to manage possibility and requirement; and probabilistic logics to handle reasoning and likelihood together.

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

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

Reasoning in knowledge-based systems

Knowledge-based systems have an explicit knowledge base, typically of guidelines, to enhance reusability across domains by separating procedural code and domain knowledge. A different inference engine processes rules and includes, deletes, or modifies a knowledge 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 sensible representation is used, Horn Clauses. Pattern-matching, specifically marriage, is utilized in Prolog.

A more flexible sort of problem-solving occurs when reasoning about what to do next happens, instead of simply choosing among the available actions. This kind of meta-level reasoning is utilized in Soar and in the BB1 chalkboard architecture.

Cognitive architectures such as ACT-R may have extra capabilities, such as the capability to put together regularly used knowledge into higher-level chunks.

Commonsense reasoning

Marvin Minsky first proposed frames as a way of analyzing common visual scenarios, such as a workplace, and Roger Schank extended this concept to scripts for typical routines, such as dining out. Cyc has tried to capture beneficial sensible understanding and has “micro-theories” to manage particular kinds of domain-specific thinking.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] estimates human reasoning about naive physics, such as what happens when we warm a liquid in a pot on the range. We anticipate it to heat and possibly boil over, even though we may not understand its temperature, its boiling point, or other information, such as atmospheric pressure.

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

Constraints and constraint-based reasoning

Constraint solvers carry out a more restricted sort of inference than first-order logic. They can streamline sets of spatiotemporal restrictions, such as those for RCC or Temporal Algebra, together with fixing other sort of puzzle issues, such as Wordle, Sudoku, cryptarithmetic issues, and so on. Constraint reasoning programming can be utilized to solve scheduling issues, for example with constraint managing rules (CHR).

Automated preparation

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

Natural language processing

Natural language processing focuses on dealing with language as information to perform tasks such as recognizing topics without necessarily comprehending the desired meaning. Natural language understanding, on the other hand, constructs a significance representation and utilizes that for more 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, but considering that enhanced by deep knowing methods. In symbolic AI, discourse representation theory and first-order reasoning have been used to represent sentence significances. Latent semantic analysis (LSA) and explicit semantic analysis also provided vector representations of documents. In the latter case, vector parts are interpretable as ideas named by Wikipedia short articles.

New deep learning techniques based on Transformer models have now eclipsed these earlier symbolic AI methods and achieved 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 significance of the vector components 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 standard textbook on synthetic intelligence is arranged to reflect agent architectures of increasing elegance. [91] The elegance of representatives differs from simple reactive agents, to those with a model of the world and automated planning capabilities, possibly a BDI agent, i.e., one with beliefs, desires, and intentions – or additionally a support discovering model found out gradually to select actions – approximately a mix of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep knowing for perception. [92]

In contrast, a multi-agent system includes several representatives that communicate amongst themselves with some inter-agent interaction language such as Knowledge Query and Manipulation Language (KQML). The representatives need not all have the very same internal architecture. Advantages of multi-agent systems consist of the ability to divide work amongst the agents and to increase fault tolerance when agents are lost. Research problems include how representatives reach agreement, distributed problem solving, multi-agent learning, multi-agent preparation, and dispersed restriction optimization.

Controversies arose from early on in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who accepted AI but turned down symbolic approaches-primarily connectionists-and those outside the field. Critiques from outside of the field were mostly from philosophers, on intellectual premises, but likewise from financing agencies, specifically during the 2 AI winter seasons.

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

Limitations were found in utilizing basic first-order reasoning to factor about vibrant domains. Problems were found both with regards to enumerating the prerequisites for an action to prosper and in offering axioms for what did not change after an action was performed.

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

A comparable problem, called the Qualification Problem, happens in trying to enumerate the prerequisites for an action to be successful. A boundless number of pathological conditions can be thought of, e.g., a banana in a tailpipe might prevent a vehicle from operating properly.

McCarthy’s method to repair the frame issue was circumscription, a type of non-monotonic reasoning where reductions could be made from actions that require only define what would change while not having to clearly define everything that would not change. Other non-monotonic logics supplied reality maintenance systems that revised beliefs leading to contradictions.

Other ways of managing more open-ended domains consisted of probabilistic reasoning systems and artificial intelligence to discover new ideas and rules. McCarthy’s Advice Taker can be considered as a motivation here, as it could integrate brand-new understanding offered by a human in the type of assertions or guidelines. For example, experimental symbolic device discovering systems checked out the ability to take high-level natural language guidance and to analyze it into domain-specific actionable guidelines.

Similar to the issues in managing vibrant domains, sensible thinking is also difficult to capture in formal thinking. Examples of common-sense reasoning include implicit thinking about how people believe or basic knowledge of everyday events, objects, and living animals. This kind of understanding is taken for approved 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 capture essential parts of this knowledge over more than a years) and neural systems (e.g., self-driving cars that do not understand not to drive into cones or not to hit pedestrians strolling a bicycle).

McCarthy viewed his Advice Taker as having common-sense, however his definition 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 repercussions of anything it is told and what it already understands. “

Connectionist AI: philosophical obstacles and sociological conflicts

Connectionist methods consist of 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 sophisticated techniques, such as Transformers, GANs, and other work in deep knowing.

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

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

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

The 3rd and last position I wish to examine here is what I call the moderate connectionist view, a more eclectic view of the existing debate between connectionism and symbolic AI. One of the researchers who has actually 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 sort of theories are required in order to study and model cognition. On the one hand, for some information-processing jobs (such as pattern recognition) connectionism has advantages over symbolic models. But on the other hand, for other cognitive procedures (such as serial, deductive thinking, and generative sign manipulation procedures) the symbolic paradigm offers sufficient models, and not just “approximations” (contrary to what extreme connectionists would claim). [97]

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

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

And yet, for the a lot of part, that’s how most existing AI profits. Hinton and numerous others have attempted difficult to banish symbols completely. The deep learning hope-seemingly grounded not so much in science, but in a sort of historic grudge-is that intelligent habits will emerge simply from the confluence of enormous data and deep learning. Where classical computer systems and software solve tasks by specifying sets of symbol-manipulating guidelines devoted to specific jobs, such as editing a line in a word processor or performing a calculation in a spreadsheet, neural networks usually try to solve tasks by analytical approximation and learning from examples.

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

When deep knowing reemerged in 2012, it was with a sort of take-no-prisoners attitude that has actually characterized many of the last years. By 2015, his hostility towards all things signs had totally taken shape. He offered a talk at an AI workshop at Stanford comparing symbols to aether, one of science’s greatest mistakes.

…

Since then, his anti-symbolic campaign has actually only increased in strength. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep knowing in among science’s essential journals, Nature. It closed with a direct attack on sign manipulation, calling not for reconciliation but for straight-out replacement. Later, Hinton told a gathering of European Union leaders that investing any more cash in symbol-manipulating approaches was “a substantial error,” likening it to investing in internal combustion engines in the period of electrical cars. [98]

Part of these disputes might be because of uncertain terms:

Turing award winner Judea Pearl uses a review of device knowing which, unfortunately, conflates the terms device learning and deep learning. Similarly, when Geoffrey Hinton describes symbolic AI, the connotation of the term tends to be that of professional systems dispossessed of any capability to learn. Using 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 distinctions to deep knowing being the choice of representation, localist logical rather than distributed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not simply about production guidelines composed by hand. A proper definition of AI issues knowledge representation and thinking, self-governing multi-agent systems, preparation and argumentation, in addition to knowing. [99]

Situated robotics: the world as a design

Another critique of symbolic AI is the embodied cognition method:

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

Rodney Brooks developed behavior-based robotics, one approach to embodied cognition. Nouvelle AI, another name for this method, is deemed an alternative to both symbolic AI and connectionist AI. His technique declined representations, either symbolic or distributed, as not just unnecessary, however as harmful. Instead, he developed the subsumption architecture, a layered architecture for embodied agents. Each layer achieves a different function and should function in the real world. For example, the very first robot he explains in Intelligence Without Representation, has 3 layers. The bottom layer translates finder sensors to prevent items. The middle layer causes the robot to roam around when there are no obstacles. The top layer causes the robot to go to more far-off places for more exploration. Each layer can temporarily hinder or suppress a lower-level layer. He criticized AI scientists for defining AI problems for their systems, when: “There is no tidy division in between perception (abstraction) and reasoning in the real world.” [101] He called his robotics “Creatures” and each layer was “made up of a fixed-topology network of easy finite state devices.” [102] In the Nouvelle AI approach, “First, it is critically important to test the Creatures we integrate in the real life; i.e., in the very same world that we human beings populate. It is dreadful to fall under the temptation of checking them in a simplified world initially, even with the very best intents of later moving activity to an unsimplified world.” [103] His emphasis on real-world screening was in contrast to “Early work in AI focused on video games, geometrical problems, symbolic algebra, theorem proving, and other official systems” [104] and using the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has benefits, but has actually been criticized by the other methods. Symbolic AI has been criticized as disembodied, liable to the qualification issue, and bad in managing the affective issues where deep finding out excels. In turn, connectionist AI has been criticized as inadequately fit for deliberative step-by-step issue fixing, incorporating knowledge, and dealing with planning. Finally, Nouvelle AI stands out in reactive and real-world robotics domains however has actually been slammed for troubles in including knowing and knowledge.

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

Overall, Dreyfus saw locations where AI did not have complete responses and said that Al is for that reason impossible; we now see a lot of these exact same locations undergoing continued research study and development resulting in increased capability, not impossibility. [100]

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

Notes

^ McCarthy once said: “This is AI, so we don’t care if it’s psychologically genuine”. [4] McCarthy restated 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 composes that there are “2 significant branches of synthetic intelligence: one intended at producing smart behavior regardless of how it was accomplished, and the other focused on modeling intelligent procedures discovered in nature, particularly human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not define the goal of their field as making ‘makers that fly so exactly like pigeons that they can fool even other pigeons.'” [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). “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.
^ 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 expert system: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating errors”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
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^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. “Thinking Fast and Slow in AI”. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. “AAAI Presidential Address: The State of AI”. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
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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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