Symbolic Artificial Intelligence

In expert system, symbolic synthetic intelligence (also referred to as classical synthetic intelligence or logic-based expert system) [1] [2] is the term for the collection of all methods in synthetic intelligence research study that are based on top-level symbolic (human-readable) representations of problems, reasoning and search. [3] Symbolic AI utilized tools such as logic programs, production rules, semantic internet and frames, and it established applications such as knowledge-based systems (in specific, skilled systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to seminal concepts in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of formal understanding and reasoning systems.

Symbolic AI was the of AI research from the mid-1950s up until the mid-1990s. [4] Researchers in the 1960s and the 1970s were convinced that symbolic methods would ultimately succeed in developing a maker with synthetic basic intelligence and considered this the ultimate 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 unrealistic expectations and pledges and was followed by the very first AI Winter as moneying dried up. [5] [6] A second boom (1969-1986) accompanied the increase of professional systems, their guarantee of recording corporate proficiency, and an enthusiastic business welcome. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later on frustration. [8] Problems with difficulties in understanding acquisition, preserving large understanding bases, and brittleness in handling out-of-domain problems developed. Another, 2nd, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists concentrated on dealing with hidden problems in dealing with unpredictability and in knowledge acquisition. [10] Uncertainty was addressed with official techniques such as hidden Markov models, Bayesian reasoning, and analytical relational knowing. [11] [12] Symbolic maker discovering attended to 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 shows to learn relations. [13]

Neural networks, a subsymbolic method, had actually been pursued from early days and reemerged highly in 2012. Early examples are Rosenblatt’s perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and work in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not considered as successful until about 2012: “Until Big Data became commonplace, the basic consensus in the Al neighborhood was that the so-called neural-network approach was helpless. Systems simply didn’t work that well, compared to other methods. … A revolution was available in 2012, when a variety of people, consisting of a team of scientists working with Hinton, worked out a method to utilize the power of GPUs to enormously increase the power of neural networks.” [16] Over the next numerous years, deep learning had spectacular success in handling vision, speech acknowledgment, speech synthesis, image generation, and maker translation. However, since 2020, as fundamental problems with predisposition, description, coherence, and effectiveness ended up being more evident with deep knowing approaches; an increasing number of AI scientists have actually called for combining the best of both the symbolic and neural network approaches [17] [18] and dealing with locations that both techniques have trouble with, such as sensible reasoning. [16]

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

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

Success at early efforts in AI occurred in three main locations: artificial neural networks, knowledge representation, and heuristic search, adding to high expectations. This area sums up Kautz’s reprise of early AI history.

Approaches inspired by human or animal cognition or behavior

Cybernetic approaches tried to reproduce the feedback loops in between animals and their environments. A robotic turtle, with sensing units, motors for driving and steering, and seven vacuum tubes for control, based upon a preprogrammed neural net, was built as early as 1948. This work can be viewed as an early precursor to later operate in neural networks, support knowing, 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 prove 38 elementary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later generalized this work to create a domain-independent issue solver, GPS (General Problem Solver). GPS resolved problems represented with official operators via state-space search utilizing means-ends analysis. [21]

During the 1960s, symbolic techniques accomplished fantastic success at simulating intelligent habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was concentrated in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Each one developed its own design of research study. Earlier techniques based on cybernetics or artificial neural networks were abandoned or pressed into the background.

Herbert Simon and Allen Newell studied human problem-solving skills and attempted to formalize them, and their work laid the structures of the field of synthetic intelligence, as well as cognitive science, operations research and management science. Their research study group utilized the results of psychological experiments to develop programs that simulated the strategies that people used to resolve issues. [22] [23] This tradition, focused at Carnegie Mellon University would eventually culminate in the development of the Soar architecture in the middle 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific type of understanding that we will see later on used in expert systems, early symbolic AI scientists found another more basic application of knowledge. These were called heuristics, guidelines that guide a search in appealing instructions: “How can non-enumerative search be practical when the underlying issue is greatly tough? The approach promoted by Simon and Newell is to employ heuristics: fast algorithms that might stop working on some inputs or output suboptimal options.” [26] Another essential advance was to discover a method to apply these heuristics that guarantees a service will be discovered, if there is one, not withstanding the occasional fallibility of heuristics: “The A * algorithm offered a basic frame for complete and optimal heuristically directed search. A * is used as a subroutine within virtually every AI algorithm today but is still no magic bullet; its guarantee of completeness is purchased the cost of worst-case exponential time. [26]

Early work on knowledge representation and thinking

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

Modeling official reasoning with logic: the “neats”

Unlike Simon and Newell, John McCarthy felt that machines did not require to replicate the precise mechanisms of human idea, but might instead try to discover the essence of abstract reasoning and analytical with reasoning, [27] despite whether individuals used the same algorithms. [a] His lab at Stanford (SAIL) concentrated on using official reasoning to fix a large range of problems, consisting of knowledge representation, planning and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and in other places in Europe which resulted in the advancement of the programs language Prolog and the science of reasoning shows. [32] [33]

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

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that fixing difficult issues in vision and natural language processing required advertisement hoc solutions-they argued that no basic and general concept (like reasoning) would capture all the aspects of smart habits. Roger Schank described their “anti-logic” approaches as “scruffy” (instead of the “neat” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “scruffy” AI, since they must be built by hand, one complex idea at a time. [38] [39] [40]

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

The first AI winter was a shock:

During the first AI summer, lots of people believed that machine intelligence might be attained in just a couple of years. The Defense Advance Research Projects Agency (DARPA) released programs to support AI research to utilize AI to fix problems of national security; in specific, to automate the translation of Russian to English for intelligence operations and to develop self-governing tanks for the battleground. Researchers had begun to understand that accomplishing AI was going to be much harder than was supposed a years previously, however a mix of hubris and disingenuousness led many university and think-tank researchers to accept funding with guarantees of deliverables that they must have understood they might not satisfy. By the mid-1960s neither beneficial natural language translation systems nor self-governing tanks had actually been produced, and a dramatic reaction embeded in. New DARPA management canceled existing AI funding programs.

Beyond the United States, the most fertile ground for AI research was the UK. The AI winter season in the United Kingdom was spurred on not a lot by dissatisfied military leaders as by competing academics who saw AI scientists as charlatans and a drain on research funding. A professor of applied mathematics, Sir James Lighthill, was commissioned by Parliament to examine the state of AI research in the nation. The report specified that all of the problems being worked on in AI would be better managed by scientists from other disciplines-such as applied mathematics. The report likewise claimed that AI successes on toy problems might never ever scale to real-world applications due to combinatorial surge. [41]

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

Knowledge-based systems

As constraints with weak, domain-independent approaches became increasingly more evident, [42] researchers from all three traditions began to construct understanding into AI applications. [43] [7] The knowledge transformation was driven by the awareness that understanding underlies high-performance, domain-specific AI applications.

Edward Feigenbaum said:

– “In the understanding lies the power.” [44]
to 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 perform a complicated job well, it must understand a lot about the world in which it runs.
( 2) A plausible extension of that concept, called the Breadth Hypothesis: there are two additional abilities needed for smart behavior in unexpected situations: drawing on increasingly basic understanding, and analogizing to specific however remote understanding. [45]

Success with professional systems

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

Key expert systems were:

DENDRAL, which found the structure of natural particles from their chemical formula and mass spectrometer readings.
MYCIN, which identified bacteremia – and recommended further laboratory tests, when required – by analyzing lab outcomes, client history, and physician observations. “With about 450 guidelines, MYCIN had the ability to perform in addition to some specialists, and substantially better than junior medical professionals.” [49] INTERNIST and CADUCEUS which tackled internal medication medical diagnosis. Internist tried to record the competence of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS could ultimately identify approximately 1000 different diseases.
– GUIDON, which demonstrated how an understanding base developed for specialist issue solving could be repurposed for mentor. [50] XCON, to set up VAX computer systems, a then laborious process that could use up to 90 days. XCON decreased the time to about 90 minutes. [9]
DENDRAL is thought about the first professional system that count on knowledge-intensive problem-solving. It is explained below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

Among the individuals at Stanford thinking about computer-based models of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I wanted 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 great at heuristic search techniques, and he had an algorithm that was proficient at producing the chemical problem area.

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 appreciated mass spectrometrists. Carl and his postdocs were first-rate specialists in mass spectrometry. We began to add to their understanding, creating understanding of engineering as we went along. These experiments amounted to titrating DENDRAL a growing number of understanding. The more you did that, the smarter the program ended up being. We had great results.

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

The other professional systems discussed above followed DENDRAL. MYCIN exhibits the timeless expert system architecture of a knowledge-base of guidelines paired to a symbolic reasoning mechanism, consisting of the usage of certainty elements to manage unpredictability. GUIDON shows how a specific understanding base can be repurposed for a second application, tutoring, and is an example of an intelligent tutoring system, a particular type of knowledge-based application. Clancey revealed that it was not sufficient simply to use MYCIN’s guidelines for guideline, however that he likewise required to add guidelines for dialogue management and student modeling. [50] XCON is substantial since of the countless dollars it conserved DEC, which set off the professional system boom where most all significant corporations in the US had expert systems groups, to record business expertise, protect it, and automate it:

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

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

Architecture of knowledge-based and professional systems

An essential component of the system architecture for all expert systems is the understanding base, which shops facts and guidelines for problem-solving. [53] The simplest approach for a skilled system knowledge base is merely a collection or network of production rules. Production rules link symbols in a relationship similar to an If-Then statement. The expert system processes the guidelines to make reductions and to determine what additional information it requires, i.e. what concerns to ask, using human-readable signs. For example, OPS5, CLIPS and their followers Jess and Drools run in this fashion.

Expert systems can run in either a forward chaining – from evidence to conclusions – or backward chaining – from objectives to needed information and prerequisites – manner. Advanced knowledge-based systems, such as Soar can likewise perform meta-level thinking, that is thinking about their own thinking in terms of choosing how to solve issues and monitoring the success of problem-solving methods.

Blackboard systems are a second sort of knowledge-based or professional system architecture. They model a community of professionals incrementally contributing, where they can, to resolve an issue. The problem is represented in several levels of abstraction or alternate views. The professionals (understanding sources) volunteer their services whenever they acknowledge they can contribute. Potential problem-solving actions are represented on an agenda that is updated as the problem scenario changes. A controller chooses how helpful each contribution is, and who need to make the next problem-solving action. One example, the BB1 chalkboard architecture [54] was initially motivated by research studies of how human beings plan to carry out multiple jobs in a trip. [55] A development of BB1 was to use the very same chalkboard model to fixing its control problem, i.e., its controller carried out meta-level thinking with knowledge sources that monitored how well a plan or the analytical was proceeding and might switch from one method to another as conditions – such as goals or times – altered. BB1 has actually been applied in numerous domains: building site planning, smart tutoring systems, and real-time client tracking.

The second AI winter, 1988-1993

At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were offering LISP devices particularly targeted to accelerate the development of AI applications and research. In addition, a number of artificial intelligence business, such as Teknowledge and Inference Corporation, were offering expert 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 second AI winter season. The hardware business stopped working when much more cost-efficient basic Unix workstations from Sun together with excellent compilers for LISP and Prolog came onto the marketplace. Many industrial implementations of specialist systems were terminated when they showed too pricey to preserve. Medical expert systems never caught on for several reasons: the difficulty in keeping them up to date; the difficulty for physician to learn how to use an overwelming variety of different specialist systems for different medical conditions; and perhaps most crucially, the reluctance of physicians to rely on a computer-made medical diagnosis over their gut instinct, even for particular domains where the expert systems could outperform an average medical professional. Venture capital money deserted AI almost overnight. The world AI conference IJCAI hosted a huge and luxurious trade program and countless nonacademic guests in 1987 in Vancouver; the main AI conference the list below year, AAAI 1988 in St. Paul, was a small and strictly scholastic affair. [9]

Adding in more rigorous structures, 1993-2011

Uncertain thinking

Both analytical approaches and extensions to reasoning were tried.

One statistical technique, hidden Markov models, had actually already been promoted in the 1980s for speech acknowledgment work. [11] Subsequently, in 1988, Judea Pearl popularized making use of Bayesian Networks as a noise however efficient way of handling unpredictable thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian approaches were used successfully in specialist systems. [57] Even later, in the 1990s, analytical relational knowing, a method that combines likelihood with logical solutions, enabled possibility to be combined with first-order reasoning, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order reasoning to assistance were also attempted. For example, non-monotonic reasoning might be used with fact upkeep systems. A fact upkeep system tracked assumptions and validations for all reasonings. It permitted reasonings to be withdrawn when assumptions were found out to be inaccurate or a contradiction was obtained. Explanations could be attended to a reasoning by describing which guidelines were used to create it and after that continuing through underlying reasonings and guidelines all the method back to root presumptions. [58] Lofti Zadeh had actually introduced a various sort of extension to manage the representation of ambiguity. For instance, in deciding how “heavy” or “high” a man is, there is often no clear “yes” or “no” response, and a predicate for heavy or high would rather return values in between 0 and 1. Those worths represented to what degree the predicates held true. His fuzzy logic further provided a means for propagating combinations of these values through sensible formulas. [59]

Artificial intelligence

Symbolic maker finding out techniques were investigated to deal with the understanding acquisition traffic jam. One of the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test strategy to generate plausible guideline hypotheses to evaluate against spectra. Domain and job understanding decreased the variety of candidates tested to a workable size. Feigenbaum explained Meta-DENDRAL as

… the conclusion of my dream of the early to mid-1960s involving 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 steer and prune the search. That understanding got in there since we spoke with individuals. 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 utilize to resolve individual hypothesis development problems. 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, really did it. We were able to do something that had been a dream: to have a computer program developed a new and publishable piece of science. [51]

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

Advances were made in understanding machine learning theory, too. Tom Mitchell introduced variation area learning which describes learning as a search through an area of hypotheses, with upper, more general, and lower, more particular, boundaries including all practical hypotheses consistent 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 machine learning. [63]

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

Inductive reasoning programming was another method to finding out that enabled logic programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) might synthesize Prolog programs from examples. [65] John R. Koza used genetic algorithms to program synthesis to produce genetic programs, which he used to synthesize LISP programs. Finally, Zohar Manna and Richard Waldinger offered a more basic technique to program synthesis that manufactures a functional program in the course of showing its specifications to be right. [66]

As an option to reasoning, Roger Schank presented case-based reasoning (CBR). The CBR approach described in his book, Dynamic Memory, [67] focuses initially on remembering crucial analytical cases for future use and generalizing them where suitable. When confronted with a brand-new issue, CBR retrieves the most comparable previous case and adjusts it to the specifics of the existing problem. [68] Another alternative to logic, genetic algorithms and genetic programming are based upon an evolutionary model of knowing, where sets of rules are encoded into populations, the guidelines govern the habits of people, and choice of the fittest prunes out sets of unsuitable guidelines over lots of generations. [69]

Symbolic artificial intelligence was used to finding out concepts, guidelines, heuristics, and problem-solving. Approaches, besides those above, include:

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

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

Neuro-symbolic AI: incorporating neural and symbolic methods

Neuro-symbolic AI attempts to integrate 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 reasoning, learning, and cognitive modeling. As argued by Valiant [77] and lots of others, [78] the effective building and construction of rich computational cognitive designs requires the combination of sound symbolic reasoning and effective (device) knowing designs. Gary Marcus, similarly, argues that: “We can not build abundant cognitive models in an adequate, automatic method without the triumvirate of hybrid architecture, rich anticipation, and advanced methods for thinking.”, [79] and in particular: “To construct a robust, knowledge-driven method to AI we should 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 manipulate such abstract understanding dependably is the device of sign manipulation. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based upon a need to attend to the 2 type of believing discussed in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having two components, System 1 and System 2. System 1 is quickly, automatic, user-friendly and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is the kind utilized for pattern acknowledgment while System 2 is far much better suited for preparation, deduction, and deliberative thinking. In this view, deep knowing best models the first sort of believing while symbolic reasoning best models the second kind and both are required.

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

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

The combination of the symbolic and connectionist paradigms of AI has been pursued by a reasonably little research study neighborhood over the last 2 decades and has actually yielded numerous significant outcomes. Over the last decade, neural symbolic systems have actually been revealed capable of overcoming the so-called propositional fixation of neural networks, as McCarthy (1988) put it in reaction to Smolensky (1988 ); see also (Hinton, 1990). Neural networks were revealed capable of representing modal and temporal reasonings (d’Avila Garcez and Lamb, 2006) and fragments 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 problems in the areas of bioinformatics, control engineering, software verification and adaptation, visual intelligence, ontology knowing, and computer games. [78]

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

– Symbolic Neural symbolic-is the existing technique of lots of neural designs in natural language processing, where words or subword tokens are both the supreme input and output of big language models. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic methods are used to call neural methods. In this case the symbolic method is Monte Carlo tree search and the neural strategies learn how to examine video game positions.
– Neural|Symbolic-uses a neural architecture to interpret affective information as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to generate or identify training information that is consequently learned by a deep knowing model, e.g., to train a neural model for symbolic computation by using a Macsyma-like symbolic mathematics system to develop or label examples.
– Neural _ Symbolic -uses a neural internet that is generated from symbolic guidelines. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR evidence tree generated from understanding base rules and terms. Logic Tensor Networks [86] also fall into this classification.
– Neural [Symbolic] -permits a neural model to directly call a symbolic reasoning engine, e.g., to perform an action or assess a state.

Many key research study questions stay, such as:

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

Techniques and contributions

This area offers an overview of techniques and contributions in an overall context leading to numerous other, more in-depth posts in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered earlier in the history area.

AI shows languages

The essential AI programs language in the US throughout the last symbolic AI boom duration was LISP. LISP is the 2nd oldest programming language after FORTRAN and was produced in 1958 by John McCarthy. LISP offered the very first read-eval-print loop to support quick program advancement. Compiled functions might be easily mixed with analyzed functions. Program tracing, stepping, and breakpoints were likewise provided, together with the ability to alter values or functions and continue from breakpoints or errors. It had the very first self-hosting compiler, meaning that the compiler itself was initially written in LISP and after that ran interpretively to put together the compiler code.

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

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

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

In contrast to the US, in Europe the crucial AI programming language during that same period was Prolog. Prolog provided an integrated shop of truths and stipulations that could be queried by a read-eval-print loop. The shop could act as a knowledge base and the provisions could function as rules or a restricted type of logic. As a subset of first-order logic Prolog was based upon Horn clauses with a closed-world assumption-any realities not known were considered false-and a distinct name presumption for primitive terms-e.g., the identifier barack_obama was considered to refer to exactly one things. Backtracking and marriage are integrated to Prolog.

Alain Colmerauer and Philippe Roussel are credited as the developers of Prolog. Prolog is a kind of logic programming, which was invented by Robert Kowalski. Its history was likewise influenced by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of approaches. For more detail see the area on the origins of Prolog in the PLANNER post.

Prolog is also a sort of declarative shows. The reasoning stipulations that explain programs are directly interpreted to run the programs specified. No explicit series of actions is required, as holds true with imperative shows languages.

Japan championed Prolog for its Fifth Generation Project, intending to build special hardware for high performance. Similarly, LISP makers were built to run LISP, but 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 influential AI shows language. For instance, it presented metaclasses and, in addition to Flavors and CommonLoops, influenced the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the existing standard Lisp dialect. CLOS is a Lisp-based object-oriented system that permits several inheritance, in addition to incremental extensions to both classes and metaclasses, therefore providing a run-time meta-object protocol. [88]

For other AI programming languages see this list of programming languages for synthetic intelligence. Currently, Python, a multi-paradigm shows language, is the most popular shows language, partially due to its comprehensive plan 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 shows that includes metaclasses.

Search

Search emerges in lots of type of issue resolving, consisting of preparation, restraint complete satisfaction, 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 stipulation learning, and the DPLL algorithm. For adversarial search when playing games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and reasoning

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

Knowledge representation

Semantic networks, conceptual graphs, frames, and logic are all techniques to modeling understanding such as domain knowledge, analytical understanding, and the semantic significance of language. Ontologies design key ideas and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be utilized for any domain while WordNet is a lexical resource that can also be viewed as an ontology. YAGO integrates WordNet as part of its ontology, to line up realities drawn out from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being utilized.

Description logic is a logic for automated category of ontologies and for finding inconsistent classification information. OWL is a language utilized to represent ontologies with description reasoning. 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 gone over listed below can prove theorems in first-order reasoning. Horn stipulation logic is more restricted than first-order logic and is utilized in logic programming languages such as Prolog. Extensions to first-order logic include temporal logic, to handle time; epistemic logic, to reason about representative understanding; modal logic, to manage possibility and necessity; and probabilistic reasonings to deal with reasoning and likelihood together.

Automatic theorem proving

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

Prover9.
ACL2.
Vampire.

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

Reasoning in knowledge-based systems

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

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

A more versatile kind of analytical takes place when thinking about what to do next occurs, rather than merely picking one of the offered actions. This kind of meta-level thinking is used in Soar and in the BB1 chalkboard architecture.

Cognitive architectures such as ACT-R may have extra abilities, such as the capability to compile frequently used understanding into higher-level chunks.

Commonsense thinking

Marvin Minsky initially proposed frames as a way of translating common visual circumstances, such as a workplace, and Roger Schank extended this concept to scripts for typical routines, such as eating in restaurants. Cyc has attempted to catch helpful common-sense understanding and has “micro-theories” to manage particular type of domain-specific reasoning.

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

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

Constraints and constraint-based reasoning

Constraint solvers carry out a more limited kind of reasoning than first-order logic. They can streamline sets of spatiotemporal restrictions, such as those for RCC or Temporal Algebra, along with resolving other kinds of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint reasoning shows can be utilized to resolve scheduling issues, for example with constraint managing rules (CHR).

Automated preparation

The General Problem Solver (GPS) cast preparation as problem-solving utilized means-ends analysis to create plans. STRIPS took a various approach, seeing planning as theorem proving. Graphplan takes a least-commitment method to preparation, rather than sequentially choosing actions from a preliminary state, working forwards, or an objective state if working backwards. Satplan is a method to preparing where a preparation issue is reduced to a Boolean satisfiability problem.

Natural language processing

Natural language processing focuses on dealing with language as information to perform tasks such as determining subjects without always comprehending the desired meaning. Natural language understanding, on the other hand, constructs a significance representation and uses that for additional processing, such as responding to questions.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all elements of natural language processing long dealt with by symbolic AI, however considering that enhanced by deep learning approaches. In symbolic AI, discourse representation theory and first-order logic have actually been used to represent sentence significances. Latent semantic analysis (LSA) and explicit semantic analysis also supplied vector representations of documents. In the latter case, vector elements are interpretable as ideas called by Wikipedia short articles.

New deep learning techniques based upon Transformer models have now eclipsed these earlier symbolic AI approaches and obtained state-of-the-art efficiency in natural language processing. However, Transformer models 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 components 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 book on expert system is arranged to show representative architectures of increasing sophistication. [91] The elegance of representatives varies from basic reactive representatives, to those with a model of the world and automated preparation abilities, possibly a BDI agent, i.e., one with beliefs, desires, and intents – or alternatively a support finding out model learned gradually to select actions – up to a combination of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep knowing for perception. [92]

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

Controversies developed from early in symbolic AI, both within the field-e.g., between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who accepted AI but declined symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were mostly from philosophers, on intellectual grounds, but likewise from funding companies, particularly during the 2 AI winter seasons.

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

Limitations were found in using easy first-order logic to reason about dynamic domains. Problems were found both with regards to identifying the preconditions for an action to prosper and in supplying axioms for what did not change after an action was performed.

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

A comparable issue, called the Qualification Problem, happens in attempting to identify the preconditions for an action to be successful. A limitless number of pathological conditions can be pictured, e.g., a banana in a tailpipe might prevent an automobile from operating properly.

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

Other ways of handling more open-ended domains consisted of probabilistic thinking systems and artificial intelligence to find out brand-new concepts and rules. McCarthy’s Advice Taker can be deemed a motivation here, as it might incorporate brand-new understanding provided by a human in the form of assertions or guidelines. For example, speculative symbolic device discovering systems checked out the capability to take top-level natural language recommendations and to translate it into domain-specific actionable rules.

Similar to the issues in dealing with dynamic domains, sensible reasoning is likewise difficult to record in official reasoning. Examples of sensible reasoning include implicit reasoning about how people think or basic understanding of daily occasions, things, and living animals. This kind of understanding is considered granted and not considered as noteworthy. Common-sense thinking is an open location of research and challenging both for symbolic systems (e.g., Cyc has tried to catch crucial parts of this understanding over more than a years) and neural systems (e.g., self-driving vehicles that do not know not to drive into cones or not to hit pedestrians strolling a bike).

McCarthy saw his Advice Taker as having sensible, but his meaning 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 immediate consequences of anything it is informed and what it already knows. “

Connectionist AI: philosophical challenges and sociological disputes

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

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

1. Implementationism-where connectionist architectures execute the abilities for symbolic processing,
2. Radical connectionism-where symbolic processing is turned down completely, and connectionist architectures underlie intelligence and are fully enough to discuss it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are seen as complementary and both are required for intelligence

Olazaran, in his sociological history of the debates within the neural network neighborhood, described the moderate connectionism consider as basically suitable with current research in neuro-symbolic hybrids:

The 3rd and last position I wish to examine here is what I call the moderate connectionist view, a more diverse view of the existing debate between connectionism and symbolic AI. Among the scientists 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 safeguarded hybrid (partly symbolic, partially connectionist) systems. He declared that (at least) 2 type of theories are needed in order to study and model cognition. On the one hand, for some information-processing jobs (such as pattern recognition) connectionism has benefits over symbolic designs. But on the other hand, for other cognitive procedures (such as serial, deductive reasoning, and generative sign manipulation processes) the symbolic paradigm offers adequate designs, and not just “approximations” (contrary to what extreme connectionists would claim). [97]

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

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

And yet, for the many part, that’s how most existing AI proceeds. Hinton and numerous others have tried difficult to eliminate symbols altogether. The deep learning hope-seemingly grounded not a lot in science, however in a sort of historical grudge-is that smart habits will emerge simply from the confluence of massive information and deep knowing. Where classical computers and software application resolve tasks by specifying sets of symbol-manipulating rules dedicated to particular jobs, such as modifying a line in a word processor or carrying out an estimation in a spreadsheet, neural networks typically attempt to solve jobs by analytical approximation and gaining from examples.

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

When deep learning reemerged in 2012, it was with a sort of take-no-prisoners attitude that has identified many of the last years. By 2015, his hostility towards all things signs had fully taken shape. He gave a talk at an AI workshop at Stanford comparing signs to aether, among science’s greatest errors.

…

Since then, his anti-symbolic campaign has actually only increased in strength. 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 manipulation, calling not for reconciliation but for straight-out replacement. Later, Hinton told a gathering of European Union leaders that investing any additional money in symbol-manipulating methods was “a substantial error,” likening it to investing in internal combustion engines in the era of electric vehicles. [98]

Part of these conflicts may be due to uncertain terms:

Turing award winner Judea Pearl offers a review of artificial intelligence which, regrettably, conflates the terms artificial intelligence and deep knowing. Similarly, when Geoffrey Hinton refers to symbolic AI, the undertone of the term tends to be that of specialist systems dispossessed of any ability to discover. Making use of the terminology requires clarification. Artificial intelligence is not restricted to association rule mining, c.f. the body of work on symbolic ML and relational learning (the differences to deep learning being the choice of representation, localist logical instead of dispersed, and the non-use of gradient-based knowing algorithms). Equally, symbolic AI is not just about production rules composed by hand. A proper meaning of AI issues understanding representation and reasoning, autonomous multi-agent systems, planning and argumentation, in addition to knowing. [99]

Situated robotics: the world as a model

Another critique of symbolic AI is the embodied cognition method:

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

Rodney Brooks developed behavior-based robotics, one method to embodied cognition. Nouvelle AI, another name for this technique, is viewed as an alternative to both symbolic AI and connectionist AI. His technique declined representations, either symbolic or distributed, as not just unnecessary, but as destructive. Instead, he produced the subsumption architecture, a layered architecture for embodied representatives. Each layer attains a various purpose and should operate in the real life. For instance, the very first robot he describes in Intelligence Without Representation, has three layers. The bottom layer translates sonar sensing units to avoid things. The middle layer causes the robotic to roam around when there are no challenges. The top layer triggers the robot to go to more distant places for further exploration. Each layer can briefly prevent or reduce a lower-level layer. He criticized AI researchers for specifying AI problems for their systems, when: “There is no tidy department between understanding (abstraction) and reasoning in the genuine world.” [101] He called his robots “Creatures” and each layer was “composed of a fixed-topology network of simple limited state machines.” [102] In the Nouvelle AI method, “First, it is critically important to check the Creatures we build in the real life; i.e., in the exact same world that we people occupy. It is disastrous to fall into the temptation of evaluating them in a simplified world initially, even with the finest objectives of later moving 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 official systems” [104] and using the blocks world in symbolic AI systems such as SHRDLU.

Current views

Each approach-symbolic, connectionist, and behavior-based-has advantages, however has been criticized by the other techniques. Symbolic AI has actually been criticized as disembodied, liable to the credentials issue, and poor in managing the perceptual problems where deep finding out excels. In turn, connectionist AI has actually been slammed as improperly fit for deliberative detailed problem solving, including knowledge, and dealing with planning. Finally, Nouvelle AI masters reactive and real-world robotics domains but has been slammed for problems in integrating knowing and understanding.

Hybrid AIs integrating several of these methods are presently seen as the course forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw areas where AI did not have total responses and said that Al is for that reason impossible; we now see many of these same areas undergoing ongoing research and advancement resulting in increased capability, not impossibility. [100]

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

Notes

^ McCarthy as soon as said: “This is AI, so we do not care if it’s mentally 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 writes that there are “2 major branches of synthetic intelligence: one focused on producing intelligent behavior despite how it was accomplished, and the other intended at modeling intelligent processes discovered in nature, particularly human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not specify the objective of their field as making ‘machines that fly so exactly like pigeons that they can trick even other pigeons.'” [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). “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.
^ 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 learning 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 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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