Symbolic Artificial Intelligence

In artificial intelligence, symbolic artificial intelligence (also known as classical synthetic intelligence or logic-based artificial intelligence) [1] [2] is the term for the collection of all approaches in artificial intelligence research that are based upon top-level symbolic (human-readable) representations of issues, reasoning and search. [3] Symbolic AI utilized tools such as reasoning programming, production guidelines, semantic internet and frames, and it developed applications such as knowledge-based systems (in particular, skilled systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to influential concepts in search, symbolic shows languages, representatives, multi-agent systems, the semantic web, and the strengths and limitations of formal knowledge and thinking systems.

Symbolic AI was the dominant paradigm of AI research study from the mid-1950s until the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic methods would eventually be successful in creating a machine with artificial general intelligence and considered this the ultimate goal of their field. [citation required] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, led to impractical expectations and pledges and was followed by the very first AI Winter as moneying dried up. [5] [6] A second boom (1969-1986) accompanied the increase of professional systems, their guarantee of recording business proficiency, 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 on dissatisfaction. [8] Problems with troubles in understanding acquisition, keeping large knowledge bases, and brittleness in managing out-of-domain issues emerged. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers concentrated on dealing with underlying problems in managing uncertainty and in knowledge acquisition. [10] Uncertainty was attended to with formal techniques such as hidden Markov models, Bayesian thinking, and analytical relational knowing. [11] [12] Symbolic device discovering resolved the understanding acquisition problem with contributions including Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree learning, case-based knowing, and inductive reasoning programming to find out relations. [13]

Neural networks, a subsymbolic method, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt’s perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and work in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not deemed successful until about 2012: “Until Big Data ended up being commonplace, the basic agreement in the Al neighborhood was that the so-called neural-network approach was helpless. Systems just didn’t work that well, compared to other approaches. … A revolution came in 2012, when a number of individuals, consisting of a group of researchers working with Hinton, exercised a method to use the power of GPUs to immensely increase the power of neural networks.” [16] Over the next several years, deep learning had incredible success in handling vision, speech recognition, speech synthesis, image generation, and device translation. However, considering that 2020, as fundamental difficulties with predisposition, description, coherence, and effectiveness ended up being more apparent with deep learning approaches; an increasing variety of AI researchers have required integrating the very best of both the symbolic and neural network techniques [17] [18] and attending to areas that both techniques have difficulty with, such as sensible thinking. [16]

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

The very first AI summertime: unreasonable vitality, 1948-1966

Success at early attempts in AI occurred in 3 primary areas: synthetic neural networks, understanding representation, and heuristic search, adding to high expectations. This section sums up Kautz’s reprise of early AI history.

Approaches influenced by human or animal cognition or behavior

Cybernetic approaches attempted to duplicate the feedback loops between animals and their environments. A robotic turtle, with sensing units, motors for driving and steering, and 7 vacuum tubes for control, based on a preprogrammed neural web, 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]

A crucial early symbolic AI program was the Logic theorist, composed by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it had the ability to prove 38 elementary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later generalized this work to create a domain-independent issue solver, GPS (General Problem Solver). GPS fixed problems represented with formal operators through state-space search utilizing means-ends analysis. [21]

During the 1960s, symbolic techniques attained terrific success at mimicing smart behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was concentrated in 4 organizations in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Each one developed its own design of research study. Earlier approaches based on cybernetics or artificial neural networks were abandoned or pressed into the background.

Herbert Simon and Allen Newell studied human problem-solving abilities and tried to formalize them, and their work laid the structures of the field of expert system, in addition to cognitive science, operations research study and . Their research study team utilized the results of mental experiments to develop programs that simulated the strategies that individuals utilized to fix problems. [22] [23] This tradition, focused at Carnegie Mellon University would ultimately culminate in the advancement of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the highly specialized domain-specific kinds of understanding that we will see later utilized in professional systems, early symbolic AI scientists discovered another more general application of understanding. These were called heuristics, guidelines that assist a search in promising instructions: “How can non-enumerative search be practical when the underlying problem is significantly difficult? The technique advocated by Simon and Newell is to use heuristics: quick algorithms that might stop working on some inputs or output suboptimal options.” [26] Another important advance was to discover a method to apply these heuristics that ensures a solution will be discovered, if there is one, not enduring the periodic fallibility of heuristics: “The A * algorithm supplied a general frame for complete and optimum heuristically directed search. A * is utilized as a subroutine within almost every AI algorithm today however is still no magic bullet; its warranty of efficiency is bought at the expense of worst-case exponential time. [26]

Early deal with knowledge representation and thinking

Early work covered both applications of formal thinking stressing first-order logic, together with attempts to manage sensible reasoning in a less official way.

Modeling formal reasoning with logic: the “neats”

Unlike Simon and Newell, John McCarthy felt that devices did not require to replicate the precise systems of human idea, but might rather look for the essence of abstract thinking and problem-solving with reasoning, [27] despite whether individuals used the same algorithms. [a] His lab at Stanford (SAIL) focused on utilizing formal reasoning to resolve a wide range of issues, consisting of understanding representation, planning and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and elsewhere in Europe which caused the advancement of the programs 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 resolving difficult problems in vision and natural language processing needed advertisement hoc solutions-they argued that no basic and general concept (like logic) would record all the aspects of intelligent habits. Roger Schank explained their “anti-logic” approaches as “scruffy” (as opposed to the “cool” paradigms at CMU and Stanford). [36] [37] Commonsense knowledge bases (such as Doug Lenat’s Cyc) are an example of “shabby” AI, because they must be developed by hand, one complex principle at a time. [38] [39] [40]

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

The very first AI winter season was a shock:

During the first AI summertime, many individuals thought that maker intelligence could be accomplished in simply a couple of years. The Defense Advance Research Projects Agency (DARPA) introduced programs to support AI research to use AI to fix issues of nationwide security; in specific, to automate the translation of Russian to English for intelligence operations and to produce self-governing tanks for the battleground. Researchers had begun to recognize that accomplishing AI was going to be much harder than was expected a decade earlier, however a mix of hubris and disingenuousness led many university and think-tank researchers to accept funding with promises of deliverables that they should have understood they could not fulfill. By the mid-1960s neither beneficial natural language translation systems nor self-governing tanks had been developed, and a significant reaction set in. New DARPA management canceled existing AI financing programs.

Beyond the United States, the most fertile ground for AI research was the United Kingdom. The AI winter in the United Kingdom was stimulated on not a lot by dissatisfied military leaders as by competing academics who viewed AI researchers as charlatans and a drain on research financing. A professor of applied mathematics, Sir James Lighthill, was commissioned by Parliament to assess the state of AI research study in the country. The report stated that all of the issues being worked on in AI would be much better dealt with by researchers from other disciplines-such as used mathematics. The report likewise declared that AI successes on toy issues could never ever scale to real-world applications due to combinatorial explosion. [41]

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

Knowledge-based systems

As restrictions with weak, domain-independent techniques became a growing number of apparent, [42] researchers from all three customs began to construct knowledge into AI applications. [43] [7] The knowledge revolution 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 describe that high efficiency in a specific domain needs both basic and highly domain-specific understanding. Ed Feigenbaum and Doug Lenat called this The Knowledge Principle:

( 1) The Knowledge Principle: if a program is to perform an intricate job well, it needs to know a lot about the world in which it runs.
( 2) A plausible extension of that concept, called the Breadth Hypothesis: there are 2 extra abilities essential for intelligent behavior in unforeseen situations: falling back on significantly general understanding, and analogizing to particular however far-flung understanding. [45]

Success with professional systems

This “knowledge revolution” resulted in the advancement and deployment of specialist systems (presented by Edward Feigenbaum), the very first commercially effective type of AI software. [46] [47] [48]

Key expert systems were:

DENDRAL, which found 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 laboratory results, patient history, and doctor observations. “With about 450 rules, MYCIN had the ability to carry out in addition to some specialists, and significantly much better than junior medical professionals.” [49] INTERNIST and CADUCEUS which tackled internal medication diagnosis. Internist attempted to catch the know-how of the chairman of internal medicine at the University of Pittsburgh School of Medicine while CADUCEUS could ultimately identify as much as 1000 various diseases.
– GUIDON, which demonstrated how a knowledge base built for specialist problem solving could be repurposed for teaching. [50] XCON, to configure VAX computers, a then laborious procedure that could use up to 90 days. XCON reduced the time to about 90 minutes. [9]
DENDRAL is considered the very first professional system that depend on knowledge-intensive problem-solving. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

One of the individuals at Stanford interested in computer-based models of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I desired 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 taking a look at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we began the DENDRAL Project: I was good at heuristic search approaches, and he had an algorithm that was great at creating the chemical problem space.

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, innovator of the chemical behind the birth control tablet, and likewise one of the world’s most respected mass spectrometrists. Carl and his postdocs were first-rate professionals in mass spectrometry. We started to contribute to their understanding, inventing understanding of engineering as we went along. These experiments amounted to titrating DENDRAL more and more knowledge. The more you did that, the smarter the program ended up being. We had great results.

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

The other expert systems pointed out above came after DENDRAL. MYCIN exhibits the timeless specialist system architecture of a knowledge-base of guidelines coupled to a symbolic reasoning system, including making use of certainty factors to deal with uncertainty. GUIDON demonstrates how an explicit knowledge base can be repurposed for a 2nd application, tutoring, and is an example of an intelligent tutoring system, a specific type of knowledge-based application. Clancey showed that it was not enough merely to utilize MYCIN’s rules for direction, but that he likewise needed to include guidelines for dialogue management and trainee modeling. [50] XCON is significant because of the countless dollars it conserved DEC, which set off the professional system boom where most all significant corporations in the US had skilled systems groups, to record business competence, protect it, and automate it:

By 1988, DEC’s AI group had 40 specialist systems deployed, with more en route. DuPont had 100 in use and 500 in advancement. Nearly every major U.S. corporation had its own Al group and was either utilizing or examining specialist systems. [49]

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

Architecture of knowledge-based and professional systems

A crucial part of the system architecture for all specialist systems is the knowledge base, which shops truths and rules for analytical. [53] The simplest approach for a professional system understanding base is simply a collection or network of production guidelines. Production guidelines connect signs in a relationship similar to an If-Then declaration. The specialist system processes the rules to make deductions and to determine what extra details it requires, i.e. what questions 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 backwards chaining – from goals to required data and requirements – way. Advanced knowledge-based systems, such as Soar can also carry out meta-level reasoning, that is thinking about their own thinking in terms of choosing how to fix issues and monitoring the success of problem-solving methods.

Blackboard systems are a second kind of knowledge-based or skilled system architecture. They model a community of experts incrementally contributing, where they can, to solve a problem. The problem is represented in multiple levels of abstraction or alternate views. The professionals (knowledge sources) offer their services whenever they recognize they can contribute. Potential problem-solving actions are represented on a program that is upgraded as the problem situation modifications. A controller decides how beneficial each contribution is, and who must make the next analytical action. One example, the BB1 blackboard architecture [54] was originally influenced by studies of how humans prepare to perform numerous jobs in a trip. [55] An innovation of BB1 was to apply the very same chalkboard design to solving its control issue, i.e., its controller performed meta-level thinking with understanding sources that monitored how well a strategy or the analytical was continuing and could change from one method to another as conditions – such as objectives or times – changed. BB1 has been applied in multiple domains: building site planning, intelligent tutoring systems, and real-time client monitoring.

The second AI winter, 1988-1993

At the height of the AI boom, business such as Symbolics, LMI, and Texas Instruments were selling LISP devices specifically targeted to speed up the development of AI applications and research study. In addition, numerous synthetic intelligence business, such as Teknowledge and Inference Corporation, were selling skilled system shells, training, and speaking with to corporations.

Unfortunately, the AI boom did not last and Kautz finest explains 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 excellent compilers for LISP and Prolog came onto the marketplace. Many industrial deployments of expert systems were discontinued when they showed too pricey to keep. Medical specialist systems never captured on for several reasons: the trouble in keeping them up to date; the difficulty for physician to find out how to utilize a bewildering variety of various expert systems for various medical conditions; and perhaps most crucially, the hesitation of medical professionals to trust a computer-made diagnosis over their gut impulse, even for particular domains where the specialist systems could outshine an average doctor. Equity capital money deserted AI virtually overnight. 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 list below year, AAAI 1988 in St. Paul, was a little and strictly scholastic affair. [9]

Including more rigorous structures, 1993-2011

Uncertain thinking

Both analytical methods and extensions to reasoning were attempted.

One statistical technique, hidden Markov models, had currently been popularized in the 1980s for speech acknowledgment work. [11] Subsequently, in 1988, Judea Pearl promoted making use of Bayesian Networks as a noise however effective way of handling unpredictable reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian methods were applied successfully in professional systems. [57] Even later, in the 1990s, statistical relational knowing, a method that integrates probability with logical formulas, enabled probability 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 also attempted. For example, non-monotonic reasoning could be utilized with truth maintenance systems. A fact maintenance system tracked presumptions and validations for all reasonings. It allowed inferences to be withdrawn when presumptions were discovered to be inaccurate or a contradiction was obtained. Explanations could be offered for a reasoning by discussing which rules were used to create it and after that continuing through underlying inferences and rules all the method back to root assumptions. [58] Lofti Zadeh had actually introduced a various kind of extension to handle the representation of vagueness. For instance, in choosing how “heavy” or “tall” a man is, there is regularly no clear “yes” or “no” response, and a predicate for heavy or tall would instead return worths between 0 and 1. Those values represented to what degree the predicates were real. His fuzzy reasoning further supplied a means for propagating mixes of these worths through sensible formulas. [59]

Machine learning

Symbolic maker finding out techniques were examined to resolve the knowledge acquisition bottleneck. Among the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test strategy to create plausible guideline hypotheses to check versus spectra. Domain and job understanding lowered the number of prospects tested to a manageable size. Feigenbaum explained Meta-DENDRAL as

… the culmination of my imagine 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 utilized layers of knowledge to steer and prune the search. That understanding acted due to the fact that we talked to people. But how did individuals get the understanding? By taking a look at thousands of spectra. So we wanted a program that would look at countless spectra and infer the understanding of mass spectrometry that DENDRAL might utilize to resolve specific hypothesis formation issues. We did it. We were even able to publish brand-new understanding of mass spectrometry in the Journal of the American Chemical Society, offering credit only in a footnote that a program, Meta-DENDRAL, actually did it. We were able to do something that had been a dream: to have a computer program created a new and publishable piece of science. [51]

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

Advances were made in comprehending maker knowing theory, too. Tom Mitchell introduced version area knowing which explains knowing as a search through a space of hypotheses, with upper, more basic, and lower, more particular, borders encompassing all feasible 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 knowing. [63]

Symbolic machine learning encompassed more than finding out by example. E.g., John Anderson provided a cognitive model of human knowing where skill practice results in a compilation of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a student may find out to use “Supplementary angles are two angles whose steps sum 180 degrees” as several various procedural rules. E.g., one guideline may state that if X and Y are supplemental and you understand X, then Y will be 180 – X. He called his technique “understanding compilation”. ACT-R has been used successfully to design aspects of human cognition, such as discovering and retention. ACT-R is likewise used in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer programming, and algebra to school kids. [64]

Inductive logic programming was another technique to learning that enabled reasoning programs to be synthesized from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) might synthesize Prolog programs from examples. [65] John R. Koza used hereditary algorithms to program synthesis to 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 manufactures a functional program in the course of showing its specs to be appropriate. [66]

As an alternative to logic, Roger Schank introduced case-based thinking (CBR). The CBR method detailed in his book, Dynamic Memory, [67] focuses first on keeping in mind crucial analytical cases for future usage and generalizing them where appropriate. When faced with a brand-new problem, CBR retrieves the most similar previous case and adapts it to the specifics of the current issue. [68] Another alternative to logic, genetic algorithms and genetic shows are based on an evolutionary model of knowing, where sets of rules are encoded into populations, the guidelines govern the behavior of people, and choice of the fittest prunes out sets of unsuitable guidelines over lots of generations. [69]

Symbolic machine knowing was applied to finding out principles, guidelines, heuristics, and problem-solving. Approaches, other than those above, include:

1. Learning from guideline or advice-i.e., taking human instruction, impersonated advice, and determining how to operationalize it in specific situations. For example, in a video game of Hearts, learning precisely how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving efficiency by accepting subject-matter expert (SME) feedback during training. When problem-solving fails, querying the expert to either discover a new prototype for analytical or to discover a new explanation regarding precisely why one exemplar is more pertinent than another. For example, the program Protos found out to identify ringing in the ears cases by interacting with an audiologist. [71] 3. Learning by analogy-constructing problem services based on similar issues seen in the past, and then customizing their options to fit a new situation or domain. [72] [73] 4. Apprentice knowing systems-learning novel options to issues by observing human analytical. Domain knowledge discusses why unique solutions are proper and how the option can be generalized. LEAP learned how to design VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing jobs to perform experiments and after that gaining from the outcomes. Doug Lenat’s Eurisko, for instance, discovered heuristics to beat human gamers at the Traveller role-playing game for 2 years in a row. [75] 6. Learning macro-operators-i.e., looking for helpful macro-operators to be gained from sequences of fundamental analytical actions. Good macro-operators simplify analytical by enabling issues to be solved at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now

With the rise of deep knowing, the symbolic AI technique has been compared to deep knowing as complementary “… with parallels having actually been drawn lot of times by AI scientists in between Kahneman’s research study on human reasoning and choice making – reflected 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 reasoning, respectively.” In this view, symbolic thinking is more apt for deliberative reasoning, planning, and description while deep knowing is more apt for fast pattern acknowledgment in affective applications with noisy data. [17] [18]

Neuro-symbolic AI: integrating neural and symbolic methods

Neuro-symbolic AI efforts to incorporate neural and symbolic architectures in a way that addresses strengths and weak points of each, in a complementary style, in order to support robust AI capable of reasoning, learning, and cognitive modeling. As argued by Valiant [77] and many others, [78] the reliable construction of rich computational cognitive models demands the mix of sound symbolic reasoning and efficient (device) knowing models. Gary Marcus, similarly, argues that: “We can not build abundant cognitive designs in an adequate, automatic method without the triumvirate of hybrid architecture, abundant prior knowledge, and sophisticated methods for reasoning.”, [79] and in specific: “To build a robust, knowledge-driven method to AI we must have the equipment of symbol-manipulation in our toolkit. Too much of beneficial knowledge is abstract to make do without tools that represent and control abstraction, and to date, the only equipment that we understand of that can manipulate such abstract knowledge reliably is the device of sign adjustment. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based upon a requirement to deal with the two sort of believing talked about 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 fast, automated, intuitive and unconscious. System 2 is slower, detailed, and specific. System 1 is the kind utilized for pattern recognition while System 2 is far much better fit for preparation, deduction, and deliberative thinking. In this view, deep learning finest models the very first type of thinking while symbolic thinking finest models the second kind and both are needed.

Garcez and Lamb explain research in this area as being continuous for at least the previous twenty years, [83] dating from their 2002 book on neurosymbolic knowing systems. [84] A series of workshops on neuro-symbolic thinking has been held every year since 2005, see http://www.neural-symbolic.org/ for information.

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

The integration of the symbolic and connectionist paradigms of AI has been pursued by a reasonably little research study community over the last 20 years and has yielded several significant results. Over the last decade, neural symbolic systems have been shown capable of getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in reaction to Smolensky (1988 ); see likewise (Hinton, 1990). Neural networks were shown efficient in representing modal and temporal logics (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 used to a number of issues in the areas of bioinformatics, control engineering, software application verification and adaptation, visual intelligence, ontology knowing, and video game. [78]

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

– Symbolic Neural symbolic-is the existing method of lots of neural designs in natural language processing, where words or subword tokens are both the supreme input and output of big language models. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic methods are utilized to call neural methods. In this case the symbolic method is Monte Carlo tree search and the neural techniques find out how to examine game positions.
– Neural|Symbolic-uses a neural architecture to interpret perceptual data as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to create or identify training information that is subsequently discovered by a deep learning design, e.g., to train a neural model for symbolic calculation by utilizing a Macsyma-like symbolic mathematics system to develop or label examples.
– Neural _ Symbolic -uses a neural net that is produced from symbolic guidelines. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR proof tree generated from knowledge base rules and terms. Logic Tensor Networks [86] likewise fall under this category.
– Neural [Symbolic] -enables a neural design to directly call a symbolic reasoning engine, e.g., to carry out an action or evaluate a state.

Many essential research questions remain, such as:

– What is the best method to integrate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and extracted from them?
– How should common-sense knowledge be found out and reasoned about?
– How can abstract knowledge that is tough to encode logically be managed?

Techniques and contributions

This section supplies an introduction of methods and contributions in a general context causing lots of other, more in-depth articles in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered earlier in the history area.

AI programming languages

The essential AI shows language in the US during the last symbolic AI boom period was LISP. LISP is the 2nd oldest programming language after FORTRAN and was developed in 1958 by John McCarthy. LISP supplied the first read-eval-print loop to support rapid program development. Compiled functions could be freely combined with interpreted functions. Program tracing, stepping, and breakpoints were likewise supplied, together with the ability to change values or functions and continue from breakpoints or mistakes. It had the very first self-hosting compiler, suggesting that the compiler itself was originally composed in LISP and then ran interpretively to compile the compiler code.

Other key developments pioneered by LISP that have actually spread to other programs languages consist of:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

Programs were themselves data structures that other programs could run on, allowing the simple definition of higher-level languages.

In contrast to the US, in Europe the crucial AI programming language throughout that very same period was Prolog. Prolog offered a built-in store of truths and stipulations that might be queried by a read-eval-print loop. The shop might serve as a knowledge base and the clauses might function as rules or a restricted kind of logic. As a subset of first-order logic Prolog was based on Horn provisions with a closed-world assumption-any facts not known were considered false-and a special name assumption for primitive terms-e.g., the identifier barack_obama was considered to describe precisely one object. Backtracking and unification are integrated to Prolog.

Alain Colmerauer and Philippe Roussel are credited as the developers of Prolog. Prolog is a type of reasoning programs, which was invented by Robert Kowalski. Its history was likewise affected by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of methods. For more detail see the section on the origins of Prolog in the PLANNER short article.

Prolog is likewise a type of declarative programs. The reasoning clauses that explain programs are straight analyzed to run the programs specified. No explicit series of actions is required, as holds true with vital programming languages.

Japan championed Prolog for its Fifth Generation Project, intending to construct unique hardware for high performance. Similarly, LISP makers were built to run LISP, but as the second AI boom turned to bust these companies might not compete with brand-new workstations that might now run LISP or Prolog natively at similar speeds. See the history section for more information.

Smalltalk was another prominent AI programs language. For instance, it introduced metaclasses and, together with Flavors and CommonLoops, affected the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the current standard Lisp dialect. CLOS is a Lisp-based object-oriented system that permits numerous inheritance, in addition to incremental extensions to both classes and metaclasses, hence supplying a run-time meta-object protocol. [88]

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

Search

Search develops in many kinds of issue resolving, consisting of preparation, restriction complete satisfaction, and playing 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 stipulation knowing, and the DPLL algorithm. For adversarial search when playing games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and reasoning

Multiple various methods to represent understanding and after that factor with those representations have actually been examined. Below is a fast overview of approaches to understanding representation and automated thinking.

Knowledge representation

Semantic networks, conceptual charts, frames, and logic are all methods to modeling knowledge such as domain understanding, problem-solving knowledge, and the semantic significance of language. Ontologies model essential principles and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be used for any domain while WordNet is a lexical resource that can likewise be deemed 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 logic is a reasoning for automated category of ontologies and for spotting inconsistent category 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 then check consistency with deductive classifiers such as such as HermiT. [89]

First-order reasoning is more general than description logic. The automated theorem provers gone over below can show theorems in first-order reasoning. Horn clause reasoning is more restricted than first-order reasoning and is utilized in logic shows languages such as Prolog. Extensions to first-order reasoning consist of temporal logic, to deal with time; epistemic reasoning, to reason about agent knowledge; modal reasoning, to handle possibility and need; and probabilistic reasonings to handle reasoning and possibility together.

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

Prover9 can be utilized in combination with the Mace4 design checker. ACL2 is a theorem prover that can manage proofs by induction and is a descendant of the Boyer-Moore Theorem Prover, also known as Nqthm.

Reasoning in knowledge-based systems

Knowledge-based systems have a specific understanding base, generally of rules, to enhance reusability throughout domains by separating procedural code and domain understanding. A different inference engine processes rules and includes, deletes, or customizes an understanding store.

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

A more flexible type of problem-solving occurs when reasoning about what to do next happens, rather than just selecting one of the readily available actions. This type of meta-level reasoning is utilized in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R may have extra abilities, such as the ability to put together frequently utilized understanding into higher-level pieces.

Commonsense reasoning

Marvin Minsky first proposed frames as a method of translating typical visual scenarios, such as an office, and Roger Schank extended this concept to scripts for typical routines, such as dining out. Cyc has attempted to record helpful common-sense understanding and has “micro-theories” to manage particular type of domain-specific thinking.

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

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

Constraints and constraint-based thinking

Constraint solvers carry out a more restricted kind of reasoning than first-order reasoning. They can simplify sets of spatiotemporal restrictions, such as those for RCC or Temporal Algebra, together with fixing other type of puzzle issues, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint reasoning programming can be used to solve scheduling issues, for example with restraint dealing with rules (CHR).

Automated preparation

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

Natural language processing

Natural language processing focuses on treating language as information to perform jobs such as determining topics without necessarily understanding the designated meaning. Natural language understanding, on the other hand, constructs a significance representation and utilizes that for more processing, such as addressing concerns.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all aspects of natural language processing long dealt with by symbolic AI, but because enhanced by deep learning approaches. In symbolic AI, discourse representation theory and first-order logic have been used to represent sentence meanings. Latent semantic analysis (LSA) and specific semantic analysis likewise offered vector representations of documents. In the latter case, vector components are interpretable as principles named by Wikipedia short articles.

New deep learning methods based on Transformer models have now eclipsed these earlier symbolic AI methods and attained state-of-the-art performance in natural language processing. However, Transformer designs are nontransparent and do not yet produce human-interpretable semantic representations for sentences and documents. Instead, they produce task-specific vectors where the significance of the vector components is opaque.

Agents and multi-agent systems

Agents are autonomous systems embedded in an environment they perceive and act on in some sense. Russell and Norvig’s standard textbook on artificial intelligence is organized to reflect representative architectures of increasing sophistication. [91] The elegance of agents varies from simple reactive representatives, to those with a model of the world and automated planning abilities, possibly a BDI representative, i.e., one with beliefs, desires, and intentions – or additionally a support learning design found out with time to pick actions – up to a combination of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep knowing for perception. [92]

On the other hand, a multi-agent system consists of numerous representatives that interact amongst themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The agents need not all have the very same internal architecture. Advantages of multi-agent systems consist of the ability to divide work amongst the representatives and to increase fault tolerance when agents are lost. Research issues include how representatives reach agreement, dispersed problem fixing, multi-agent knowing, multi-agent planning, and dispersed restriction optimization.

Controversies occurred from early in symbolic AI, both within the field-e.g., between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who welcomed AI however rejected symbolic approaches-primarily connectionists-and those outside the field. Critiques from beyond the field were mostly from theorists, on intellectual premises, however likewise from financing agencies, particularly throughout the two AI winters.

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

Limitations were discovered in utilizing easy first-order logic to factor about dynamic domains. Problems were discovered both with concerns to identifying the preconditions for an action to prosper and in offering 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 Expert System.” [93] A simple example takes place in “proving that one individual could enter into conversation with another”, as an axiom asserting “if a person has a telephone he still has it after searching for a number in the telephone directory” would be needed for the deduction to be successful. Similar axioms would be needed for other domain actions to specify what did not alter.

A similar issue, called the Qualification Problem, happens in attempting to mention the prerequisites for an action to prosper. An unlimited number of pathological conditions can be imagined, e.g., a banana in a tailpipe could prevent an automobile from operating properly.

McCarthy’s method to fix the frame problem was circumscription, a kind of non-monotonic reasoning where deductions could be made from actions that require only define what would change while not needing to clearly define everything that would not change. Other non-monotonic reasonings provided fact maintenance systems that modified beliefs leading to contradictions.

Other ways of managing more open-ended domains included probabilistic thinking systems and device knowing to discover new principles and rules. McCarthy’s Advice Taker can be deemed an inspiration here, as it could include new understanding supplied by a human in the form of assertions or rules. For instance, speculative symbolic machine finding out systems explored the capability to take high-level natural language guidance and to interpret it into domain-specific actionable guidelines.

Similar to the problems in dealing with vibrant domains, common-sense thinking is also challenging to record in formal reasoning. Examples of common-sense thinking consist of implicit thinking about how people believe or general knowledge of everyday occasions, things, and living animals. This type of understanding is considered given and not considered as noteworthy. Common-sense thinking is an open location of research and challenging both for symbolic systems (e.g., Cyc has actually attempted to catch crucial parts of this understanding over more than a decade) and neural systems (e.g., self-driving cars and trucks that do not know not to drive into cones or not to hit pedestrians walking a bike).

McCarthy saw his Advice Taker as having sensible, but his meaning of sensible was different than the one above. [94] He specified a program as having sound judgment “if it instantly deduces for itself a sufficiently wide class of instant repercussions of anything it is informed and what it already knows. “

Connectionist AI: philosophical challenges and sociological conflicts

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 advanced approaches, such as Transformers, GANs, and other work in deep knowing.

Three philosophical positions [96] have actually been described amongst connectionists:

1. Implementationism-where connectionist architectures implement the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is declined completely, and connectionist architectures underlie intelligence and are completely enough to explain it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are viewed as complementary and both are required for intelligence

Olazaran, in his sociological history of the debates within the neural network neighborhood, described the moderate connectionism consider as essentially compatible with existing research 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 present argument in between connectionism and symbolic AI. Among the scientists who has actually 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 protected hybrid (partly symbolic, partially connectionist) systems. He claimed that (at least) two kinds of theories are required in order to study and design cognition. On the one hand, for some information-processing tasks (such as pattern acknowledgment) connectionism has benefits over symbolic models. But on the other hand, for other cognitive procedures (such as serial, deductive reasoning, and generative sign manipulation processes) the symbolic paradigm offers adequate models, and not only “approximations” (contrary to what radical connectionists would claim). [97]

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

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

And yet, for the many part, that’s how most current AI earnings. Hinton and lots of others have actually attempted tough to eradicate signs entirely. The deep knowing hope-seemingly grounded not a lot in science, but in a sort of historical grudge-is that smart behavior will emerge simply from the confluence of massive information and deep knowing. Where classical computers and software resolve tasks by specifying sets of symbol-manipulating guidelines devoted to particular tasks, such as modifying a line in a word processor or carrying out an estimation in a spreadsheet, neural networks typically try to solve jobs by statistical approximation and gaining from examples.

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

When deep knowing reemerged in 2012, it was with a kind of take-no-prisoners mindset that has defined many of the last years. By 2015, his hostility toward all things symbols had completely taken shape. He provided a talk at an AI workshop at Stanford comparing signs to aether, among science’s biggest mistakes.

…

Since then, his anti-symbolic project has actually just increased in strength. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep learning in one of science’s most important journals, Nature. It closed with a direct attack on sign manipulation, calling not for reconciliation however for outright replacement. Later, Hinton informed an event of European Union leaders that investing any further cash in symbol-manipulating methods was “a substantial error,” comparing it to purchasing internal combustion engines in the age of electric vehicles. [98]

Part of these disputes might be due to uncertain terminology:

Turing award winner Judea Pearl offers a review of maker learning which, sadly, conflates the terms device knowing and deep learning. Similarly, when Geoffrey Hinton refers to symbolic AI, the connotation of the term tends to be that of specialist systems dispossessed of any capability to learn. Using the terminology is in need of clarification. Artificial intelligence is not confined to association guideline mining, c.f. the body of work on symbolic ML and relational knowing (the distinctions to deep learning being the option of representation, localist logical rather than dispersed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not practically production rules written by hand. A proper meaning of AI concerns understanding representation and thinking, autonomous multi-agent systems, planning and argumentation, in addition to knowing. [99]

Situated robotics: the world as a model

Another review of symbolic AI is the embodied cognition technique:

The embodied cognition method declares that it makes no sense to consider the brain individually: cognition takes location 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 technique, robotics, vision, and other sensing units become main, not peripheral. [100]

Rodney Brooks developed behavior-based robotics, one technique to embodied cognition. Nouvelle AI, another name for this approach, is viewed as an alternative to both symbolic AI and connectionist AI. His method turned down representations, either symbolic or dispersed, as not just unneeded, however as detrimental. Instead, he developed the subsumption architecture, a layered architecture for embodied representatives. Each layer accomplishes a different function and must work in the genuine world. For example, the first robot he describes in Intelligence Without Representation, has three layers. The bottom layer analyzes sonar sensors to prevent objects. The middle layer triggers the robotic to wander around when there are no challenges. The leading layer triggers the robotic to go to more remote places for more expedition. Each layer can momentarily prevent or suppress a lower-level layer. He criticized AI scientists for specifying AI issues for their systems, when: “There is no tidy division 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 technique, “First, it is vitally crucial to evaluate the Creatures we construct in the real life; i.e., in the same world that we people occupy. It is devastating to fall into the temptation of checking them in a simplified world first, even with the very best intentions of later transferring activity to an unsimplified world.” [103] His emphasis on real-world screening remained in contrast to “Early operate in AI focused on video games, geometrical problems, symbolic algebra, theorem proving, and other formal systems” [104] and making use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has benefits, but has actually been slammed by the other techniques. Symbolic AI has been criticized as disembodied, responsible to the certification problem, and bad in dealing with the affective issues where deep learning excels. In turn, connectionist AI has been slammed as inadequately matched for deliberative step-by-step problem resolving, incorporating understanding, and dealing with planning. Finally, Nouvelle AI excels in reactive and real-world robotics domains but has actually been slammed for difficulties in integrating knowing and knowledge.

Hybrid AIs integrating one or more of these techniques are currently considered as the path forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw locations where AI did not have complete responses and stated that Al is therefore difficult; we now see a number of these same locations undergoing continued research and advancement causing increased ability, not impossibility. [100]

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

Notes

^ McCarthy when said: “This is AI, so we do not care if it’s psychologically genuine”. [4] McCarthy reiterated his position in 2006 at the AI@50 conference where he said “Artificial intelligence is not, by meaning, simulation of human intelligence”. [28] Pamela McCorduck writes that there are “2 major branches of artificial intelligence: one targeted at producing intelligent habits no matter how it was accomplished, and the other focused on modeling intelligent processes found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not specify the goal of their field as making ‘machines 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 artificial intelligence: representing objects and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). “Logic-Based Artificial Intelligence”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep knowing with symbolic synthetic intelligence: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating errors”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten Postal 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.
^ Lenat, Douglas B; Feigenbaum, Edward A (1988 ). “On the thresholds of knowledge”. Proceedings of the International Workshop on Expert System for Industrial Applications: 291-300. doi:10.1109/ AIIA.1988.13308. S2CID 11778085.
^ 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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