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Symbolic Expert System

In expert system, symbolic artificial intelligence (likewise called classical expert system or logic-based artificial intelligence) [1] [2] is the term for the collection of all approaches in artificial intelligence research study that are based on high-level symbolic (human-readable) representations of problems, reasoning and search. [3] Symbolic AI used tools such as reasoning programs, production guidelines, semantic nets and frames, and it established applications such as knowledge-based systems (in specific, professional systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm resulted in influential ideas in search, symbolic shows languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of official understanding and thinking systems.

Symbolic AI was the dominant paradigm of AI research from the mid-1950s up until the mid-1990s. [4] Researchers in the 1960s and the 1970s were encouraged that symbolic techniques would ultimately be successful in producing a maker with artificial basic intelligence and considered this the supreme objective of their field. [citation required] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, caused impractical expectations and promises and was followed by the first AI Winter as funding dried up. [5] [6] A 2nd boom (1969-1986) happened with the increase of expert systems, their promise of catching corporate competence, and an enthusiastic business welcome. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later disappointment. [8] Problems with difficulties in understanding acquisition, preserving large understanding bases, and brittleness in dealing with out-of-domain issues arose. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers concentrated on attending to hidden problems in managing unpredictability and in understanding acquisition. [10] Uncertainty was attended to with formal methods such as hidden Markov models, Bayesian thinking, and statistical relational learning. [11] [12] Symbolic maker finding out addressed the knowledge acquisition problem with contributions consisting of Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree learning, case-based learning, and inductive reasoning programs to learn relations. [13]

Neural networks, a subsymbolic technique, had actually been pursued from early days and reemerged highly in 2012. Early examples are Rosenblatt’s perceptron knowing work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and work in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not deemed successful up until about 2012: “Until Big Data ended up being prevalent, the basic agreement in the Al community was that the so-called neural-network method was hopeless. Systems simply didn’t work that well, compared to other approaches. … A revolution can be found in 2012, when a variety of people, consisting of a group of scientists dealing with Hinton, worked out a method to utilize the power of GPUs to enormously increase the power of neural networks.” [16] Over the next a number of years, deep learning had spectacular success in managing vision, speech acknowledgment, speech synthesis, image generation, and device translation. However, since 2020, as inherent troubles with predisposition, explanation, coherence, and robustness became more evident with deep knowing methods; an increasing variety of AI researchers have actually required integrating the best of both the symbolic and neural network techniques [17] [18] and attending to areas that both techniques have problem with, such as sensible reasoning. [16]

A brief history of symbolic AI to the present day follows below. Period 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 varying a little for increased clarity.

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

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

Approaches influenced by human or animal cognition or behavior

Cybernetic techniques tried to reproduce the feedback loops between animals and their environments. A robotic turtle, with sensing units, motors for driving and guiding, and 7 vacuum tubes for control, based upon a preprogrammed neural net, was built as early as 1948. This work can be seen 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 was able to prove 38 elementary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later on generalized this work to create a domain-independent problem solver, GPS (General Problem Solver). GPS fixed problems represented with formal operators via state-space search using means-ends analysis. [21]

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

Herbert Simon and Allen Newell studied human analytical skills and attempted to formalize them, and their work laid the structures of the field of synthetic intelligence, in addition to cognitive science, operations research and management science. Their research team used the results of psychological experiments to develop programs that simulated the strategies that people used to fix problems. [22] [23] This custom, 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 extremely specialized domain-specific type of knowledge that we will see later used in professional systems, early symbolic AI researchers found another more general application of knowledge. These were called heuristics, general rules that direct a search in promising instructions: “How can non-enumerative search be useful when the underlying problem is exponentially difficult? The approach promoted by Simon and Newell is to employ heuristics: fast algorithms that may stop working on some inputs or output suboptimal options.” [26] Another essential advance was to discover a way to apply these heuristics that guarantees a service will be discovered, if there is one, not standing up to the periodic fallibility of heuristics: “The A * algorithm offered a general frame for total and optimal heuristically assisted search. A * is used as a subroutine within virtually every AI algorithm today but is still no magic bullet; its assurance of completeness is purchased at the cost of worst-case rapid time. [26]

Early work on understanding representation and reasoning

Early work covered both applications of formal reasoning highlighting first-order reasoning, together with attempts to deal with sensible thinking in a less formal way.

Modeling formal reasoning with reasoning: the “neats”

Unlike Simon and Newell, John McCarthy felt that machines did not need to imitate the specific systems of human idea, but could rather attempt to find the essence of abstract thinking and problem-solving with logic, [27] no matter whether people used the exact same algorithms. [a] His lab at Stanford (SAIL) concentrated on utilizing official logic to solve a variety of issues, consisting of knowledge representation, preparation and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and somewhere else in Europe which caused the advancement of the programs language Prolog and the science of logic programming. [32] [33]

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

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that resolving difficult issues in vision and natural language processing required advertisement hoc solutions-they argued that no basic and general principle (like logic) would catch all the aspects of smart behavior. Roger Schank explained their “anti-logic” approaches as “shabby” (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 need to be constructed by hand, one complicated principle at a time. [38] [39] [40]

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

The very first AI winter was a shock:

During the first AI summer season, many individuals believed that maker intelligence could be achieved in just a few years. The Defense Advance Research Projects Agency (DARPA) released programs to support AI research to use AI to resolve problems of nationwide security; in particular, to automate the translation of Russian to English for intelligence operations and to develop autonomous tanks for the battleground. Researchers had begun to realize that achieving AI was going to be much more difficult than was expected a decade earlier, but a mix of hubris and disingenuousness led many university and think-tank researchers to accept financing with pledges of deliverables that they should have understood they could not meet. By the mid-1960s neither beneficial natural language translation systems nor autonomous tanks had been developed, and a significant reaction embeded in. New DARPA management canceled existing AI financing programs.

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

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

Knowledge-based systems

As constraints with weak, domain-independent methods ended up being increasingly more apparent, [42] scientists from all three customs started to develop knowledge into AI applications. [43] [7] The knowledge revolution was driven by the awareness that understanding underlies high-performance, domain-specific AI applications.

Edward Feigenbaum stated:

– “In the understanding lies the power.” [44]
to explain that high performance in a specific domain requires both basic and extremely domain-specific knowledge. Ed Feigenbaum and Doug Lenat called this The Knowledge Principle:

( 1) The Knowledge Principle: if a program is to perform a complicated job well, it must know a terrific deal about the world in which it runs.
( 2) A possible extension of that concept, called the Breadth Hypothesis: there are 2 extra abilities required for smart habits in unanticipated situations: falling back on significantly general knowledge, and analogizing to specific however far-flung knowledge. [45]

Success with professional systems

This “understanding transformation” caused the development and release of specialist systems (presented by Edward Feigenbaum), the first commercially effective type of AI software application. [46] [47] [48]

Key professional systems were:

DENDRAL, which found the structure of natural molecules from their chemical formula and mass spectrometer readings.
MYCIN, which detected bacteremia – and recommended more lab tests, when necessary – by interpreting laboratory outcomes, client history, and medical professional observations. “With about 450 rules, MYCIN had the ability to perform as well as some experts, and significantly better than junior physicians.” [49] INTERNIST and CADUCEUS which took on internal medication medical diagnosis. Internist tried to catch the expertise of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS might ultimately detect approximately 1000 various diseases.
– GUIDON, which revealed how a knowledge base constructed for professional issue fixing might be repurposed for mentor. [50] XCON, to set up VAX computer systems, a then laborious procedure that could take up to 90 days. XCON reduced the time to about 90 minutes. [9]
DENDRAL is considered the very first specialist system that count on knowledge-intensive analytical. It is described listed below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

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

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, inventor of the chemical behind the birth control tablet, and likewise among the world’s most appreciated mass spectrometrists. Carl and his postdocs were world-class professionals in mass spectrometry. We started to include to their knowledge, creating understanding of engineering as we went along. These experiments totaled up to titrating DENDRAL a growing number of understanding. The more you did that, the smarter the program became. We had really excellent results.

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

The other specialist systems mentioned above followed DENDRAL. MYCIN exemplifies the traditional professional system architecture of a knowledge-base of rules paired to a symbolic reasoning mechanism, including making use of certainty aspects to manage unpredictability. GUIDON reveals how an explicit understanding base can be repurposed for a 2nd application, tutoring, and is an example of an intelligent tutoring system, a specific kind of knowledge-based application. Clancey revealed that it was not adequate just to use MYCIN’s guidelines for instruction, but that he likewise needed to add guidelines for dialogue management and trainee modeling. [50] XCON is significant since of the countless dollars it conserved DEC, which activated the professional system boom where most all major corporations in the US had expert systems groups, to record corporate expertise, protect it, and automate it:

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

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

Architecture of knowledge-based and skilled systems

A key part of the system architecture for all professional systems is the knowledge base, which shops facts and guidelines for problem-solving. [53] The easiest method for a skilled system knowledge base is merely a collection or network of production guidelines. Production rules link signs in a relationship comparable to an If-Then statement. The expert system processes the guidelines to make deductions and to determine what additional info it requires, i.e. what questions to ask, utilizing human-readable symbols. For example, OPS5, CLIPS and their successors Jess and Drools operate in this style.

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

Blackboard systems are a second type of knowledge-based or professional system architecture. They model a neighborhood of professionals incrementally contributing, where they can, to solve a problem. The issue is represented in multiple levels of abstraction or alternate views. The professionals (knowledge sources) offer their services whenever they acknowledge they can contribute. Potential analytical actions are represented on an agenda that is upgraded as the issue scenario changes. A controller decides how helpful each contribution is, and who need to make the next analytical action. One example, the BB1 blackboard architecture [54] was initially inspired by research studies of how human beings plan to carry out several jobs in a trip. [55] A development of BB1 was to use the exact same blackboard model to fixing its control issue, i.e., its controller performed meta-level reasoning with understanding sources that monitored how well a strategy or the analytical was proceeding and could switch from one method to another as conditions – such as objectives or times – changed. BB1 has been applied in numerous domains: building and construction site planning, intelligent tutoring systems, and real-time patient monitoring.

The second AI winter, 1988-1993

At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were selling LISP machines particularly targeted to speed up the advancement of AI applications and research. In addition, numerous artificial intelligence business, 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 best describes the second AI winter season that followed:

Many factors can be provided for the arrival of the 2nd AI winter. The hardware companies failed when far more economical basic Unix workstations from Sun together with great compilers for LISP and Prolog came onto the marketplace. Many commercial releases of professional systems were terminated when they showed too expensive to maintain. Medical professional systems never ever caught on for numerous reasons: the problem in keeping them approximately date; the obstacle for medical specialists to learn how to utilize a bewildering range of different professional systems for different medical conditions; and perhaps most crucially, the unwillingness of doctors to trust a computer-made diagnosis over their gut impulse, even for specific domains where the expert systems might outperform an average medical professional. Equity capital cash deserted AI practically overnight. The world AI conference IJCAI hosted a huge and luxurious exhibition and thousands of nonacademic guests in 1987 in Vancouver; the main AI conference the list below year, AAAI 1988 in St. Paul, was a small and strictly academic affair. [9]

Adding in more rigorous structures, 1993-2011

Uncertain thinking

Both analytical approaches and extensions to reasoning were attempted.

One analytical method, hidden Markov designs, had currently been popularized in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized the use of Bayesian Networks as a noise however efficient way of managing uncertain thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian approaches were applied successfully in expert systems. [57] Even later, in the 1990s, analytical relational knowing, a technique that combines probability with rational formulas, allowed possibility to be combined with first-order logic, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order reasoning to assistance were likewise attempted. For example, non-monotonic reasoning could be used with reality upkeep systems. A truth upkeep system tracked presumptions and reasons for all inferences. It allowed inferences to be withdrawn when presumptions were learnt to be inaccurate or a contradiction was derived. Explanations could be provided for an inference by discussing which rules were applied to develop it and then continuing through underlying reasonings and guidelines all the method back to root assumptions. [58] Lofti Zadeh had introduced a various kind of extension to manage the representation of vagueness. For example, in deciding how “heavy” or “tall” a guy is, there is frequently 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 true. His fuzzy logic further provided a means for propagating combinations of these values through rational formulas. [59]

Machine knowing

Symbolic maker learning approaches were examined to deal with the knowledge acquisition traffic jam. One of the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test method to generate possible rule hypotheses to test against spectra. Domain and job knowledge lowered the variety of prospects evaluated to a workable size. Feigenbaum explained Meta-DENDRAL as

… the conclusion of my imagine the early to mid-1960s relating to theory development. The conception was that you had a problem solver like DENDRAL that took some inputs and produced an output. In doing so, it utilized layers of understanding to steer and prune the search. That understanding acted because we spoke with people. But how did individuals get the understanding? By looking at thousands of spectra. So we desired a program that would take a look at countless spectra and infer the knowledge of mass spectrometry that DENDRAL might use to fix individual hypothesis formation issues. We did it. We were even able to publish new knowledge of mass spectrometry in the Journal of the American Chemical Society, giving credit only in a footnote that a program, Meta-DENDRAL, in fact did it. We were able to do something that had been a dream: to have a computer program developed a brand-new and publishable piece of science. [51]

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

Advances were made in understanding artificial intelligence theory, too. Tom Mitchell presented variation area learning which describes learning as a search through a space of hypotheses, with upper, more basic, and lower, more particular, boundaries encompassing all viable hypotheses constant with the examples seen up until now. [62] More officially, Valiant introduced Probably Approximately Correct Learning (PAC Learning), a framework for the mathematical analysis of device knowing. [63]

Symbolic machine finding out included more than finding out by example. E.g., John Anderson offered a cognitive model of human learning where skill practice leads to a collection of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a student might learn to use “Supplementary angles are two angles whose measures sum 180 degrees” as several different procedural guidelines. E.g., one rule may say that if X and Y are additional and you understand X, then Y will be 180 – X. He called his technique “knowledge collection”. ACT-R has actually been utilized successfully to design elements of human cognition, such as finding out and retention. ACT-R is likewise used in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer programs, and algebra to school children. [64]

Inductive logic programs was another method to learning that permitted reasoning programs to be synthesized from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) might manufacture Prolog programs from examples. [65] John R. Koza used hereditary algorithms to program synthesis to develop hereditary programming, which he utilized to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger offered a more basic approach to program synthesis that manufactures a functional program in the course of showing its specifications to be correct. [66]

As an alternative to reasoning, Roger Schank presented case-based reasoning (CBR). The CBR technique laid out in his book, Dynamic Memory, [67] focuses first on keeping in mind key problem-solving cases for future usage and generalizing them where suitable. When faced with a brand-new problem, CBR recovers the most comparable previous case and adapts it to the specifics of the present issue. [68] Another option to logic, hereditary algorithms and hereditary shows are based on an evolutionary design of learning, where sets of rules are encoded into populations, the rules govern the habits of individuals, and selection of the fittest prunes out sets of unsuitable rules over lots of generations. [69]

Symbolic device knowing was used to discovering ideas, rules, heuristics, and analytical. Approaches, besides those above, include:

1. Learning from instruction or advice-i.e., taking human direction, impersonated suggestions, and determining how to operationalize it in specific circumstances. For example, in a game of Hearts, discovering precisely how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving performance by accepting subject-matter professional (SME) feedback throughout training. When problem-solving stops working, querying the professional to either learn a new exemplar for analytical or to discover a brand-new explanation as to exactly why one prototype is more appropriate than another. For instance, the program Protos found out to diagnose tinnitus cases by interacting with an audiologist. [71] 3. Learning by analogy-constructing issue options based on similar issues seen in the past, and after that customizing their services to fit a new circumstance or domain. [72] [73] 4. Apprentice knowing systems-learning novel solutions to issues by observing human problem-solving. Domain knowledge describes why unique solutions are correct and how the solution can be generalized. LEAP found out how to create VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing tasks to perform experiments and then finding out from the results. Doug Lenat’s Eurisko, for instance, learned heuristics to beat human gamers at the Traveller role-playing game for 2 years in a row. [75] 6. Learning macro-operators-i.e., looking for helpful macro-operators to be discovered from sequences of standard problem-solving actions. Good macro-operators streamline analytical by permitting issues to be resolved at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now

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

Neuro-symbolic AI: incorporating neural and symbolic methods

Neuro-symbolic AI attempts 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, finding out, and cognitive modeling. As argued by Valiant [77] and many others, [78] the reliable construction of abundant computational cognitive designs demands the combination of sound symbolic reasoning and effective (maker) learning models. Gary Marcus, similarly, argues that: “We can not build rich cognitive designs in a sufficient, automatic way without the set of three of hybrid architecture, abundant prior knowledge, and sophisticated techniques for thinking.”, [79] and in particular: “To build a robust, knowledge-driven approach to AI we need to have the machinery of symbol-manipulation in our toolkit. Excessive 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 symbol 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 resolve the two type of believing gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having two parts, System 1 and System 2. System 1 is quickly, automatic, intuitive and unconscious. System 2 is slower, step-by-step, and specific. System 1 is the kind used for pattern acknowledgment while System 2 is far better fit for preparation, deduction, and deliberative thinking. In this view, deep learning best designs the first sort of believing while symbolic reasoning best models the second kind and both are needed.

Garcez and Lamb describe research in this location as being ongoing for a minimum of the past 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 integration of the symbolic and connectionist paradigms of AI has been pursued by a reasonably little research study neighborhood over the last 20 years and has yielded numerous considerable results. Over the last decade, 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 efficient in representing modal and temporal reasonings (d’Avila Garcez and Lamb, 2006) and pieces of first-order logic (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have been used to a variety of issues in the areas of bioinformatics, control engineering, software confirmation and adjustment, visual intelligence, ontology learning, and computer video games. [78]

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

– Symbolic Neural symbolic-is the existing technique of numerous neural designs in natural language processing, where words or subword tokens are both the supreme input and output of big language designs. Examples consist of BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic methods are used to call neural strategies. In this case the symbolic method is Monte Carlo tree search and the neural strategies find out how to evaluate video game positions.
– Neural|Symbolic-uses a neural architecture to translate perceptual information as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to produce or label training data that is subsequently learned by a deep learning design, e.g., to train a neural model for symbolic calculation by utilizing a Macsyma-like symbolic mathematics system to produce or identify examples.
– Neural _ Symbolic -utilizes a neural net that is created from symbolic guidelines. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR proof tree generated from understanding base rules and terms. Logic Tensor Networks [86] likewise fall under this classification.
– Neural [Symbolic] -permits a neural model to directly call a symbolic thinking engine, e.g., to perform an action or evaluate a state.

Many key research study concerns stay, such as:

– What is the finest method to incorporate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and extracted from them?
– How should sensible knowledge be found out and reasoned about?
– How can abstract knowledge that is hard to encode logically be handled?

Techniques and contributions

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

AI programs languages

The crucial AI programs language in the US throughout the last symbolic AI boom period was LISP. LISP is the second earliest shows language after FORTRAN and was produced in 1958 by John McCarthy. LISP provided the first read-eval-print loop to support rapid program advancement. Compiled functions might be easily blended with translated functions. Program tracing, stepping, and breakpoints were likewise offered, along with the ability to alter worths or functions and continue from breakpoints or errors. It had the very first self-hosting compiler, suggesting that the compiler itself was originally written in LISP and after that ran interpretively to compile the compiler code.

Other crucial innovations pioneered by LISP that have actually infected other programming languages include:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

Programs were themselves data structures that other programs might run on, enabling the easy definition of higher-level languages.

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

Alain Colmerauer and Philippe Roussel are credited as the creators of Prolog. Prolog is a type of reasoning programs, 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 detail see the section on the origins of Prolog in the PLANNER short article.

Prolog is also a sort of declarative shows. The reasoning provisions that describe programs are straight interpreted to run the programs specified. No specific series of actions is needed, as is the case with necessary shows languages.

Japan promoted Prolog for its Fifth Generation Project, meaning to construct unique hardware for high performance. Similarly, LISP devices were built to run LISP, however as the 2nd AI boom turned to bust these business could not compete with brand-new workstations that could now run LISP or Prolog natively at similar speeds. See the history area for more detail.

Smalltalk was another influential AI programming 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 present basic Lisp dialect. CLOS is a Lisp-based object-oriented system that allows multiple inheritance, in addition to incremental extensions to both classes and metaclasses, thus supplying a run-time meta-object protocol. [88]

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

Search

Search develops in many type of problem solving, including planning, restraint fulfillment, and playing games such as checkers, chess, and go. The very best understood AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven 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 thinking

Multiple various techniques to represent knowledge and after that factor with those representations have actually been examined. Below is a fast summary of techniques to knowledge representation and automated reasoning.

Knowledge representation

Semantic networks, conceptual graphs, frames, and reasoning are all methods to modeling understanding such as domain knowledge, analytical knowledge, and the semantic significance of language. Ontologies model key principles and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be used for any domain while WordNet is a lexical resource that can likewise be deemed an ontology. YAGO incorporates WordNet as part of its ontology, to align truths extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being utilized.

Description reasoning is a reasoning for automated classification of ontologies and for spotting inconsistent classification data. OWL is a language utilized to represent ontologies with description logic. Protégé is an ontology editor that can read in OWL ontologies and then inspect consistency with deductive classifiers such as such as HermiT. [89]

First-order reasoning is more basic than description logic. The automated theorem provers talked about below can show theorems in first-order reasoning. Horn clause reasoning is more limited than first-order logic and is utilized in reasoning programming languages such as Prolog. Extensions to first-order reasoning consist of temporal reasoning, to manage time; epistemic reasoning, to factor about representative knowledge; modal reasoning, to deal with possibility and necessity; and probabilistic logics to deal with logic and likelihood together.

Automatic theorem proving

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

Prover9.
ACL2.
Vampire.

Prover9 can be used in conjunction with the Mace4 model checker. ACL2 is a theorem prover that can manage evidence by induction and is a descendant of the Boyer-Moore Theorem Prover, likewise referred to as Nqthm.

Reasoning in knowledge-based systems

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

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

A more versatile type of analytical happens when thinking about what to do next occurs, rather than just picking one of the available actions. This kind of meta-level reasoning is used in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R might have additional capabilities, such as the ability to assemble regularly used understanding into higher-level portions.

Commonsense reasoning

Marvin Minsky initially proposed frames as a way of analyzing common visual situations, such as an office, and Roger Schank extended this concept to scripts for typical regimens, such as dining out. Cyc has actually tried to record helpful sensible knowledge and has “micro-theories” to deal with specific sort of domain-specific reasoning.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human thinking about ignorant physics, such as what occurs when we heat a liquid in a pot on the stove. We expect it to heat and potentially boil over, despite the fact that we may not know its temperature level, its boiling point, or other details, 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 solved with restriction solvers.

Constraints and constraint-based thinking

Constraint solvers carry out a more limited kind of inference than first-order logic. They can streamline sets of spatiotemporal restraints, such as those for RCC or Temporal Algebra, along with resolving other sort of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic programming can be utilized to fix scheduling issues, for example with restriction dealing with rules (CHR).

Automated planning

The General Problem Solver (GPS) cast planning as analytical used means-ends analysis to produce strategies. STRIPS took a various approach, 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 an approach to planning where a planning issue is lowered to a Boolean satisfiability problem.

Natural language processing

Natural language processing concentrates on dealing with language as data to perform jobs such as determining subjects without always comprehending the designated meaning. Natural language understanding, in contrast, constructs a significance representation and utilizes that for additional processing, such as answering questions.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb phrase chunking are all aspects of natural language processing long managed by symbolic AI, but because enhanced by deep knowing methods. In symbolic AI, discourse representation theory and first-order reasoning have actually been utilized to represent sentence significances. Latent semantic analysis (LSA) and explicit semantic analysis likewise provided vector representations of files. In the latter case, vector elements are interpretable as principles called by Wikipedia short articles.

New deep learning approaches based on Transformer designs have actually now eclipsed these earlier symbolic AI methods and attained cutting edge efficiency 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 meaning of the vector parts is opaque.

Agents and multi-agent systems

Agents are autonomous systems embedded in an environment they view and act upon in some sense. Russell and Norvig’s standard textbook on artificial intelligence is organized to reflect agent architectures of increasing sophistication. [91] The sophistication of agents varies from simple reactive representatives, to those with a design of the world and automated preparation capabilities, possibly a BDI agent, i.e., one with beliefs, desires, and objectives – or additionally a reinforcement learning model learned over time to choose actions – as much as a combination of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep knowing for understanding. [92]

In contrast, a multi-agent system includes multiple representatives that interact among themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The representatives need not all have the very same internal architecture. Advantages of multi-agent systems consist of the ability to divide work among the agents and to increase fault tolerance when representatives are lost. Research issues include how representatives reach agreement, distributed issue fixing, multi-agent learning, multi-agent preparation, and distributed restraint optimization.

Controversies developed from at an early stage in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and between those who embraced AI but rejected symbolic approaches-primarily connectionists-and those outside the field. Critiques from beyond the field were mainly from thinkers, on intellectual grounds, however likewise from funding agencies, particularly throughout the 2 AI winter seasons.

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

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

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

A comparable problem, called the Qualification Problem, happens in trying to enumerate the prerequisites for an action to succeed. An unlimited variety of pathological conditions can be imagined, e.g., a banana in a tailpipe could prevent a car from operating properly.

McCarthy’s method to fix the frame issue was circumscription, a kind of non-monotonic reasoning where reductions could be made from actions that need only specify what would alter while not having to clearly specify everything that would not alter. Other non-monotonic logics offered reality upkeep systems that modified beliefs leading to contradictions.

Other ways of handling more open-ended domains consisted of probabilistic thinking systems and artificial intelligence to find out brand-new concepts and guidelines. McCarthy’s Advice Taker can be deemed an inspiration here, as it might include brand-new understanding provided by a human in the kind of assertions or guidelines. For example, speculative symbolic device learning systems explored the ability to take high-level natural language suggestions and to translate it into domain-specific actionable rules.

Similar to the problems in dealing with dynamic domains, sensible thinking is likewise challenging to capture in formal reasoning. Examples of sensible reasoning include implicit reasoning about how individuals think or general understanding of day-to-day occasions, things, and living creatures. This kind of understanding is considered given and not considered as noteworthy. Common-sense reasoning is an open area of research and challenging both for symbolic systems (e.g., Cyc has actually tried to catch essential parts of this knowledge over more than a decade) and neural systems (e.g., self-driving vehicles that do not understand not to drive into cones or not to hit pedestrians strolling a bike).

McCarthy viewed his Advice Taker as having sensible, however his meaning of sensible was various than the one above. [94] He defined a program as having sound judgment “if it automatically deduces for itself an adequately broad class of immediate consequences of anything it is told and what it currently knows. “

Connectionist AI: philosophical obstacles and sociological disputes

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

Three philosophical positions [96] have actually been detailed 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 completely adequate to describe it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are deemed complementary and both are needed for intelligence

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

The third and last position I want 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 researchers who has actually elaborated this position most explicitly is Andy Clark, a thinker from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark protected hybrid (partly symbolic, partially connectionist) systems. He claimed that (at least) 2 sort of theories are required in order to study and design cognition. On the one hand, for some information-processing jobs (such as pattern acknowledgment) connectionism has advantages over symbolic models. But on the other hand, for other cognitive processes (such as serial, deductive thinking, and generative symbol adjustment procedures) the symbolic paradigm offers appropriate models, and not just “approximations” (contrary to what extreme connectionists would declare). [97]

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

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

And yet, for the most part, that’s how most current AI profits. Hinton and lots of others have striven to get rid of signs altogether. The deep knowing hope-seemingly grounded not a lot in science, but in a sort of historic grudge-is that intelligent behavior will emerge simply from the confluence of huge data and deep knowing. Where classical computers and software application solve tasks by specifying sets of symbol-manipulating guidelines committed to particular tasks, such as editing a line in a word processor or performing a calculation in a spreadsheet, neural networks normally attempt to fix jobs by statistical approximation and discovering from examples.

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

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

Ever since, his anti-symbolic project has only increased in strength. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep learning in one of science’s essential journals, Nature. It closed with a direct attack on sign adjustment, calling not for reconciliation but for outright replacement. Later, Hinton told an event of European Union leaders that investing any more cash in symbol-manipulating techniques was “a big error,” comparing it to investing in internal combustion engines in the age of electrical vehicles. [98]

Part of these conflicts might be because of unclear terms:

Turing award winner Judea Pearl provides a critique of artificial intelligence which, unfortunately, conflates the terms artificial intelligence and deep learning. Similarly, when Geoffrey Hinton describes symbolic AI, the undertone of the term tends to be that of professional systems dispossessed of any ability to discover. Making use of the terms is in need of explanation. Machine learning is not restricted to association rule mining, c.f. the body of work on symbolic ML and relational learning (the distinctions to deep learning being the option of representation, localist rational instead of distributed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not just about production rules composed by hand. A proper definition of AI concerns knowledge representation and reasoning, self-governing multi-agent systems, planning and argumentation, along with knowing. [99]

Situated robotics: the world as a model

Another critique of symbolic AI is the embodied cognition technique:

The embodied cognition technique claims that it makes no sense to consider the brain separately: cognition occurs within a body, which is embedded in an environment. We require to study the system as a whole; the brain’s operating exploits consistencies in its environment, including the rest of its body. Under the embodied cognition method, robotics, vision, and other sensors end up being main, not peripheral. [100]

Rodney Brooks developed behavior-based robotics, one technique to embodied cognition. Nouvelle AI, another name for this approach, is deemed an alternative to both symbolic AI and connectionist AI. His approach rejected representations, either symbolic or dispersed, as not just unnecessary, however as detrimental. Instead, he developed the subsumption architecture, a layered architecture for embodied agents. Each layer achieves a various purpose and should operate in the real life. For example, the first robot he describes in Intelligence Without Representation, has 3 layers. The bottom layer translates sonar sensors to avoid items. The middle layer causes the robot to roam around when there are no barriers. The leading layer causes the robot to go to more far-off locations for more exploration. Each layer can briefly prevent or reduce a lower-level layer. He criticized AI scientists for specifying AI issues for their systems, when: “There is no clean department in between understanding (abstraction) and thinking in the real life.” [101] He called his robotics “Creatures” and each layer was “composed of a fixed-topology network of simple limited state makers.” [102] In the Nouvelle AI method, “First, it is extremely important to test the Creatures we construct in the real life; i.e., in the same world that we humans occupy. It is devastating to fall into the temptation of checking them in a simplified world initially, even with the best objectives of later transferring activity to an unsimplified world.” [103] His emphasis on real-world testing remained in contrast to “Early work in AI focused on games, geometrical problems, symbolic algebra, theorem proving, and other official systems” [104] and the use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has advantages, but has been criticized by the other approaches. Symbolic AI has actually been slammed as disembodied, liable to the qualification problem, and bad in handling the affective issues where deep learning excels. In turn, connectionist AI has actually been slammed as inadequately matched for deliberative detailed problem resolving, including understanding, and managing planning. Finally, Nouvelle AI excels in reactive and real-world robotics domains however has actually been slammed for difficulties in integrating knowing and knowledge.

Hybrid AIs incorporating several of these techniques are presently considered as the course forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw areas where AI did not have total answers and stated that Al is therefore difficult; we now see a lot of these very same areas undergoing ongoing research study and development leading to increased capability, not impossibility. [100]

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

Notes

^ McCarthy as soon as stated: “This is AI, so we do not care if it’s psychologically real”. [4] McCarthy reiterated 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 synthetic intelligence: one focused on producing intelligent habits no matter how it was accomplished, and the other targeted at modeling intelligent processes found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig composed “Aeronautical engineering texts do not specify the goal of their field as making ‘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 items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). “Logic-Based Artificial Intelligence”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep knowing with symbolic expert system: representing objects and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating errors”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten Zip Code Recognition”. Neural Computation. 1 (4 ): 541-551. doi:10.1162/ neco.1989.1.4.541. S2CID 41312633.
^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. “Thinking Fast and Slow in AI“. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. “AAAI Presidential Address: The State of AI“. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
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^ Russell & Norvig 2021, pp. 22-24.
^ McCorduck 2004, pp. 327-335, 434-435.
^ Crevier 1993, pp. 145-62, 197-203.
^ a b Russell & Norvig 2021, p. 23.
^ a b Clancey 1987.
^ a b Shustek, Len (2010 ). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-08-05.
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^ Garcez et al. 2002.
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