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  • Founded Date April 5, 2018
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Symbolic Artificial Intelligence

In synthetic intelligence, symbolic artificial intelligence (likewise called classical synthetic intelligence or logic-based synthetic intelligence) [1] [2] is the term for the collection of all techniques in expert system research that are based upon top-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 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 ideas in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and restrictions of formal understanding and reasoning systems.

Symbolic AI was the dominant paradigm of AI research from the mid-1950s up until the mid-1990s. [4] Researchers in the 1960s and the 1970s were convinced that symbolic techniques would eventually prosper in developing a machine with synthetic general 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 promises and was followed by the very first AI Winter as funding dried up. [5] [6] A second boom (1969-1986) accompanied the increase of specialist systems, their promise of capturing business competence, and an enthusiastic business accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later on disappointment. [8] Problems with difficulties in knowledge acquisition, preserving big knowledge bases, and brittleness in handling out-of-domain issues arose. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers concentrated on addressing hidden problems in handling uncertainty and in knowledge acquisition. [10] Uncertainty was resolved with official methods such as hidden Markov designs, Bayesian thinking, and analytical relational learning. [11] [12] Symbolic device finding out dealt with the understanding acquisition issue with contributions including Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree knowing, case-based learning, and inductive logic programming to learn relations. [13]

Neural networks, a subsymbolic approach, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt’s perceptron knowing work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and work in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not deemed successful till about 2012: „Until Big Data ended up being prevalent, the general consensus in the Al community was that the so-called neural-network technique was hopeless. Systems simply didn’t work that well, compared to other techniques. … A revolution was available in 2012, when a variety of people, consisting of a group of researchers working with Hinton, worked out a way to utilize the power of GPUs to immensely increase the power of neural networks.“ [16] Over the next a number of years, deep knowing had amazing success in dealing with vision, speech acknowledgment, speech synthesis, image generation, and device translation. However, since 2020, as inherent troubles with bias, explanation, comprehensibility, and robustness became more apparent with deep knowing techniques; an increasing variety of AI researchers have actually required integrating the very best of both the symbolic and neural network methods [17] [18] and addressing locations that both approaches have difficulty with, such as sensible reasoning. [16]

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

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

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

Approaches influenced by human or animal cognition or behavior

Cybernetic techniques attempted to replicate the feedback loops between animals and their environments. A robotic turtle, with sensors, motors for driving and steering, and seven vacuum tubes for control, based on a preprogrammed neural web, was constructed as early as 1948. This work can be seen as an early precursor to later operate in neural networks, support learning, and situated robotics. [20]

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

During the 1960s, symbolic methods attained excellent success at replicating smart 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 style of research. Earlier methods based on cybernetics or synthetic neural networks were or pushed into the background.

Herbert Simon and Allen Newell studied human problem-solving skills and tried to formalize them, and their work laid the structures of the field of artificial intelligence, along with cognitive science, operations research study and management science. Their research group used the results of psychological experiments to develop programs that simulated the strategies that individuals utilized to fix issues. [22] [23] This tradition, centered at Carnegie Mellon University would eventually culminate in the advancement of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific sort of understanding that we will see later on utilized in professional systems, early symbolic AI scientists discovered another more basic application of understanding. These were called heuristics, general rules that direct a search in promising instructions: „How can non-enumerative search be practical when the underlying issue is greatly tough? The approach promoted by Simon and Newell is to use heuristics: quick algorithms that might fail on some inputs or output suboptimal options.“ [26] Another important advance was to discover a way to use these heuristics that ensures a solution will be found, if there is one, not enduring the periodic fallibility of heuristics: „The A * algorithm offered a basic frame for total and ideal heuristically guided search. A * is used as a subroutine within almost every AI algorithm today but is still no magic bullet; its guarantee of efficiency is purchased the expense of worst-case rapid time. [26]

Early deal with knowledge representation and reasoning

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

Modeling formal thinking with reasoning: the „neats“

Unlike Simon and Newell, John McCarthy felt that devices did not require to mimic the precise mechanisms of human thought, however might instead look for the essence of abstract thinking and analytical with logic, [27] despite whether individuals utilized the same algorithms. [a] His laboratory at Stanford (SAIL) concentrated on utilizing official logic to resolve a variety of problems, including understanding representation, preparation and learning. [31] Logic was also the focus of the work at the University of Edinburgh and somewhere else in Europe which resulted in the development of the shows language Prolog and the science of reasoning programs. [32] [33]

Modeling implicit sensible understanding with frames and scripts: the „scruffies“

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] found that fixing hard problems in vision and natural language processing required advertisement hoc solutions-they argued that no easy and general concept (like reasoning) would catch all the elements of smart behavior. Roger Schank explained their „anti-logic“ techniques as „scruffy“ (instead of the „neat“ paradigms at CMU and Stanford). [36] [37] Commonsense knowledge bases (such as Doug Lenat’s Cyc) are an example of „shabby“ AI, since they should be developed by hand, one complicated concept at a time. [38] [39] [40]

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

The first AI winter was a shock:

During the first AI summer, many individuals believed that machine intelligence might be achieved in just a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research to utilize AI to solve issues of nationwide 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 actually started to realize that achieving AI was going to be much more difficult than was expected a years previously, but a mix of hubris and disingenuousness led numerous university and think-tank researchers to accept funding with pledges of deliverables that they must have understood they could not satisfy. By the mid-1960s neither beneficial natural language translation systems nor autonomous tanks had been produced, and a significant reaction embeded in. New DARPA leadership canceled existing AI financing programs.

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

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

Knowledge-based systems

As restrictions with weak, domain-independent methods became increasingly more obvious, [42] researchers from all three traditions began to develop understanding into AI applications. [43] [7] The understanding transformation was driven by the realization that understanding underlies high-performance, domain-specific AI applications.

Edward Feigenbaum stated:

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

( 1) The Knowledge Principle: if a program is to carry out an intricate job well, it needs to understand a fantastic offer about the world in which it runs.
( 2) A plausible extension of that principle, called the Breadth Hypothesis: there are two additional capabilities necessary for intelligent behavior in unforeseen scenarios: drawing on increasingly basic knowledge, and analogizing to particular however far-flung understanding. [45]

Success with specialist systems

This „knowledge transformation“ led to the development and release of specialist systems (introduced by Edward Feigenbaum), the first commercially effective kind of AI software application. [46] [47] [48]

Key specialist systems were:

DENDRAL, which found the structure of organic molecules from their chemical formula and mass spectrometer readings.
MYCIN, which detected bacteremia – and recommended further laboratory tests, when required – by analyzing lab results, client history, and medical professional observations. „With about 450 guidelines, MYCIN had the ability to perform as well as some experts, and considerably much better than junior doctors.“ [49] INTERNIST and CADUCEUS which dealt with internal medicine medical diagnosis. Internist attempted to capture the knowledge of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS might ultimately detect up to 1000 different diseases.
– GUIDON, which demonstrated how a knowledge base built for expert problem solving could be repurposed for teaching. [50] XCON, to configure VAX computers, a then laborious 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:

Among the individuals at Stanford thinking about computer-based models of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genetics. When I informed him I wanted an induction „sandbox“, he stated, „I have simply the one for you.“ His laboratory was doing mass spectrometry of amino acids. The concern was: how do you go from taking a look at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we started the DENDRAL Project: I was good at heuristic search methods, and he had an algorithm that was good at producing the chemical issue space.

We did not have a grand vision. We worked bottom up. Our chemist was Carl Djerassi, creator of the chemical behind the contraceptive pill, and also among the world’s most respected mass spectrometrists. Carl and his postdocs were first-rate specialists in mass spectrometry. We started to add to their knowledge, creating understanding of engineering as we went along. These experiments amounted to titrating DENDRAL more and more knowledge. The more you did that, the smarter the program became. We had great outcomes.

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

The other expert systems mentioned above came after DENDRAL. MYCIN exemplifies the timeless expert system architecture of a knowledge-base of guidelines coupled to a symbolic reasoning mechanism, including using certainty aspects to handle unpredictability. GUIDON reveals how an explicit understanding base can be repurposed for a 2nd application, tutoring, and is an example of an intelligent tutoring system, a specific type of knowledge-based application. Clancey showed that it was not adequate just to use MYCIN’s rules for guideline, however that he also needed to add guidelines for discussion management and student modeling. [50] XCON is substantial due to the fact that of the millions of dollars it saved DEC, which activated the expert system boom where most all significant corporations in the US had professional systems groups, to catch corporate expertise, preserve it, and automate it:

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

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

Architecture of knowledge-based and expert systems

A key part of the system architecture for all professional systems is the knowledge base, which shops truths and rules for analytical. [53] The simplest technique for a skilled system understanding base is simply a collection or network of production rules. Production rules link signs in a relationship comparable to an If-Then declaration. The specialist system processes the rules to make deductions and to identify what additional details it needs, i.e. what concerns to ask, using human-readable symbols. For instance, OPS5, CLIPS and their successors Jess and Drools run in this style.

Expert systems can operate in either a forward chaining – from evidence to conclusions – or backward chaining – from objectives to required data and prerequisites – way. More sophisticated knowledge-based systems, such as Soar can also perform meta-level thinking, that is reasoning about their own thinking in terms of choosing how to solve issues and keeping an eye on the success of analytical methods.

Blackboard systems are a 2nd sort of knowledge-based or skilled system architecture. They design a neighborhood of specialists incrementally contributing, where they can, to fix an issue. The problem is represented in several levels of abstraction or alternate views. The specialists (understanding sources) offer their services whenever they recognize they can contribute. Potential problem-solving actions are represented on a program that is upgraded as the problem situation modifications. A controller chooses how helpful each contribution is, and who must make the next analytical action. One example, the BB1 chalkboard architecture [54] was originally motivated by research studies of how people prepare to perform several tasks in a trip. [55] A development of BB1 was to apply the same chalkboard design to resolving its control issue, i.e., its controller performed meta-level reasoning with understanding sources that monitored how well a plan or the problem-solving was continuing and could switch from one technique to another as conditions – such as objectives or times – changed. BB1 has actually been used in multiple domains: construction website planning, smart tutoring systems, and real-time patient monitoring.

The 2nd AI winter season, 1988-1993

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

Many factors can be provided for the arrival of the 2nd AI winter. The hardware business stopped working when far more cost-efficient basic Unix workstations from Sun together with good compilers for LISP and Prolog came onto the market. Many commercial implementations of expert systems were stopped when they proved too costly to maintain. Medical professional systems never captured on for numerous reasons: the trouble in keeping them as much as date; the challenge for doctor to find out how to utilize an overwelming variety of different expert systems for different medical conditions; and possibly most crucially, the reluctance of doctors to rely on a computer-made medical diagnosis over their gut instinct, even for particular domains where the expert systems could outperform a typical doctor. Venture capital cash deserted AI almost over night. The world AI conference IJCAI hosted an enormous and luxurious exhibition and countless nonacademic participants in 1987 in Vancouver; the main AI conference the list below year, AAAI 1988 in St. Paul, was a little and strictly scholastic affair. [9]

Including more extensive structures, 1993-2011

Uncertain thinking

Both analytical methods and extensions to reasoning were attempted.

One statistical method, hidden Markov designs, had already been popularized in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized using Bayesian Networks as a sound but efficient method of handling uncertain reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian approaches were applied successfully in specialist systems. [57] Even later on, in the 1990s, statistical relational knowing, a method that integrates likelihood with sensible formulas, permitted 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 assistance were likewise attempted. For instance, non-monotonic reasoning could be used with truth upkeep systems. A fact upkeep system tracked presumptions and validations for all reasonings. It permitted reasonings to be withdrawn when presumptions were discovered out to be incorrect or a contradiction was obtained. Explanations could be provided for a reasoning by describing which rules were applied to develop it and then continuing through underlying inferences and guidelines all the way back to root presumptions. [58] Lofti Zadeh had actually presented a various type of extension to manage the representation of vagueness. For instance, in choosing how „heavy“ or „high“ a man is, there is often no clear „yes“ or „no“ answer, and a predicate for heavy or high would instead return worths between 0 and 1. Those values represented to what degree the predicates held true. His fuzzy reasoning further supplied a method for propagating mixes of these values through rational solutions. [59]

Artificial intelligence

Symbolic device learning approaches were investigated to attend to the knowledge acquisition traffic jam. Among the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test technique to generate plausible guideline hypotheses to test versus spectra. Domain and task knowledge reduced 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 pertaining to theory development. The conception was that you had an issue solver like DENDRAL that took some inputs and produced an output. In doing so, it used layers of knowledge to steer and prune the search. That knowledge acted due to the fact that we interviewed individuals. But how did the people get the knowledge? By taking a look at thousands of spectra. So we desired a program that would take a look at thousands of spectra and infer the understanding of mass spectrometry that DENDRAL could utilize to resolve private hypothesis formation issues. We did it. We were even able to publish new understanding of mass spectrometry in the Journal of the American Chemical Society, giving 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 created a new and publishable piece of science. [51]

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

Advances were made in comprehending maker knowing theory, too. Tom Mitchell presented variation area knowing which describes learning as a search through a space of hypotheses, with upper, more basic, and lower, more specific, borders incorporating all viable hypotheses consistent with the examples seen so far. [62] More formally, Valiant introduced Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of artificial intelligence. [63]

Symbolic machine finding out encompassed more than finding out by example. E.g., John Anderson supplied a cognitive model of human learning where skill practice leads to a collection of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a trainee might learn to apply „Supplementary angles are 2 angles whose steps sum 180 degrees“ as several different procedural guidelines. E.g., one guideline might state that if X and Y are additional and you understand X, then Y will be 180 – X. He called his technique „understanding collection“. ACT-R has actually been used successfully to design aspects of human cognition, such as discovering and retention. ACT-R is also used in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer system programs, and algebra to school kids. [64]

Inductive logic programming was another approach to discovering that allowed 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 applied hereditary algorithms to program synthesis to produce hereditary programming, which he utilized to synthesize LISP programs. Finally, Zohar Manna and Richard Waldinger offered a more general method to program synthesis that synthesizes a functional program in the course of showing its specifications to be correct. [66]

As an alternative to reasoning, Roger Schank introduced case-based thinking (CBR). The CBR approach laid out 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 issue, CBR recovers the most comparable previous case and adjusts it to the specifics of the current issue. [68] Another alternative to logic, genetic algorithms and hereditary programming are based upon an evolutionary design of learning, where sets of rules are encoded into populations, the rules govern the behavior of people, and choice of the fittest prunes out sets of unsuitable guidelines over numerous generations. [69]

Symbolic device knowing was applied to discovering concepts, rules, heuristics, and problem-solving. Approaches, aside from those above, include:

1. Learning from instruction or advice-i.e., taking human guideline, postured as advice, and figuring out how to operationalize it in specific scenarios. For instance, in a game of Hearts, learning precisely how to play a hand to „prevent taking points.“ [70] 2. Learning from exemplars-improving performance by accepting subject-matter specialist (SME) feedback during training. When problem-solving fails, querying the expert to either learn a new exemplar for problem-solving or to discover a new description as to precisely why one exemplar is more pertinent than another. For example, the program Protos found out to detect tinnitus cases by communicating with an audiologist. [71] 3. Learning by analogy-constructing problem solutions based on similar problems seen in the past, and then modifying their solutions to fit a brand-new scenario or domain. [72] [73] 4. Apprentice knowing systems-learning unique options to issues by observing human analytical. Domain understanding explains why unique services are appropriate and how the service can be generalized. LEAP discovered how to develop VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., developing jobs to bring out experiments and then finding out from the results. Doug Lenat’s Eurisko, for instance, discovered heuristics to beat human gamers at the Traveller role-playing video game for two years in a row. [75] 6. Learning macro-operators-i.e., searching for beneficial macro-operators to be learned from series of standard analytical actions. Good macro-operators streamline problem-solving by permitting problems to be fixed at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now

With the increase of deep knowing, the symbolic AI approach has actually been compared to deep knowing as complementary „… with parallels having actually been drawn sometimes by AI researchers between Kahneman’s research study on human reasoning and decision making – shown in his book Thinking, Fast and Slow – and the so-called „AI systems 1 and 2″, which would in principle be modelled by deep knowing and symbolic thinking, respectively.“ In this view, symbolic reasoning is more apt for deliberative thinking, preparation, and explanation while deep learning is more apt for fast pattern acknowledgment in perceptual applications with loud data. [17] [18]

Neuro-symbolic AI: integrating 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 fashion, in order to support robust AI efficient in thinking, discovering, and cognitive modeling. As argued by Valiant [77] and lots of others, [78] the reliable building and construction of rich computational cognitive models demands the combination of sound symbolic thinking and effective (maker) knowing designs. Gary Marcus, similarly, argues that: „We can not construct abundant cognitive models in an appropriate, automated method without the triune of hybrid architecture, rich prior knowledge, and sophisticated strategies for thinking.“, [79] and in specific: „To build a robust, knowledge-driven technique to AI we need to have the machinery of symbol-manipulation in our toolkit. Too much of helpful knowledge is abstract to make do without tools that represent and manipulate abstraction, and to date, the only equipment that we know of that can manipulate such abstract knowledge dependably is the apparatus of sign control. “ [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have likewise argued for a synthesis. Their arguments are based on a need to resolve the two sort of thinking gone over in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having two elements, System 1 and System 2. System 1 is quickly, automatic, intuitive and unconscious. System 2 is slower, detailed, and specific. System 1 is the kind utilized for pattern recognition while System 2 is far much better matched for preparation, reduction, and deliberative thinking. In this view, deep learning finest models the first kind of thinking while symbolic thinking finest models the 2nd 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 thinking has actually been held every year because 2005, see http://www.neural-symbolic.org/ for information.

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

The integration of the symbolic and connectionist paradigms of AI has been pursued by a reasonably little research study community over the last twenty years and has actually yielded a number of significant outcomes. Over the last decade, neural symbolic systems have actually been shown capable of getting rid of 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 reasonings (d’Avila Garcez and Lamb, 2006) and fragments of first-order reasoning (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have actually been applied to a number of problems in the locations of bioinformatics, control engineering, software verification and adjustment, visual intelligence, ontology knowing, and video game. [78]

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

– Symbolic Neural symbolic-is the present method of many neural designs in natural language processing, where words or subword tokens are both the ultimate input and output of large language designs. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic strategies are used to call neural techniques. In this case the symbolic method is Monte Carlo tree search and the neural methods learn how to evaluate game positions.
– Neural|Symbolic-uses a neural architecture to interpret perceptual information as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to generate or label training information that is subsequently discovered by a deep knowing model, e.g., to train a neural model for symbolic computation by using a Macsyma-like symbolic mathematics system to create or identify examples.
– Neural _ Symbolic -utilizes a neural web that is created 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 guidelines and terms. Logic Tensor Networks [86] also fall under this category.
– Neural [Symbolic] -allows a neural model to straight call a symbolic reasoning engine, e.g., to perform an action or assess a state.

Many crucial research study concerns remain, 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 extracted from them?
– How should common-sense knowledge be learned and reasoned about?
– How can abstract knowledge that is hard to encode rationally be managed?

Techniques and contributions

This section supplies an overview of strategies and contributions in a total context resulting in many other, more comprehensive posts in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered previously in the history area.

AI programming languages

The crucial AI shows language in the US throughout the last symbolic AI boom period was LISP. LISP is the 2nd earliest programming language after FORTRAN and was developed in 1958 by John McCarthy. LISP supplied the very first read-eval-print loop to support quick program advancement. Compiled functions might be easily blended with translated functions. Program tracing, stepping, and breakpoints were likewise provided, along with the capability to alter values or functions and continue from breakpoints or mistakes. It had the first self-hosting compiler, suggesting that the compiler itself was initially composed in LISP and then ran interpretively to assemble the compiler code.

Other essential developments originated by LISP that have infected other shows languages include:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

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

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

Alain Colmerauer and Philippe Roussel are credited as the creators of Prolog. Prolog is a type of logic programming, which was invented by Robert Kowalski. Its history was also influenced by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of techniques. For more information see the section on the origins of Prolog in the PLANNER article.

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

Japan promoted Prolog for its Fifth Generation Project, planning to develop special hardware for high performance. Similarly, LISP machines were constructed to run LISP, however as the second AI boom turned to bust these business might not take on brand-new workstations that might now run LISP or Prolog natively at similar speeds. See the history section for more information.

Smalltalk was another influential AI programming language. For instance, it presented metaclasses and, along with Flavors and CommonLoops, affected the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the present standard Lisp dialect. CLOS is a Lisp-based object-oriented system that allows several inheritance, in addition to incremental extensions to both classes and metaclasses, hence supplying a run-time meta-object protocol. [88]

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

Search

Search emerges in numerous kinds of issue resolving, including planning, restriction fulfillment, and playing games such as checkers, chess, and go. The very best known AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven provision knowing, and the DPLL algorithm. For adversarial search when playing video games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and reasoning

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

Knowledge representation

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

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

First-order reasoning is more basic than description reasoning. The automated theorem provers discussed below can prove theorems in first-order reasoning. Horn provision reasoning is more limited than first-order reasoning and is used in logic programming languages such as Prolog. Extensions to first-order reasoning consist of temporal logic, to manage time; epistemic reasoning, to reason about representative understanding; modal reasoning, to manage possibility and necessity; and probabilistic logics to manage logic and possibility together.

Automatic theorem showing

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

Prover9.
ACL2.
Vampire.

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

Reasoning in knowledge-based systems

Knowledge-based systems have a specific knowledge base, usually of rules, to boost reusability across domains by separating procedural code and domain understanding. A different reasoning engine processes guidelines and includes, deletes, or modifies a knowledge shop.

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

A more versatile sort of analytical takes place when reasoning about what to do next takes place, rather than merely selecting among the readily available 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 capabilities, such as the capability to assemble often utilized understanding into higher-level pieces.

Commonsense thinking

Marvin Minsky initially proposed frames as a way of analyzing common visual scenarios, such as an office, and Roger Schank extended this concept to scripts for typical routines, such as eating in restaurants. Cyc has actually tried to record useful sensible understanding and has „micro-theories“ to manage specific sort of domain-specific thinking.

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

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

Constraints and constraint-based thinking

Constraint solvers perform a more minimal sort of inference than first-order reasoning. They can simplify sets of spatiotemporal restraints, such as those for RCC or Temporal Algebra, in addition to fixing other type of puzzle issues, such as Wordle, Sudoku, cryptarithmetic issues, and so on. Constraint logic programming can be used to fix scheduling issues, for instance with restraint dealing with guidelines (CHR).

Automated preparation

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

Natural language processing

Natural language processing focuses on dealing with language as data to perform jobs such as identifying subjects without necessarily comprehending the intended meaning. Natural language understanding, on the other hand, constructs a significance representation and uses that for further processing, such as answering questions.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all aspects of natural language processing long managed by symbolic AI, however considering that enhanced by deep knowing techniques. In symbolic AI, discourse representation theory and first-order logic have actually been utilized to represent sentence significances. Latent semantic analysis (LSA) and specific semantic analysis also provided vector representations of documents. In the latter case, vector components are interpretable as principles named by Wikipedia short articles.

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

Agents and multi-agent systems

Agents are self-governing systems embedded in an environment they view and act on in some sense. Russell and Norvig’s basic book on expert system is organized to reflect representative architectures of increasing elegance. [91] The elegance of representatives differs from simple reactive representatives, to those with a model of the world and automated preparation capabilities, potentially a BDI representative, i.e., one with beliefs, desires, and intents – or alternatively a support finding out model learned in time to select actions – as much as a combination of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep learning for understanding. [92]

In contrast, a multi-agent system includes multiple agents that interact amongst themselves with some inter-agent interaction 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 capability to divide work amongst the agents and to increase fault tolerance when agents are lost. Research problems consist of how representatives reach agreement, distributed issue solving, multi-agent knowing, multi-agent planning, and dispersed restriction optimization.

Controversies developed from at an early stage in symbolic AI, both within the field-e.g., between logicists (the pro-logic „neats“) and non-logicists (the anti-logic „scruffies“)- and in between those who accepted AI but turned down symbolic approaches-primarily connectionists-and those outside the field. Critiques from beyond the field were mainly from philosophers, on intellectual premises, but also from financing companies, especially during the 2 AI winters.

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

Limitations were found in utilizing basic first-order logic to factor about vibrant domains. Problems were found both with concerns to mentioning the prerequisites for an action to be successful and in providing axioms for what did not change after an action was performed.

McCarthy and Hayes introduced the Frame Problem in 1969 in the paper, „Some Philosophical Problems from the Standpoint of Expert System.“ [93] A simple example happens in „proving that one person might enter discussion with another“, as an axiom asserting „if a person has a telephone he still has it after searching for a number in the telephone book“ would be needed for the reduction to be successful. Similar axioms would be required for other domain actions to specify what did not alter.

A similar problem, called the Qualification Problem, occurs in attempting to identify the prerequisites for an action to succeed. An unlimited number of pathological conditions can be imagined, e.g., a banana in a tailpipe might avoid an automobile from running correctly.

McCarthy’s technique to repair the frame problem was circumscription, a kind of non-monotonic logic where deductions could be made from actions that need only define what would change while not having to clearly define everything that would not change. Other non-monotonic reasonings supplied fact upkeep systems that revised beliefs causing contradictions.

Other methods of managing more open-ended domains included probabilistic reasoning systems and maker learning to discover new ideas and guidelines. McCarthy’s Advice Taker can be deemed an inspiration here, as it could integrate new knowledge supplied by a human in the form of assertions or rules. For example, speculative symbolic machine learning systems checked out the ability to take top-level natural language suggestions and to interpret it into domain-specific actionable guidelines.

Similar to the issues in managing dynamic domains, common-sense reasoning is also difficult to catch in official thinking. Examples of sensible thinking consist of implicit reasoning about how people think or basic knowledge of everyday events, objects, and living animals. This type of understanding is considered approved and not deemed noteworthy. Common-sense thinking is an open location of research and challenging both for symbolic systems (e.g., Cyc has actually tried to catch key parts of this knowledge over more than a decade) and neural systems (e.g., self-driving vehicles that do not understand not to drive into cones or not to hit pedestrians walking a bicycle).

McCarthy viewed his Advice Taker as having common-sense, but his meaning of sensible was various than the one above. [94] He specified a program as having sound judgment „if it automatically deduces for itself an adequately wide class of immediate repercussions of anything it is informed and what it currently understands. „

Connectionist AI: philosophical challenges and sociological disputes

Connectionist methods consist of earlier work on 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 advanced methods, such as Transformers, GANs, and other work in deep learning.

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

1. Implementationism-where connectionist architectures implement the abilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected absolutely, and connectionist architectures underlie intelligence and are fully enough to describe it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are deemed complementary and both are required for intelligence

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

The third and last position I want to analyze here is what I call the moderate connectionist view, a more eclectic view of the present dispute in between connectionism and symbolic AI. One of the researchers who has elaborated this position most clearly is Andy Clark, a theorist from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark protected hybrid (partly symbolic, partially connectionist) systems. He claimed that (at least) 2 type of theories are needed in order to study and design cognition. On the one hand, for some information-processing jobs (such as pattern acknowledgment) connectionism has benefits over symbolic models. But on the other hand, for other cognitive procedures (such as serial, deductive reasoning, and generative sign manipulation processes) the symbolic paradigm offers adequate designs, and not just „approximations“ (contrary to what extreme connectionists would declare). [97]

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

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

And yet, for the most part, that’s how most existing AI profits. Hinton and many others have actually striven to get rid of symbols altogether. The deep knowing hope-seemingly grounded not a lot in science, however in a sort of historic grudge-is that intelligent behavior will emerge purely from the confluence of enormous information and deep knowing. Where classical computer systems and software application fix tasks by defining sets of symbol-manipulating guidelines dedicated to particular tasks, such as modifying a line in a word processor or carrying out a computation in a spreadsheet, neural networks generally try to fix jobs by statistical approximation and finding out from examples.

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

When deep learning reemerged in 2012, it was with a sort of take-no-prisoners mindset that has characterized the majority of the last decade. By 2015, his hostility toward all things symbols had actually totally crystallized. He offered a talk at an AI workshop at Stanford comparing signs to aether, among science’s biggest mistakes.

Since then, his anti-symbolic campaign has just increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep learning in among science’s most essential journals, Nature. It closed with a direct attack on symbol adjustment, calling not for reconciliation however for straight-out replacement. Later, Hinton told an event of European Union leaders that investing any more money in symbol-manipulating methods was „a huge error,“ comparing it to investing in internal combustion engines in the age of electric cars and trucks. [98]

Part of these disputes may be due to unclear terms:

Turing award winner Judea Pearl offers a review of machine knowing which, unfortunately, 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 expert systems dispossessed of any ability to discover. Making use of the terminology requires explanation. Artificial intelligence is not restricted to association guideline mining, c.f. the body of work on symbolic ML and relational knowing (the distinctions to deep knowing being the option of representation, localist rational instead of dispersed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not just about production rules composed by hand. A proper definition of AI concerns understanding representation and thinking, autonomous multi-agent systems, preparation and argumentation, in addition to learning. [99]

Situated robotics: the world as a model

Another critique of symbolic AI is the embodied cognition approach:

The embodied cognition approach claims that it makes no sense to think about 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 functioning exploits consistencies in its environment, including the rest of its body. Under the embodied cognition technique, robotics, vision, and other sensors end up being main, not peripheral. [100]

Rodney Brooks invented behavior-based robotics, one technique to embodied cognition. Nouvelle AI, another name for this technique, is viewed as an alternative to both symbolic AI and connectionist AI. His method turned down representations, either symbolic or distributed, as not only unnecessary, however as damaging. Instead, he created the subsumption architecture, a layered architecture for embodied representatives. Each layer achieves a various function and should function in the real life. For instance, the first robotic he explains in Intelligence Without Representation, has 3 layers. The bottom layer translates sonar sensing units to prevent things. The middle layer triggers the robot to wander around when there are no barriers. The top layer triggers the robotic to go to more distant locations for additional exploration. Each layer can momentarily inhibit or suppress a lower-level layer. He slammed AI researchers for defining AI problems for their systems, when: „There is no tidy department in between understanding (abstraction) and reasoning in the genuine world.“ [101] He called his robots „Creatures“ and each layer was „made up of a fixed-topology network of basic finite state machines.“ [102] In the Nouvelle AI approach, „First, it is critically important to check the Creatures we build in the genuine world; i.e., in the same world that we humans populate. It is dreadful to fall under the temptation of testing them in a streamlined world first, even with the best objectives of later moving activity to an unsimplified world.“ [103] His emphasis on real-world screening was in contrast to „Early work in AI focused on video games, geometrical problems, symbolic algebra, theorem proving, and other formal systems“ [104] and making use of the blocks world in symbolic AI systems such as SHRDLU.

Current views

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

Hybrid AIs including several of these methods are presently considered as the path forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw locations where AI did not have complete responses and said that Al is therefore impossible; we now see much of these exact same locations undergoing ongoing research study and advancement leading to increased ability, not impossibility. [100]

Expert system.
Automated preparation and scheduling
Automated theorem proving
Belief modification
Case-based thinking
Cognitive architecture
Cognitive science
Connectionism
Constraint programs
Deep knowing
First-order reasoning
GOFAI
History of synthetic intelligence
Inductive reasoning shows
Knowledge-based systems
Knowledge representation and reasoning
Logic shows
Machine knowing
Model checking
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 said: „This is AI, so we don’t care if it’s mentally real“. [4] McCarthy restated his position in 2006 at the AI@50 conference where he said „Artificial intelligence is not, by definition, simulation of human intelligence“. [28] Pamela McCorduck composes that there are „2 major branches of expert system: one intended at producing smart habits no matter how it was accomplished, and the other focused on modeling intelligent processes discovered in nature, particularly human ones.“, [29] Stuart Russell and Peter Norvig composed „Aeronautical engineering texts do not define the goal of their field as making ‚makers that fly so exactly like pigeons that they can trick even other pigeons.'“ [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). „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.
^ 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 synthetic intelligence: representing objects and relations“. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). „Learning representations by back-propagating errors“. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). „Backpropagation Applied to Handwritten Zip Code Recognition“. Neural Computation. 1 (4 ): 541-551. doi:10.1162/ neco.1989.1.4.541. S2CID 41312633.
^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. „Thinking Fast and Slow in AI“. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. „AAAI Presidential Address: The State of AI“. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). „An interview with Ed Feigenbaum“. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
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^ Russell & Norvig 2021, pp. 22-24.
^ McCorduck 2004, pp. 327-335, 434-435.
^ Crevier 1993, pp. 145-62, 197-203.
^ a b Russell & Norvig 2021, p. 23.
^ a b Clancey 1987.
^ a b Shustek, Len (2010 ). „An interview with Ed Feigenbaum“. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-08-05.
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