Symbolic Artificial Intelligence

In expert system, symbolic artificial intelligence (likewise called classical artificial intelligence or logic-based expert system) [1] [2] is the term for the collection of all techniques in expert system research that are based upon high-level symbolic (human-readable) representations of issues, logic and search. [3] Symbolic AI utilized tools such as reasoning programs, production rules, semantic internet and frames, and it established applications such as knowledge-based systems (in particular, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm caused critical concepts in search, symbolic programs languages, representatives, multi-agent systems, the semantic web, and the strengths and limitations of formal understanding and thinking systems.

Symbolic AI was the dominant paradigm of AI research study from the mid-1950s until the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic approaches would eventually succeed in creating a maker with artificial basic intelligence and considered this the supreme goal of their field. [citation needed] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, resulted in impractical expectations and guarantees and was followed by the first AI Winter as moneying dried up. [5] [6] A 2nd boom (1969-1986) accompanied the rise of specialist systems, their guarantee of catching business expertise, and a passionate corporate embrace. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later dissatisfaction. [8] Problems with difficulties in knowledge acquisition, maintaining large knowledge bases, and brittleness in handling out-of-domain problems emerged. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists focused on dealing with hidden issues in handling unpredictability and in knowledge acquisition. [10] Uncertainty was addressed with formal methods such as covert Markov models, Bayesian reasoning, and analytical relational learning. [11] [12] Symbolic maker discovering dealt with the knowledge acquisition issue with contributions consisting of Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree knowing, case-based learning, and inductive logic programming to find out relations. [13]

Neural networks, a subsymbolic method, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt’s perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and work in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not viewed as effective until about 2012: “Until Big Data became commonplace, the basic agreement in the Al community was that the so-called neural-network method was hopeless. Systems just didn’t work that well, compared to other methods. … A transformation was available in 2012, when a variety of people, consisting of a group of researchers dealing with Hinton, worked out a method to use the power of GPUs to tremendously increase the power of neural networks.” [16] Over the next a number of years, deep learning had incredible success in dealing with vision, speech acknowledgment, speech synthesis, image generation, and device translation. However, considering that 2020, as fundamental troubles with bias, description, comprehensibility, and effectiveness became more obvious with deep learning methods; an increasing number of AI scientists have required integrating the best of both the symbolic and neural network techniques [17] [18] and attending to locations that both methods have trouble with, such as common-sense reasoning. [16]

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

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

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

Approaches influenced by human or animal cognition or behavior

Cybernetic approaches tried to duplicate the feedback loops in 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 internet, was developed as early as 1948. This work can be seen as an early precursor to later operate in neural networks, support learning, and positioned robotics. [20]

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

During the 1960s, symbolic methods achieved excellent success at mimicing smart habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was concentrated in four institutions in the 1960s: University, Stanford, MIT and (later on) University of Edinburgh. Each one developed its own style of research. Earlier approaches based on cybernetics or artificial neural networks were deserted or pushed into the background.

Herbert Simon and Allen Newell studied human analytical abilities and tried to formalize them, and their work laid the foundations of the field of expert system, along with cognitive science, operations research study and management science. Their research team used the results of psychological experiments to develop programs that simulated the techniques that people utilized to resolve issues. [22] [23] This tradition, focused at Carnegie Mellon University would ultimately culminate in the development of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific kinds of knowledge that we will see later utilized in expert systems, early symbolic AI researchers discovered another more general application of understanding. These were called heuristics, general rules that guide a search in promising instructions: “How can non-enumerative search be practical when the underlying issue is tremendously hard? The approach promoted by Simon and Newell is to employ heuristics: quick algorithms that might fail on some inputs or output suboptimal services.” [26] Another essential advance was to discover a way to use these heuristics that ensures a service will be discovered, if there is one, not standing up to the periodic fallibility of heuristics: “The A * algorithm supplied a basic frame for total and optimal heuristically guided search. A * is utilized as a subroutine within practically every AI algorithm today but is still no magic bullet; its warranty of efficiency is bought at the expense of worst-case exponential time. [26]

Early work on understanding representation and thinking

Early work covered both applications of formal reasoning highlighting first-order reasoning, in addition to attempts to manage common-sense thinking in a less formal manner.

Modeling official reasoning with reasoning: the “neats”

Unlike Simon and Newell, John McCarthy felt that machines did not need to imitate the exact mechanisms of human thought, however might rather look for the essence of abstract reasoning and problem-solving with logic, [27] despite whether individuals utilized the same algorithms. [a] His lab at Stanford (SAIL) focused on using official reasoning to fix a wide range of problems, including understanding representation, planning and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and elsewhere in Europe which led to the advancement of the programming language Prolog and the science of reasoning programs. [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] found that solving challenging problems in vision and natural language processing required ad hoc solutions-they argued that no basic and general concept (like reasoning) would catch all the elements of intelligent habits. Roger Schank explained their “anti-logic” approaches as “shabby” (rather than the “neat” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “scruffy” AI, because they must be built by hand, one complex idea 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 thought that device intelligence could be accomplished in simply a couple of years. The Defense Advance Research Projects Agency (DARPA) released programs to support AI research to use AI to solve issues of nationwide security; in specific, to automate the translation of Russian to English for intelligence operations and to create autonomous tanks for the battleground. Researchers had begun to understand that attaining AI was going to be much harder than was supposed a decade earlier, however a combination of hubris and disingenuousness led many university and think-tank researchers to accept financing with pledges of deliverables that they need to have understood they might not fulfill. By the mid-1960s neither helpful natural language translation systems nor autonomous tanks had actually been produced, and a significant backlash set in. New DARPA leadership canceled existing AI financing programs.

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

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

Knowledge-based systems

As constraints with weak, domain-independent methods ended up being increasingly more obvious, [42] researchers from all 3 customs began to develop knowledge into AI applications. [43] [7] The knowledge revolution was driven by the realization that understanding underlies high-performance, domain-specific AI applications.

Edward Feigenbaum stated:

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

( 1) The Knowledge Principle: if a program is to carry out a complicated task well, it needs to know a great deal about the world in which it runs.
( 2) A possible extension of that principle, called the Breadth Hypothesis: there are 2 additional abilities needed for intelligent behavior in unforeseen scenarios: drawing on increasingly basic understanding, and analogizing to specific but distant understanding. [45]

Success with professional systems

This “knowledge transformation” caused the development and release of professional systems (presented by Edward Feigenbaum), the very first commercially effective type 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 additional lab tests, when needed – by interpreting laboratory results, patient history, and medical professional observations. “With about 450 rules, MYCIN was able to perform along with some specialists, and substantially much better than junior medical professionals.” [49] INTERNIST and CADUCEUS which dealt with internal medicine diagnosis. Internist attempted to record the competence of the chairman of internal medicine at the University of Pittsburgh School of Medicine while CADUCEUS might eventually detect approximately 1000 various diseases.
– GUIDON, which demonstrated how an understanding base built for expert problem resolving could be repurposed for teaching. [50] XCON, to configure VAX computer systems, a then tiresome process that could take up to 90 days. XCON reduced the time to about 90 minutes. [9]
DENDRAL is considered the very first professional system that count on knowledge-intensive analytical. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

One of the individuals at Stanford interested in computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genetics. When I informed him I desired an induction “sandbox”, he stated, “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 proficient at heuristic search approaches, and he had an algorithm that was proficient at creating the chemical issue space.

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, innovator of the chemical behind the birth control pill, and also one of the world’s most respected mass spectrometrists. Carl and his postdocs were first-rate specialists in mass spectrometry. We began to include to their understanding, 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 great results.

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

The other expert systems discussed above came after DENDRAL. MYCIN exemplifies the classic professional system architecture of a knowledge-base of rules coupled to a symbolic thinking system, including using certainty elements to handle unpredictability. GUIDON shows how an explicit understanding base can be repurposed for a second application, tutoring, and is an example of an intelligent tutoring system, a particular kind of knowledge-based application. Clancey revealed that it was not adequate simply to utilize MYCIN’s rules for instruction, but that he also needed to add rules for discussion management and student modeling. [50] XCON is substantial since of the countless dollars it conserved DEC, which activated the professional system boom where most all major corporations in the US had skilled systems groups, to capture corporate competence, protect it, and automate it:

By 1988, DEC’s AI group had 40 expert systems released, with more on the way. DuPont had 100 in use and 500 in development. Nearly every significant U.S. corporation had its own Al group and was either using or investigating specialist 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 champion at that time, Garry Kasparov. [52]

Architecture of knowledge-based and professional systems

An essential component of the system architecture for all professional systems is the understanding base, which shops realities and rules for problem-solving. [53] The most basic technique for an expert system knowledge base is simply a collection or network of production guidelines. Production rules connect symbols in a relationship similar to an If-Then statement. The professional system processes the rules to make reductions and to identify what extra details it needs, i.e. what questions to ask, utilizing human-readable signs. For instance, OPS5, CLIPS and their successors Jess and Drools run in this fashion.

Expert systems can operate in either a forward chaining – from proof to conclusions – or backwards chaining – from goals to required data and requirements – way. Advanced knowledge-based systems, such as Soar can also perform meta-level reasoning, that is reasoning about their own thinking in terms of choosing how to fix issues and keeping track of the success of analytical strategies.

Blackboard systems are a 2nd sort of knowledge-based or expert system architecture. They design a neighborhood of professionals incrementally contributing, where they can, to fix an issue. The problem is represented in several levels of abstraction or alternate views. The specialists (knowledge sources) volunteer their services whenever they acknowledge they can contribute. Potential analytical actions are represented on a program that is upgraded as the issue scenario changes. A controller chooses how beneficial each contribution is, and who must make the next problem-solving action. One example, the BB1 chalkboard architecture [54] was originally influenced by research studies of how human beings plan to carry out multiple jobs in a trip. [55] An innovation of BB1 was to use the same blackboard model to fixing its control issue, i.e., its controller carried out meta-level thinking with understanding sources that kept an eye on how well a plan or the problem-solving was proceeding and might switch from one technique to another as conditions – such as goals or times – changed. BB1 has actually been used in several domains: building and construction site preparation, smart tutoring systems, and real-time patient 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 makers particularly targeted to speed up the development of AI applications and research study. In addition, several artificial intelligence business, such as Teknowledge and Inference Corporation, were selling skilled system shells, training, and speaking with to corporations.

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

Many factors can be used for the arrival of the 2nd AI winter. The hardware companies failed when a lot more economical basic Unix workstations from Sun together with excellent compilers for LISP and Prolog came onto the market. Many commercial implementations of professional systems were terminated when they proved too expensive to keep. Medical expert systems never captured on for several reasons: the difficulty in keeping them approximately date; the challenge for medical specialists to find out how to use an overwelming range of different professional systems for various medical conditions; and possibly most crucially, the hesitation of physicians to rely on a computer-made medical diagnosis over their gut impulse, even for particular domains where the expert systems could exceed a typical medical professional. Venture capital money deserted AI almost over night. The world AI conference IJCAI hosted a massive and lavish exhibition and thousands of nonacademic participants in 1987 in Vancouver; the primary AI conference the following 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 methods and extensions to logic were attempted.

One analytical technique, hidden Markov models, had actually already been popularized in the 1980s for speech acknowledgment work. [11] Subsequently, in 1988, Judea Pearl promoted using Bayesian Networks as a noise however efficient way of handling unsure thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian methods were used effectively in expert systems. [57] Even later on, in the 1990s, analytical relational knowing, a method that integrates 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 reasoning to support were likewise attempted. For example, non-monotonic reasoning could be used with truth maintenance systems. A fact upkeep system tracked presumptions and reasons for all inferences. It permitted inferences to be withdrawn when presumptions were learnt to be incorrect or a contradiction was obtained. Explanations could be attended to a reasoning by explaining which guidelines were used to produce it and after that continuing through underlying reasonings and rules all the method back to root presumptions. [58] Lofti Zadeh had introduced a various type of extension to manage the representation of uncertainty. For instance, in deciding how “heavy” or “high” a male is, there is often 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 reasoning even more offered a way for propagating mixes of these worths through sensible formulas. [59]

Artificial intelligence

Symbolic machine discovering approaches were examined to deal with the knowledge acquisition bottleneck. Among the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test method to generate possible rule hypotheses to evaluate against spectra. Domain and task understanding lowered the number of candidates tested to a manageable size. Feigenbaum described Meta-DENDRAL as

… the culmination of my dream of the early to mid-1960s having to do with theory formation. The conception was that you had an issue solver like DENDRAL that took some inputs and produced an output. In doing so, it used layers of knowledge to guide and prune the search. That knowledge got in there because we spoke with people. But how did the people get the understanding? By looking at thousands of spectra. So we desired a program that would take a look at thousands of spectra and infer the knowledge of mass spectrometry that DENDRAL might use to fix specific hypothesis development issues. We did it. We were even able to release new knowledge of mass spectrometry in the Journal of the American Chemical Society, providing credit just in a footnote that a program, Meta-DENDRAL, in fact did it. We had the ability to do something that had been a dream: to have a computer program come up with a brand-new and publishable piece of science. [51]

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

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

Symbolic device discovering incorporated more than learning by example. E.g., John Anderson provided a cognitive model of human knowing where skill practice results in a collection of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For example, a student might find out to apply “Supplementary angles are 2 angles whose steps sum 180 degrees” as numerous different procedural guidelines. E.g., one rule might say that if X and Y are supplemental and you know X, then Y will be 180 – X. He called his technique “understanding compilation”. ACT-R has actually been used successfully to design elements of human cognition, such as learning and retention. ACT-R is also utilized in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer programming, and algebra to school kids. [64]

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

As an option to logic, Roger Schank introduced case-based thinking (CBR). The CBR approach detailed in his book, Dynamic Memory, [67] focuses initially on keeping in mind essential problem-solving cases for future use and generalizing them where suitable. When faced with a brand-new problem, CBR obtains the most similar previous case and adjusts it to the specifics of the current problem. [68] Another alternative to reasoning, genetic algorithms and hereditary shows are based on an evolutionary model of learning, where sets of guidelines are encoded into populations, the guidelines govern the behavior of individuals, and selection of the fittest prunes out sets of unsuitable guidelines over many generations. [69]

Symbolic artificial intelligence was used to learning concepts, guidelines, heuristics, and analytical. Approaches, other than those above, consist of:

1. Learning from guideline or advice-i.e., taking human direction, positioned as advice, and figuring out how to operationalize it in specific scenarios. For instance, in a video game of Hearts, learning precisely how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving efficiency by accepting subject-matter expert (SME) feedback throughout training. When analytical stops working, querying the professional to either discover a new exemplar for problem-solving or to learn a brand-new description as to exactly why one exemplar is more relevant than another. For example, the program Protos learned to identify tinnitus cases by communicating with an audiologist. [71] 3. Learning by analogy-constructing issue services based upon comparable issues seen in the past, and after that modifying their solutions to fit a brand-new circumstance or domain. [72] [73] 4. Apprentice knowing systems-learning unique options to issues by observing human analytical. Domain understanding describes why novel services are right and how the solution can be generalized. LEAP discovered how to create VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., developing tasks to perform experiments and then gaining from the results. Doug Lenat’s Eurisko, for example, found out heuristics to beat human gamers at the Traveller role-playing game for 2 years in a row. [75] 6. Learning macro-operators-i.e., browsing for useful macro-operators to be gained from sequences of fundamental problem-solving actions. Good macro-operators streamline analytical by enabling problems to be fixed at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now

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

Neuro-symbolic AI: integrating neural and symbolic techniques

Neuro-symbolic AI efforts to incorporate neural and symbolic architectures in a manner that addresses strengths and weak points of each, in a complementary fashion, in order to support robust AI efficient in reasoning, finding out, and cognitive modeling. As argued by Valiant [77] and many others, [78] the reliable construction of abundant computational cognitive designs requires the mix of sound symbolic reasoning and effective (maker) knowing designs. Gary Marcus, similarly, argues that: “We can not construct rich cognitive models in an appropriate, automated way without the triune of hybrid architecture, abundant anticipation, and sophisticated strategies for thinking.”, [79] and in specific: “To build a robust, knowledge-driven approach to AI we must have the equipment of symbol-manipulation in our toolkit. Too much of helpful 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 control such abstract knowledge dependably is the apparatus of sign adjustment. ” [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 deal with the 2 kinds of thinking gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having 2 components, System 1 and System 2. System 1 is fast, automated, user-friendly and unconscious. System 2 is slower, step-by-step, and specific. System 1 is the kind utilized for pattern recognition while System 2 is far better fit for planning, reduction, and deliberative thinking. In this view, deep knowing best models the first kind of believing while symbolic thinking finest models the 2nd kind and both are needed.

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

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

The combination of the symbolic and connectionist paradigms of AI has been pursued by a relatively little research study community over the last twenty years and has actually yielded numerous significant results. Over the last decade, neural symbolic systems have actually been shown capable of overcoming the so-called propositional fixation of neural networks, as McCarthy (1988) put it in response to Smolensky (1988 ); see likewise (Hinton, 1990). Neural networks were shown efficient in representing modal and temporal logics (d’Avila Garcez and Lamb, 2006) and fragments of first-order reasoning (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have been used to a number of issues in the locations of bioinformatics, control engineering, software verification and adaptation, visual intelligence, ontology knowing, and video game. [78]

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

– Symbolic Neural symbolic-is the current approach of numerous neural models in natural language processing, where words or subword tokens are both the supreme input and output of large language models. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic techniques are utilized to call neural strategies. In this case the symbolic approach is Monte Carlo tree search and the neural techniques learn how to evaluate game positions.
– Neural|Symbolic-uses a neural architecture to analyze affective information as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to produce or label training data that is consequently found out by a deep learning design, e.g., to train a neural design for symbolic calculation by utilizing a Macsyma-like symbolic mathematics system to develop or label examples.
– Neural _ Symbolic -utilizes a neural net that is produced from symbolic guidelines. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR proof tree created from knowledge base guidelines and terms. Logic Tensor Networks [86] also fall into this category.
– Neural [Symbolic] -allows a neural design to directly call a symbolic thinking engine, e.g., to carry out an action or examine a state.

Many crucial research 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 knowledge be found out and reasoned about?
– How can abstract knowledge that is hard to encode rationally be handled?

Techniques and contributions

This area supplies a summary of techniques and contributions in an overall context leading to lots of other, more in-depth articles in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered earlier in the history area.

AI programming languages

The key AI shows language in the US during the last symbolic AI boom duration was LISP. LISP is the second oldest shows language after FORTRAN and was developed in 1958 by John McCarthy. LISP provided the first read-eval-print loop to support fast program advancement. Compiled functions might be easily blended with interpreted functions. Program tracing, stepping, and breakpoints were likewise offered, in addition to the ability to change worths or functions and continue from breakpoints or errors. It had the first self-hosting compiler, meaning that the compiler itself was originally written in LISP and then ran interpretively to assemble the compiler code.

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

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

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

In contrast to the US, in Europe the key AI shows language throughout that exact same duration was Prolog. Prolog provided an integrated store of realities and provisions that could be queried by a read-eval-print loop. The store might serve as an understanding base and the stipulations could act as rules or a restricted type of reasoning. As a subset of first-order logic Prolog was based upon Horn provisions with a closed-world assumption-any facts not known were considered false-and a special name assumption for primitive terms-e.g., the identifier barack_obama was considered to refer to precisely one item. Backtracking and marriage are integrated to Prolog.

Alain Colmerauer and Philippe Roussel are credited as the developers of Prolog. Prolog is a form of reasoning programming, which was developed by Robert Kowalski. Its history was also influenced by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of methods. For more information see the area on the origins of Prolog in the PLANNER short article.

Prolog is likewise a sort of declarative programs. The logic stipulations that describe programs are straight translated to run the programs defined. No explicit series of actions is required, as holds true with crucial shows languages.

Japan promoted Prolog for its Fifth Generation Project, meaning to build special hardware for high performance. Similarly, LISP devices were developed to run LISP, however as the second 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 instance, it presented metaclasses and, along with Flavors and CommonLoops, influenced 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 enables 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 programs languages for artificial intelligence. Currently, Python, a multi-paradigm shows language, is the most popular programming language, partly due to its comprehensive bundle library that supports information science, natural language processing, and deep learning. Python includes a read-eval-print loop, practical elements such as higher-order functions, and object-oriented programming that consists of metaclasses.

Search

Search arises in many sort of problem solving, including planning, restriction complete satisfaction, and playing video 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 games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and reasoning

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

Knowledge representation

Semantic networks, conceptual graphs, frames, and logic are all approaches to modeling understanding such as domain understanding, problem-solving knowledge, and the semantic significance of language. Ontologies design key principles and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be used for any domain while WordNet is a lexical resource that can likewise be deemed an ontology. YAGO includes WordNet as part of its ontology, to line up truths extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology presently being utilized.

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

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

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

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

Reasoning in knowledge-based systems

Knowledge-based systems have a specific knowledge base, usually of guidelines, to improve reusability across domains by separating procedural code and domain knowledge. A different inference engine procedures rules and adds, deletes, or customizes a knowledge store.

Forward chaining inference engines are the most common, and are seen in CLIPS and OPS5. Backward chaining occurs in Prolog, where a more limited sensible representation is utilized, Horn Clauses. Pattern-matching, particularly marriage, is used in Prolog.

A more versatile kind of problem-solving takes place when thinking about what to do next takes place, instead of merely selecting one of the offered actions. This sort of meta-level reasoning is utilized in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R might have extra abilities, such as the capability to assemble regularly used knowledge into higher-level chunks.

Commonsense thinking

Marvin Minsky first proposed frames as a way of interpreting common visual situations, such as an office, and Roger Schank extended this idea to scripts for common regimens, such as eating in restaurants. Cyc has actually attempted to capture helpful common-sense understanding and has “micro-theories” to handle specific kinds of domain-specific thinking.

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

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

Constraints and constraint-based reasoning

Constraint solvers perform a more limited sort of reasoning than first-order reasoning. They can streamline sets of spatiotemporal restrictions, such as those for RCC or Temporal Algebra, together with fixing other kinds of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint reasoning programs can be utilized to resolve scheduling problems, for example with constraint dealing with rules (CHR).

Automated planning

The General Problem Solver (GPS) cast preparation as analytical utilized means-ends analysis to produce plans. STRIPS took a different technique, seeing planning as theorem proving. Graphplan takes a least-commitment approach to planning, instead of sequentially choosing actions from an initial state, working forwards, or an objective state if working in reverse. Satplan is a method to preparing where a preparation problem is minimized to a Boolean satisfiability problem.

Natural language processing

Natural language processing focuses on dealing with language as information to carry out tasks such as identifying subjects without always understanding the desired meaning. Natural language understanding, on the other hand, constructs a significance representation and utilizes that for further processing, such as addressing questions.

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

New deep knowing techniques based upon Transformer models have now eclipsed these earlier symbolic AI techniques and achieved state-of-the-art performance in natural language processing. However, Transformer models are nontransparent and do not yet produce human-interpretable semantic representations for sentences and files. Instead, they produce task-specific vectors where the meaning of the vector parts is nontransparent.

Agents and multi-agent systems

Agents are self-governing systems embedded in an environment they perceive and act upon in some sense. Russell and Norvig’s basic textbook on expert system is arranged to reflect agent architectures of increasing elegance. [91] The sophistication of agents varies from basic reactive agents, to those with a design of the world and automated planning abilities, potentially a BDI agent, i.e., one with beliefs, desires, and intentions – or additionally a reinforcement learning design discovered in time to choose actions – as much as a combination of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep learning for perception. [92]

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

Controversies occurred from early on in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and between those who welcomed AI but turned down symbolic approaches-primarily connectionists-and those outside the field. Critiques from outside of the field were mainly from thinkers, on intellectual premises, however likewise from funding companies, specifically throughout the 2 AI winter seasons.

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

Limitations were discovered in using easy first-order logic to factor about vibrant domains. Problems were discovered both with regards to specifying the prerequisites for an action to prosper and in offering axioms for what did not alter after an action was performed.

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 “showing that one individual could get into conversation with another”, as an axiom asserting “if an individual has a telephone he still has it after looking up a number in the telephone book” would be required for the deduction to prosper. Similar axioms would be needed for other domain actions to specify what did not change.

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

McCarthy’s approach to repair the frame issue was circumscription, a type of non-monotonic reasoning where reductions could be made from actions that need only specify what would change while not having to clearly define everything that would not alter. Other non-monotonic logics offered truth maintenance systems that modified beliefs causing contradictions.

Other methods of handling more open-ended domains included probabilistic thinking systems and device learning to discover new principles and guidelines. McCarthy’s Advice Taker can be considered as an inspiration here, as it might include new understanding supplied by a human in the kind of assertions or guidelines. For instance, experimental symbolic machine finding out systems explored the ability to take high-level natural language guidance and to translate it into domain-specific actionable rules.

Similar to the issues in dealing with vibrant domains, sensible reasoning is likewise hard to capture in official thinking. Examples of sensible thinking consist of implicit reasoning about how people believe or basic understanding of everyday occasions, things, and living creatures. This kind of knowledge is taken for given and not deemed noteworthy. Common-sense reasoning is an open location of research and challenging both for symbolic systems (e.g., Cyc has attempted to capture essential parts of this understanding over more than a decade) and neural systems (e.g., self-driving cars and trucks that do not understand not to drive into cones or not to strike pedestrians walking a bike).

McCarthy viewed his Advice Taker as having common-sense, however his definition of common-sense was different than the one above. [94] He defined a program as having typical sense “if it automatically deduces for itself a sufficiently broad class of instant consequences of anything it is informed and what it currently understands. “

Connectionist AI: philosophical difficulties and sociological disputes

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

Three philosophical positions [96] have been outlined amongst connectionists:

1. Implementationism-where connectionist architectures carry out the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected absolutely, and connectionist architectures underlie intelligence and are fully sufficient 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 controversies within the neural network community, explained the moderate connectionism view as essentially compatible with present research in neuro-symbolic hybrids:

The 3rd and last position I would like to examine here is what I call the moderate connectionist view, a more diverse view of the existing debate between connectionism and symbolic AI. One of the scientists who has actually elaborated this position most clearly is Andy Clark, a thinker from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark protected hybrid (partially symbolic, partly connectionist) systems. He declared that (a minimum of) 2 type of theories are required in order to study and model cognition. On the one hand, for some information-processing tasks (such as pattern recognition) connectionism has advantages over symbolic designs. But on the other hand, for other cognitive procedures (such as serial, deductive reasoning, and generative symbol control processes) the symbolic paradigm offers sufficient models, and not just “approximations” (contrary to what extreme connectionists would claim). [97]

Gary Marcus has actually claimed that the animus in the deep learning neighborhood against symbolic methods now may be more sociological than philosophical:

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

And yet, for the a lot of part, that’s how most present AI profits. Hinton and lots of others have striven to get rid of signs completely. The deep knowing hope-seemingly grounded not a lot in science, but in a sort of historic grudge-is that smart habits will emerge simply from the confluence of huge information and deep learning. Where classical computer systems and software application fix tasks by defining sets of symbol-manipulating rules dedicated to particular jobs, such as editing a line in a word processor or carrying out a computation in a spreadsheet, neural networks normally try to fix tasks by statistical approximation and finding out from examples.

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

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

…

Since then, his anti-symbolic campaign has actually just increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep learning in one of science’s crucial journals, Nature. It closed with a direct attack on sign control, calling not for reconciliation however for straight-out replacement. Later, Hinton informed a gathering of European Union leaders that investing any additional money in symbol-manipulating approaches was “a huge error,” comparing it to purchasing internal combustion engines in the period of electrical vehicles. [98]

Part of these disputes might be because of uncertain terminology:

Turing award winner Judea Pearl uses a review of artificial intelligence which, sadly, conflates the terms machine knowing and deep knowing. Similarly, when Geoffrey Hinton describes symbolic AI, the undertone of the term tends to be that of specialist systems dispossessed of any capability to learn. The usage of the terminology requires explanation. Machine learning is not restricted to association guideline 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 rather than distributed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not just about production guidelines composed by hand. A proper meaning of AI concerns understanding representation and reasoning, self-governing multi-agent systems, preparation and argumentation, along with learning. [99]

Situated robotics: the world as a model

Another review of symbolic AI is the embodied cognition technique:

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

Rodney Brooks created behavior-based robotics, one technique to embodied cognition. Nouvelle AI, another name for this technique, is seen as an alternative to both symbolic AI and connectionist AI. His technique rejected representations, either symbolic or dispersed, as not just unnecessary, however as harmful. Instead, he produced the subsumption architecture, a layered architecture for embodied representatives. Each layer achieves a different purpose and should function in the real world. For instance, the very first robot he describes in Intelligence Without Representation, has three layers. The bottom layer translates sonar sensing units to prevent objects. The middle layer causes the robotic to roam around when there are no obstacles. The top layer causes the robotic to go to more far-off places for additional expedition. Each layer can temporarily hinder or reduce a lower-level layer. He criticized AI researchers for defining AI issues for their systems, when: “There is no tidy division between understanding (abstraction) and reasoning in the real life.” [101] He called his robotics “Creatures” and each layer was “composed of a fixed-topology network of simple finite state machines.” [102] In the Nouvelle AI approach, “First, it is extremely important to check the Creatures we construct in the genuine world; i.e., in the very same world that we people inhabit. It is dreadful to fall into the temptation of testing them in a simplified world initially, even with the best intentions of later transferring activity to an unsimplified world.” [103] His emphasis on real-world testing was in contrast to “Early operate in AI focused on games, geometrical issues, symbolic algebra, theorem proving, and other formal systems” [104] and making use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has benefits, however has actually been criticized by the other approaches. Symbolic AI has been slammed as disembodied, liable to the qualification issue, and bad in handling the affective issues where deep discovering excels. In turn, connectionist AI has been criticized as improperly matched for deliberative detailed problem fixing, integrating knowledge, and handling preparation. Finally, Nouvelle AI stands out in reactive and real-world robotics domains but has been slammed for troubles in incorporating learning and understanding.

Hybrid AIs including one or more of these approaches are currently deemed the course forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw areas where AI did not have complete answers and said that Al is therefore impossible; we now see a lot of these same locations going through continued research and development causing increased capability, not impossibility. [100]

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

Notes

^ McCarthy once stated: “This is AI, so we do not care if it’s mentally real”. [4] McCarthy reiterated his position in 2006 at the AI@50 conference where he stated “Artificial intelligence is not, by meaning, simulation of human intelligence”. [28] Pamela McCorduck composes that there are “2 significant branches of synthetic intelligence: one targeted at producing intelligent behavior regardless of how it was achieved, and the other targeted at modeling intelligent processes found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not specify the objective of their field as making ‘makers that fly so precisely like pigeons that they can fool 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 Expert System”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep knowing with symbolic synthetic intelligence: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating mistakes”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten 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.
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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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