Symbolic Artificial Intelligence

In artificial intelligence, symbolic artificial intelligence (also referred to as classical expert system or logic-based expert system) [1] [2] is the term for the collection of all techniques in artificial intelligence research that are based on high-level symbolic (human-readable) representations of issues, logic and search. [3] Symbolic AI used tools such as reasoning programs, production rules, semantic nets and frames, and it established applications such as knowledge-based systems (in particular, professional systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to critical concepts in search, symbolic programs languages, agents, 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 convinced that symbolic approaches would eventually succeed in creating a device with synthetic general intelligence and considered this the ultimate objective of their field. [citation needed] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, resulted in impractical expectations and promises and was followed by the very first AI Winter as funding dried up. [5] [6] A second boom (1969-1986) occurred with the rise of professional systems, their guarantee of capturing business knowledge, and an enthusiastic business accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later dissatisfaction. [8] Problems with problems in understanding acquisition, maintaining big understanding bases, and brittleness in dealing with out-of-domain issues occurred. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists concentrated on attending to hidden issues in managing uncertainty and in understanding acquisition. [10] Uncertainty was resolved with formal approaches such as surprise Markov models, Bayesian reasoning, and learning. [11] [12] Symbolic device learning resolved the understanding acquisition problem with contributions including Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree knowing, case-based knowing, and inductive logic programs to find out relations. [13]

Neural networks, a subsymbolic approach, had been pursued from early days and reemerged highly 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 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 revolution came in 2012, when a variety of people, including a team of researchers working with Hinton, exercised a way to utilize the power of GPUs to immensely increase the power of neural networks.” [16] Over the next a number of years, deep learning had spectacular success in handling vision, speech acknowledgment, speech synthesis, image generation, and device translation. However, because 2020, as inherent difficulties with bias, explanation, comprehensibility, and robustness ended up being more evident with deep knowing techniques; an increasing number of AI scientists have actually called for combining the finest of both the symbolic and neural network approaches [17] [18] and resolving locations that both approaches have problem with, such as sensible thinking. [16]

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

The first AI summer: unreasonable vitality, 1948-1966

Success at early efforts in AI happened in 3 main locations: artificial neural networks, knowledge representation, and heuristic search, contributing to high expectations. This area summarizes Kautz’s reprise of early AI history.

Approaches motivated by human or animal cognition or behavior

Cybernetic methods attempted to replicate the feedback loops in between animals and their environments. A robotic turtle, with sensors, motors for driving and guiding, and seven vacuum tubes for control, based on a preprogrammed neural net, was developed 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]

An important early symbolic AI program was the Logic theorist, written 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 issues represented with official operators through state-space search using means-ends analysis. [21]

During the 1960s, symbolic techniques accomplished terrific success at imitating intelligent behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was focused in 4 institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Every one developed its own design of research. Earlier methods based upon cybernetics or artificial neural networks were deserted or pressed into the background.

Herbert Simon and Allen Newell studied human problem-solving skills 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 management science. Their research study group used the results of psychological experiments to establish programs that simulated the strategies that people used to resolve problems. [22] [23] This custom, focused at Carnegie Mellon University would eventually culminate in the development of the Soar architecture in the middle 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific sort of understanding that we will see later on utilized in expert systems, early symbolic AI researchers discovered another more basic application of knowledge. These were called heuristics, guidelines that assist a search in promising directions: “How can non-enumerative search be useful when the underlying problem is significantly tough? The approach promoted by Simon and Newell is to employ heuristics: fast algorithms that may fail on some inputs or output suboptimal solutions.” [26] Another important advance was to discover a way to use these heuristics that guarantees a service will be discovered, if there is one, not withstanding the periodic fallibility of heuristics: “The A * algorithm offered a basic frame for complete and ideal heuristically directed search. A * is utilized as a subroutine within practically every AI algorithm today however is still no magic bullet; its guarantee of completeness is purchased the cost of worst-case rapid time. [26]

Early deal with understanding representation and reasoning

Early work covered both applications of official thinking stressing first-order logic, in addition to efforts to handle sensible thinking in a less official way.

Modeling formal thinking with logic: the “neats”

Unlike Simon and Newell, John McCarthy felt that machines did not require to mimic the precise mechanisms of human thought, however could rather search for the essence of abstract thinking and problem-solving with reasoning, [27] no matter whether individuals utilized the exact same algorithms. [a] His lab at Stanford (SAIL) focused on utilizing official logic to resolve a variety of problems, including understanding representation, planning and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and in other places in Europe which led to the advancement of the shows language Prolog and the science of logic programs. [32] [33]

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

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] found that fixing tough issues in vision and natural language processing needed ad hoc solutions-they argued that no basic and general principle (like reasoning) would record all the elements of intelligent habits. Roger Schank explained their “anti-logic” methods as “scruffy” (instead of the “neat” paradigms at CMU and Stanford). [36] [37] Commonsense knowledge bases (such as Doug Lenat’s Cyc) are an example of “scruffy” AI, because they need to be developed by hand, one complicated principle at a time. [38] [39] [40]

The first AI winter: crushed dreams, 1967-1977

The first AI winter season was a shock:

During the first AI summertime, numerous people thought that maker intelligence could be attained in just a couple of years. The Defense Advance Research Projects Agency (DARPA) introduced programs to support AI research to use AI to solve problems of national security; in particular, to automate the translation of Russian to English for intelligence operations and to create autonomous tanks for the battlefield. Researchers had actually begun to realize that accomplishing AI was going to be much more difficult than was supposed a decade earlier, but a combination of hubris and disingenuousness led numerous university and think-tank researchers to accept funding with promises of deliverables that they need to have known they could not fulfill. By the mid-1960s neither helpful natural language translation systems nor autonomous tanks had been produced, and a dramatic backlash embeded in. New DARPA leadership canceled existing AI financing programs.

Beyond the United States, the most fertile ground for AI research was the United Kingdom. The AI winter season in the United Kingdom was spurred on not so much by disappointed military leaders as by rival academics who saw AI researchers as charlatans and a drain on research financing. A professor of used mathematics, Sir James Lighthill, was commissioned by Parliament to examine the state of AI research in the nation. The report mentioned that all of the problems being worked on in AI would be much better handled by researchers from other disciplines-such as applied mathematics. The report also declared that AI successes on toy issues might never scale to real-world applications due to combinatorial explosion. [41]

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

Knowledge-based systems

As constraints with weak, domain-independent approaches ended up being more and more evident, [42] researchers from all three traditions started to develop knowledge into AI applications. [43] [7] The knowledge revolution was driven by the realization that knowledge underlies high-performance, domain-specific AI applications.

Edward Feigenbaum stated:

– “In the understanding lies the power.” [44]
to explain that high efficiency in a specific domain 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 complex task well, it should understand a terrific deal about the world in which it operates.
( 2) A plausible extension of that principle, called the Breadth Hypothesis: there are two extra capabilities essential for intelligent habits in unforeseen situations: falling back on progressively basic understanding, and analogizing to specific but far-flung knowledge. [45]

Success with expert systems

This “understanding revolution” led to the development and deployment of specialist systems (introduced by Edward Feigenbaum), the first commercially effective form of AI software application. [46] [47] [48]

Key expert systems were:

DENDRAL, which found the structure of organic molecules from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and recommended more lab tests, when needed – by analyzing lab outcomes, client history, and medical professional observations. “With about 450 rules, MYCIN had the ability to carry out in addition to some professionals, and significantly much better than junior physicians.” [49] INTERNIST and CADUCEUS which took on internal medication medical diagnosis. Internist attempted to catch the knowledge 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 constructed for specialist problem solving might be repurposed for mentor. [50] XCON, to set up VAX computers, a then tiresome procedure that could take up to 90 days. XCON reduced the time to about 90 minutes. [9]
DENDRAL is thought about the very first specialist system that depend on knowledge-intensive problem-solving. It is explained below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

Among individuals at Stanford thinking about computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I told 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 concern 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 started the DENDRAL Project: I was proficient at heuristic search approaches, and he had an algorithm that was good at creating the chemical issue space.

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

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

The other specialist systems pointed out above followed DENDRAL. MYCIN exhibits the timeless expert system architecture of a knowledge-base of guidelines paired to a symbolic reasoning system, including making use of certainty aspects to handle unpredictability. GUIDON demonstrates how an explicit knowledge base can be repurposed for a second application, tutoring, and is an example of a smart tutoring system, a particular type of knowledge-based application. Clancey showed that it was not enough just to utilize MYCIN’s guidelines for guideline, but that he also needed to include guidelines for dialogue management and trainee modeling. [50] XCON is significant since of the millions of dollars it saved DEC, which activated the expert system boom where most all major corporations in the US had skilled systems groups, to catch business know-how, maintain it, and automate it:

By 1988, DEC’s AI group had 40 professional systems deployed, with more on the way. DuPont had 100 in usage and 500 in advancement. Nearly every major U.S. corporation had its own Al group and was either utilizing or investigating professional systems. [49]

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

A key component of the system architecture for all specialist systems is the knowledge base, which stores facts and rules for analytical. [53] The most basic method for an expert system knowledge base is simply a collection or network of production guidelines. Production guidelines link signs in a relationship comparable to an If-Then declaration. The professional system processes the rules to make deductions and to determine what extra information it needs, i.e. what concerns to ask, using human-readable symbols. For instance, OPS5, CLIPS and their followers Jess and Drools run in this fashion.

Expert systems can operate in either a forward chaining – from evidence to conclusions – or backward chaining – from goals to required information and requirements – manner. Advanced knowledge-based systems, such as Soar can also carry out meta-level reasoning, that is thinking about their own thinking in regards to choosing how to resolve problems and monitoring the success of analytical techniques.

Blackboard systems are a 2nd sort of knowledge-based or professional system architecture. They model a neighborhood of experts incrementally contributing, where they can, to solve an issue. The issue is represented in numerous levels of abstraction or alternate views. The experts (understanding sources) volunteer their services whenever they acknowledge they can contribute. Potential problem-solving actions are represented on an agenda that is upgraded as the issue circumstance changes. A controller chooses how helpful each contribution is, and who ought to make the next analytical action. One example, the BB1 chalkboard architecture [54] was initially influenced by studies of how human beings prepare to perform several tasks in a trip. [55] A development of BB1 was to use the very same chalkboard model to solving its control problem, i.e., its controller carried out meta-level reasoning with knowledge sources that kept track of how well a plan or the problem-solving was continuing and might switch from one method to another as conditions – such as objectives or times – altered. BB1 has been applied in numerous domains: building site planning, intelligent tutoring systems, and real-time client monitoring.

The second AI winter season, 1988-1993

At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were offering LISP devices particularly targeted to accelerate the advancement of AI applications and research. In addition, numerous artificial intelligence companies, such as Teknowledge and Inference Corporation, were selling professional system shells, training, and consulting to corporations.

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

Many reasons can be used for the arrival of the second AI winter season. The hardware business stopped working when far more cost-effective basic Unix workstations from Sun together with good compilers for LISP and Prolog came onto the market. Many commercial implementations of expert systems were ceased when they showed too pricey to keep. Medical expert systems never ever caught on for several reasons: the difficulty in keeping them approximately date; the obstacle for physician to learn how to use an overwelming variety of various expert systems for different medical conditions; and perhaps most crucially, the hesitation of physicians to trust a computer-made medical diagnosis over their gut instinct, even for particular domains where the expert systems might surpass an average physician. Venture capital money deserted AI almost overnight. The world AI conference IJCAI hosted a huge and lavish trade convention and thousands of nonacademic attendees in 1987 in Vancouver; the primary AI conference the following year, AAAI 1988 in St. Paul, was a small and strictly scholastic affair. [9]

Adding in more extensive foundations, 1993-2011

Uncertain thinking

Both statistical techniques and extensions to logic were attempted.

One statistical approach, concealed Markov designs, 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 efficient method of managing unsure reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian techniques were applied effectively in professional systems. [57] Even later, in the 1990s, analytical relational knowing, a method that combines likelihood with rational formulas, enabled probability to be integrated with first-order logic, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order logic to support were likewise attempted. For instance, non-monotonic thinking might be utilized with fact maintenance systems. A fact maintenance system tracked presumptions and validations for all inferences. It enabled inferences to be withdrawn when presumptions were found out to be inaccurate or a contradiction was obtained. Explanations could be attended to an inference by discussing which guidelines were used to create it and then continuing through underlying inferences and guidelines all the way back to root assumptions. [58] Lofti Zadeh had introduced a different sort of extension to deal with the representation of ambiguity. For example, in deciding how “heavy” or “tall” a guy is, there is often no clear “yes” or “no” answer, and a predicate for heavy or tall would rather return worths in between 0 and 1. Those worths represented to what degree the predicates were real. His fuzzy reasoning even more provided a way for propagating mixes of these worths through logical formulas. [59]

Artificial intelligence

Symbolic machine finding out methods were investigated to resolve the understanding acquisition traffic jam. Among the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test method to create plausible rule hypotheses to evaluate against spectra. Domain and task knowledge lowered the number of candidates evaluated to a manageable size. Feigenbaum described Meta-DENDRAL as

… the culmination of my imagine the early to mid-1960s pertaining to theory formation. 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 interviewed people. But how did the people get the knowledge? By taking a look at countless spectra. So we desired a program that would look at thousands of spectra and presume the understanding of mass spectrometry that DENDRAL could utilize to solve individual 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, providing credit only in a footnote that a program, Meta-DENDRAL, really did it. We had the ability to do something that had actually been a dream: to have a computer program created a brand-new and publishable piece of science. [51]

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

Advances were made in comprehending maker learning theory, too. Tom Mitchell presented version area learning which explains learning as a search through an area of hypotheses, with upper, more basic, and lower, more specific, borders encompassing all practical hypotheses consistent with the examples seen up until now. [62] More officially, Valiant introduced Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of artificial intelligence. [63]

Symbolic machine finding out encompassed more than finding out by example. E.g., John Anderson provided a cognitive design of human knowing where skill practice leads to a collection of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a student might discover to apply “Supplementary angles are two angles whose steps sum 180 degrees” as numerous various procedural rules. E.g., one rule may say that if X and Y are additional and you know X, then Y will be 180 – X. He called his approach “knowledge compilation”. ACT-R has actually been utilized effectively to model aspects of human cognition, such as learning and retention. ACT-R is also used in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer programs, and algebra to school kids. [64]

Inductive reasoning programming was another method to finding out that allowed logic programs to be synthesized from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) could synthesize Prolog programs from examples. [65] John R. Koza used hereditary algorithms to program synthesis to develop hereditary programs, which he utilized to synthesize LISP programs. Finally, Zohar Manna and Richard Waldinger offered a more basic method to program synthesis that synthesizes 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 remembering crucial analytical cases for future usage and generalizing them where appropriate. When confronted with a new problem, CBR obtains the most similar previous case and adjusts it to the specifics of the present issue. [68] Another alternative to logic, genetic algorithms and hereditary shows are based upon an evolutionary design of knowing, where sets of guidelines are encoded into populations, the guidelines govern the behavior of people, and choice of the fittest prunes out sets of unsuitable rules over numerous generations. [69]

Symbolic machine learning was applied to finding out ideas, rules, heuristics, and problem-solving. Approaches, besides those above, consist of:

1. Learning from instruction or advice-i.e., taking human instruction, impersonated guidance, and figuring out how to operationalize it in particular scenarios. For instance, in a video game of Hearts, finding out precisely how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving performance by accepting subject-matter professional (SME) feedback during training. When analytical stops working, querying the professional to either discover a brand-new prototype for problem-solving or to find out a brand-new explanation regarding precisely why one prototype is more relevant than another. For instance, the program Protos learned to identify tinnitus cases by connecting with an audiologist. [71] 3. Learning by analogy-constructing issue options based on comparable problems seen in the past, and then customizing their solutions to fit a brand-new circumstance or domain. [72] [73] 4. Apprentice learning systems-learning unique services to problems by observing human problem-solving. Domain understanding describes why novel options are proper and how the service can be generalized. LEAP found out how to develop VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., developing jobs to perform experiments and then discovering from the results. Doug Lenat’s Eurisko, for example, discovered heuristics to beat human players at the Traveller role-playing game for 2 years in a row. [75] 6. Learning macro-operators-i.e., looking for useful macro-operators to be gained from sequences of basic analytical actions. Good macro-operators streamline analytical by allowing problems to be solved at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now

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

Neuro-symbolic AI: incorporating neural and symbolic approaches

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 efficient in thinking, learning, and cognitive modeling. As argued by Valiant [77] and many others, [78] the effective construction of rich computational cognitive models requires the mix of sound symbolic reasoning and efficient (maker) knowing models. Gary Marcus, likewise, argues that: “We can not construct rich cognitive designs in an appropriate, automatic way without the triune of hybrid architecture, rich anticipation, and advanced techniques for thinking.”, [79] and in specific: “To develop a robust, knowledge-driven method to AI we must have the equipment of symbol-manipulation in our toolkit. Excessive of helpful knowledge is abstract to make do without tools that represent and control abstraction, and to date, the only machinery that we know of that can manipulate such abstract understanding reliably is the apparatus of symbol 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 resolve the 2 sort of thinking discussed in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having two components, System 1 and System 2. System 1 is quickly, automated, instinctive and unconscious. System 2 is slower, detailed, and specific. System 1 is the kind used for pattern acknowledgment while System 2 is far much better fit for planning, deduction, and deliberative thinking. In this view, deep learning finest models the very first sort of thinking while symbolic reasoning best designs the second kind and both are needed.

Garcez and Lamb explain research in this location as being ongoing 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 given that 2005, see http://www.neural-symbolic.org/ for information.

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

The combination of the symbolic and connectionist paradigms of AI has been pursued by a fairly little research study neighborhood over the last 20 years and has actually yielded a number of considerable outcomes. Over the last years, neural symbolic systems have been shown efficient in overcoming 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 revealed 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 been applied to a variety of issues in the areas of bioinformatics, control engineering, software application verification and adaptation, visual intelligence, ontology knowing, and video game. [78]

Approaches for combination are varied. Henry Kautz’s taxonomy of neuro-symbolic architectures, along with some examples, follows:

– Symbolic Neural symbolic-is the current method of numerous neural designs in natural language processing, where words or subword tokens are both the ultimate input and output of large language designs. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic methods are used to call neural methods. In this case the symbolic technique is Monte Carlo tree search and the neural methods find out how to evaluate video game positions.
– Neural|Symbolic-uses a neural architecture to translate perceptual information as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to produce or label training data that is subsequently discovered by a deep knowing design, e.g., to train a neural model for symbolic computation by utilizing a Macsyma-like symbolic mathematics system to produce or label 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 produced from knowledge base guidelines and terms. Logic Tensor Networks [86] likewise fall under this category.
– Neural [Symbolic] -enables a neural model to directly call a symbolic reasoning engine, e.g., to perform an action or examine a state.

Many essential research study concerns stay, such as:

– What is the very best method to integrate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and drawn out from them?
– How should sensible understanding be discovered and reasoned about?
– How can abstract understanding that is difficult to encode rationally be handled?

Techniques and contributions

This area offers an overview of strategies and contributions in a total context resulting in numerous other, more in-depth articles in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered previously in the history area.

AI shows languages

The essential AI programming language in the US throughout the last symbolic AI boom period was LISP. LISP is the second earliest shows language after FORTRAN and was developed in 1958 by John McCarthy. LISP offered the first read-eval-print loop to support fast program development. Compiled functions could be easily combined with interpreted functions. Program tracing, stepping, and breakpoints were likewise offered, in addition to the capability to change worths or functions and continue from breakpoints or errors. It had the first self-hosting compiler, implying that the compiler itself was initially written in LISP and then ran interpretively to assemble the compiler code.

Other crucial developments pioneered by LISP that have actually infected other programs languages consist of:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

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

In contrast to the US, in Europe the crucial AI shows language during that exact same period was Prolog. Prolog supplied an integrated store of truths and stipulations that could be queried by a read-eval-print loop. The shop could serve as an understanding base and the clauses could act as guidelines or a limited kind of logic. As a subset of first-order reasoning Prolog was based upon Horn clauses with a closed-world assumption-any truths not understood were considered false-and an unique name presumption for primitive terms-e.g., the identifier barack_obama was considered to refer to exactly one object. Backtracking and unification are built-in to Prolog.

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

Prolog is likewise a type of declarative programs. The logic provisions that explain programs are directly interpreted to run the programs defined. No explicit series of actions is required, as holds true with essential shows languages.

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

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

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

Search

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

Knowledge representation and reasoning

Multiple various methods to represent understanding and after that factor with those representations have been investigated. Below is a fast summary of methods to understanding representation and automated reasoning.

Knowledge representation

Semantic networks, conceptual charts, frames, and logic are all approaches to modeling knowledge such as domain understanding, problem-solving understanding, and the semantic meaning of language. Ontologies model 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 utilized for any domain while WordNet is a lexical resource that can likewise be considered as an ontology. YAGO includes WordNet as part of its ontology, to align realities extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology presently being utilized.

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

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

Automatic theorem proving

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

Prover9.
ACL2.
Vampire.

Prover9 can be utilized 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 called Nqthm.

Reasoning in knowledge-based systems

Knowledge-based systems have an explicit knowledge base, typically of guidelines, to boost reusability throughout domains by separating procedural code and domain knowledge. A different inference engine processes guidelines and adds, deletes, or customizes an understanding shop.

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

A more versatile kind of analytical takes place when reasoning about what to do next takes place, rather than simply choosing among the available actions. This type of meta-level reasoning is used in Soar and in the BB1 chalkboard architecture.

Cognitive architectures such as ACT-R may have additional abilities, such as the ability to put together regularly used knowledge into higher-level portions.

Commonsense thinking

Marvin Minsky initially proposed frames as a method of translating common visual circumstances, such as an office, and Roger Schank extended this concept to scripts for typical routines, such as dining out. Cyc has attempted to catch beneficial sensible knowledge and has “micro-theories” to handle specific sort of domain-specific reasoning.

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

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

Constraints and constraint-based reasoning

Constraint solvers carry out a more limited type of reasoning than first-order reasoning. They can simplify sets of spatiotemporal constraints, such as those for RCC or Temporal Algebra, along with fixing other sort of puzzle problems, such as Wordle, Sudoku, cryptarithmetic issues, and so on. Constraint reasoning programs can be utilized to resolve scheduling issues, for instance with restraint dealing with rules (CHR).

Automated planning

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

Natural language processing

Natural language processing concentrates on dealing with language as information to carry out jobs such as recognizing topics without always understanding the intended meaning. Natural language understanding, in contrast, constructs a significance representation and utilizes that for more processing, such as answering concerns.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all aspects of natural language processing long managed by symbolic AI, however since improved by deep knowing approaches. In symbolic AI, discourse representation theory and first-order logic have actually been used to represent sentence significances. Latent semantic analysis (LSA) and specific semantic analysis likewise supplied vector representations of files. In the latter case, vector parts are interpretable as ideas called by Wikipedia articles.

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

Agents and multi-agent systems

Agents are self-governing systems embedded in an environment they view and act on in some sense. Russell and Norvig’s standard book on artificial intelligence is organized to reflect representative architectures of increasing elegance. [91] The elegance of agents differs from easy reactive representatives, to those with a model of the world and automated planning capabilities, potentially a BDI agent, i.e., one with beliefs, desires, and intentions – or alternatively a reinforcement discovering design discovered with time to select actions – up to a mix of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep learning for understanding. [92]

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

Controversies arose from at an early stage in symbolic AI, both within the field-e.g., between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and between those who accepted AI but rejected symbolic approaches-primarily connectionists-and those outside the field. Critiques from beyond the field were primarily from philosophers, on intellectual premises, but also from financing companies, especially during the two AI winters.

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

Limitations were discovered in using simple first-order reasoning to reason about dynamic domains. Problems were found both with concerns to mentioning the prerequisites for an action to succeed and in supplying axioms for what did not alter after an action was carried out.

McCarthy and Hayes presented the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Expert System.” [93] A basic example takes place in “proving that one person might enter discussion with another”, as an axiom asserting “if an individual has a telephone he still has it after looking up a number in the telephone book” would be required for the deduction to be successful. Similar axioms would be required for other domain actions to define what did not alter.

A comparable problem, called the Qualification Problem, happens in attempting to specify the preconditions for an action to prosper. A boundless variety of pathological conditions can be pictured, e.g., a banana in a tailpipe could prevent a car from running properly.

McCarthy’s technique to repair the frame issue was circumscription, a kind of non-monotonic logic where reductions could be made from actions that need only define what would alter while not having to explicitly specify whatever that would not change. Other non-monotonic logics offered truth maintenance systems that modified beliefs leading to contradictions.

Other ways of dealing with more open-ended domains included probabilistic reasoning systems and artificial intelligence to discover new principles and rules. McCarthy’s Advice Taker can be viewed as a motivation here, as it could include brand-new knowledge offered by a human in the form of assertions or rules. For example, speculative symbolic device finding out systems checked out the capability to take top-level natural language recommendations and to interpret it into domain-specific actionable rules.

Similar to the issues in dealing with dynamic domains, sensible thinking is also tough to record in official reasoning. Examples of common-sense reasoning consist of implicit thinking about how people believe or basic knowledge of daily occasions, things, and living animals. This kind of understanding is taken for given and not seen as noteworthy. Common-sense reasoning is an open area of research study and challenging both for symbolic systems (e.g., Cyc has actually attempted to catch essential parts of this knowledge over more than a decade) and neural systems (e.g., self-driving cars that do not understand not to drive into cones or not to strike pedestrians strolling a bicycle).

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

Connectionist AI: philosophical obstacles and sociological conflicts

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

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

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

Olazaran, in his sociological history of the debates within the neural network community, explained the moderate connectionism deem essentially compatible with existing research study in neuro-symbolic hybrids:

The 3rd and last position I would like to take a look at here is what I call the moderate connectionist view, a more diverse view of the present debate in between connectionism and symbolic AI. One of the scientists who has elaborated this position most clearly is Andy Clark, a thinker from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark defended hybrid (partly symbolic, partially connectionist) systems. He claimed that (at least) 2 sort of theories are needed in order to study and model 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 thinking, and generative symbol manipulation procedures) the symbolic paradigm offers appropriate designs, and not only “approximations” (contrary to what extreme connectionists would claim). [97]

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

To think that we can just desert symbol-manipulation is to suspend shock.

And yet, for the many part, that’s how most current AI proceeds. Hinton and many others have tried hard to eradicate symbols completely. The deep learning hope-seemingly grounded not a lot in science, however in a sort of historic grudge-is that smart behavior will emerge purely from the confluence of huge data and deep learning. Where classical computer systems and software application solve jobs by defining sets of symbol-manipulating guidelines committed to specific tasks, such as modifying a line in a word processor or performing a calculation in a spreadsheet, neural networks normally attempt to resolve jobs by analytical approximation and discovering from examples.

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

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

…

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

Part of these disagreements may be because of unclear terminology:

Turing award winner Judea Pearl provides a critique of artificial intelligence which, sadly, conflates the terms artificial intelligence and deep knowing. Similarly, when Geoffrey Hinton describes symbolic AI, the connotation of the term tends to be that of specialist systems dispossessed of any ability to find out. The usage of the terms needs information. Machine learning is not restricted to association rule mining, c.f. the body of work on symbolic ML and relational knowing (the distinctions to deep learning being the option of representation, localist rational rather than dispersed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not practically production guidelines composed by hand. A proper definition of AI issues understanding representation and thinking, autonomous multi-agent systems, planning and argumentation, along with knowing. [99]

Situated robotics: the world as a model

Another review of symbolic AI is the embodied cognition method:

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

Rodney Brooks created behavior-based robotics, one method to embodied cognition. Nouvelle AI, another name for this method, is considered as an alternative to both symbolic AI and connectionist AI. His technique rejected representations, either symbolic or distributed, as not only unneeded, but as harmful. Instead, he created the subsumption architecture, a layered architecture for embodied agents. Each layer achieves a various function and should function in the real world. For instance, the first robot he explains in Intelligence Without Representation, has 3 layers. The bottom layer translates finder sensing units to prevent things. The middle layer triggers the robotic to wander around when there are no obstacles. The top layer triggers the robot to go to more distant locations for additional exploration. Each layer can briefly inhibit or suppress a lower-level layer. He slammed AI scientists for specifying AI problems for their systems, when: “There is no clean division in between perception (abstraction) and reasoning in the genuine world.” [101] He called his robotics “Creatures” and each layer was “made up of a fixed-topology network of simple finite state makers.” [102] In the Nouvelle AI technique, “First, it is essential to check the Creatures we integrate in the real life; i.e., in the same world that we human beings inhabit. It is devastating to fall under the temptation of testing them in a streamlined world first, even with the finest intents of later moving activity to an unsimplified world.” [103] His emphasis on real-world testing remained in contrast to “Early work in AI concentrated on games, geometrical issues, 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 advantages, however has actually been slammed by the other methods. Symbolic AI has been criticized as disembodied, responsible to the credentials problem, and poor in managing the perceptual problems where deep learning excels. In turn, connectionist AI has been slammed as improperly matched for deliberative step-by-step issue solving, including understanding, and handling preparation. Finally, Nouvelle AI masters reactive and real-world robotics domains however has actually been slammed for troubles in integrating knowing and knowledge.

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

Overall, Dreyfus saw areas where AI did not have complete responses and said that Al is therefore impossible; we now see a number of these exact same areas going through ongoing research and advancement resulting in increased capability, not impossibility. [100]

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

Notes

^ McCarthy as soon as said: “This is AI, so we do not care if it’s emotionally real”. [4] McCarthy restated his position in 2006 at the AI@50 conference where he said “Expert system is not, by definition, simulation of human intelligence”. [28] Pamela McCorduck composes that there are “2 significant branches of expert system: one focused on producing intelligent habits regardless of how it was accomplished, and the other targeted at modeling intelligent processes discovered in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not define the goal of their field as making ‘devices that fly so precisely like pigeons that they can deceive even other pigeons.'” [30] Citations

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