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Symbolic Expert System

In expert system, symbolic synthetic intelligence (likewise known as classical expert system or logic-based expert system) [1] [2] is the term for the collection of all methods in expert system research that are based on top-level symbolic (human-readable) representations of problems, logic and search. [3] Symbolic AI utilized tools such as reasoning shows, production guidelines, semantic internet and frames, and it established applications such as knowledge-based systems (in specific, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm caused influential concepts in search, symbolic programs languages, representatives, multi-agent systems, the semantic web, and the strengths and limitations of official understanding and thinking systems.

Symbolic AI was the dominant paradigm of AI research from the mid-1950s until the mid-1990s. [4] Researchers in the 1960s and the 1970s were encouraged that symbolic techniques would ultimately succeed in developing a device with artificial 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, caused impractical expectations and pledges and was followed by the very first AI Winter as funding dried up. [5] [6] A second boom (1969-1986) accompanied the rise of specialist systems, their promise of capturing business competence, and a passionate business accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later . [8] Problems with problems in understanding acquisition, preserving large understanding bases, and brittleness in managing out-of-domain issues occurred. Another, 2nd, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers concentrated on addressing hidden issues in managing uncertainty and in understanding acquisition. [10] Uncertainty was attended to with formal approaches such as hidden Markov designs, Bayesian thinking, and analytical relational knowing. [11] [12] Symbolic maker finding out dealt with the knowledge acquisition issue with contributions including Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree learning, case-based learning, and inductive reasoning shows to find out relations. [13]

Neural networks, a subsymbolic method, had been pursued from early days and reemerged highly in 2012. Early examples are Rosenblatt’s perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and operate in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not seen as effective up until about 2012: “Until Big Data became prevalent, the general 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 approaches. … A transformation can be found in 2012, when a number of people, including a group of researchers dealing with Hinton, worked out a way to use the power of GPUs to immensely increase the power of neural networks.” [16] Over the next a number of years, deep learning had magnificent success in managing vision, speech recognition, speech synthesis, image generation, and machine translation. However, because 2020, as intrinsic problems with bias, description, coherence, and effectiveness ended up being more evident with deep learning methods; an increasing variety of AI researchers have required combining the very best of both the symbolic and neural network approaches [17] [18] and attending to areas that both methods have difficulty with, such as common-sense reasoning. [16]

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

The first AI summer season: unreasonable liveliness, 1948-1966

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

Approaches motivated by human or animal cognition or habits

Cybernetic approaches tried to reproduce the feedback loops in 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 built as early as 1948. This work can be viewed as an early precursor to later operate in neural networks, reinforcement learning, and located robotics. [20]

A crucial 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 primary 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 solved problems represented with formal operators by means of state-space search utilizing means-ends analysis. [21]

During the 1960s, symbolic approaches accomplished fantastic success at imitating smart habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was concentrated in 4 organizations in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Each one developed its own design of research study. Earlier approaches based upon cybernetics or synthetic neural networks were deserted or pushed 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 artificial intelligence, in addition to cognitive science, operations research and management science. Their research team utilized the results of mental experiments to establish programs that simulated the strategies that people utilized to solve problems. [22] [23] This tradition, centered at Carnegie Mellon University would ultimately culminate in the advancement of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific 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 guide a search in appealing instructions: “How can non-enumerative search be practical when the underlying problem is exponentially hard? The technique promoted by Simon and Newell is to employ heuristics: quick algorithms that may fail on some inputs or output suboptimal services.” [26] Another crucial advance was to find a way to use these heuristics that ensures a service will be discovered, if there is one, not enduring the occasional fallibility of heuristics: “The A * algorithm offered a basic frame for total and optimal heuristically directed search. A * is utilized as a subroutine within almost every AI algorithm today but is still no magic bullet; its guarantee of completeness is bought at the expense of worst-case rapid time. [26]

Early deal with understanding representation and thinking

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

Modeling formal reasoning with logic: the “neats”

Unlike Simon and Newell, John McCarthy felt that makers did not need to replicate the specific systems of human idea, however might rather look for the essence of abstract reasoning and problem-solving with reasoning, [27] regardless of whether people utilized the same algorithms. [a] His lab at Stanford (SAIL) focused on utilizing formal logic to resolve a wide range of issues, including knowledge representation, preparation and knowing. [31] Logic was also the focus of the work at the University of Edinburgh and somewhere else in Europe which caused the advancement of the programs language Prolog and the science of logic programming. [32] [33]

Modeling implicit 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 tough issues in vision and natural language processing needed ad hoc solutions-they argued that no basic and basic concept (like reasoning) would record all the aspects of intelligent habits. Roger Schank described their “anti-logic” approaches as “shabby” (as opposed to the “neat” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “shabby” AI, since they need to be built by hand, one complex principle at a time. [38] [39] [40]

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

The very first AI winter season was a shock:

During the very first AI summer season, numerous people thought that maker intelligence could be accomplished in simply a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research study to use AI to solve issues of national security; in particular, to automate the translation of Russian to English for intelligence operations and to create autonomous tanks for the battleground. Researchers had begun to realize that accomplishing AI was going to be much more difficult than was supposed a years previously, however a combination of hubris and disingenuousness led lots of university and think-tank scientists to accept financing with pledges of deliverables that they must have known they might not satisfy. By the mid-1960s neither helpful natural language translation systems nor self-governing tanks had been developed, and a remarkable backlash set in. New DARPA leadership canceled existing AI financing programs.

Outside of the United States, the most fertile ground for AI research study was the UK. The AI winter in the UK 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 study funding. A professor of used mathematics, Sir James Lighthill, was commissioned by Parliament to examine the state of AI research study in the nation. The report stated that all of the problems being dealt with in AI would be much better managed by researchers from other disciplines-such as used mathematics. The report likewise claimed that AI successes on toy problems could never scale to real-world applications due to combinatorial surge. [41]

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

Knowledge-based systems

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

Edward Feigenbaum said:

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

( 1) The Knowledge Principle: if a program is to perform a complex task well, it needs to understand an excellent deal about the world in which it runs.
( 2) A possible extension of that concept, called the Breadth Hypothesis: there are 2 additional abilities essential for intelligent behavior in unanticipated scenarios: falling back on increasingly general knowledge, and analogizing to specific however remote understanding. [45]

Success with specialist systems

This “knowledge revolution” led to the development and implementation of professional systems (presented by Edward Feigenbaum), the very first commercially successful form 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 suggested more lab tests, when required – by analyzing laboratory outcomes, patient history, and doctor observations. “With about 450 rules, MYCIN had the ability to carry out in addition to some specialists, and significantly better than junior physicians.” [49] INTERNIST and CADUCEUS which tackled internal medicine medical diagnosis. Internist attempted to record the competence of the chairman of internal medicine at the University of Pittsburgh School of Medicine while CADUCEUS could ultimately identify up to 1000 different illness.
– GUIDON, which demonstrated how an understanding base constructed for expert problem solving could be repurposed for mentor. [50] XCON, to configure VAX computers, a then tiresome process that might use up to 90 days. XCON lowered the time to about 90 minutes. [9]
DENDRAL is thought about the first expert system that relied on knowledge-intensive problem-solving. It is explained below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

One of individuals at Stanford thinking about computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I wanted an induction “sandbox”, he said, “I have just the one for you.” His lab was doing mass spectrometry of amino acids. The question 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 great at heuristic search methods, and he had an algorithm that was great at generating the chemical issue area.

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, inventor of the chemical behind the contraceptive pill, and likewise one of the world’s most respected mass spectrometrists. Carl and his postdocs were first-rate professionals in mass spectrometry. We started to add to their understanding, developing knowledge of engineering as we went along. These experiments totaled up to titrating DENDRAL increasingly more knowledge. 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 profession that is the big, “Ah ha!,” and it wasn’t the way AI was being done previously. Sounds basic, however it’s most likely AI’s most effective generalization. [51]

The other professional systems discussed above followed DENDRAL. MYCIN exemplifies the traditional specialist system architecture of a knowledge-base of rules paired to a symbolic reasoning system, consisting of making use of certainty factors to deal with unpredictability. GUIDON shows how a specific understanding base can be repurposed for a 2nd application, tutoring, and is an example of a smart tutoring system, a particular sort of knowledge-based application. Clancey revealed that it was not adequate merely to use MYCIN’s rules for guideline, however that he also needed to add rules for dialogue management and trainee modeling. [50] XCON is significant since of the millions of dollars it saved DEC, which activated the expert system boom where most all significant corporations in the US had expert systems groups, to catch corporate know-how, protect it, and automate it:

By 1988, DEC’s AI group had 40 expert systems released, with more on the way. DuPont had 100 in use and 500 in development. Nearly every significant U.S. corporation had its own Al group and was either utilizing or examining professional systems. [49]

Chess professional knowledge was encoded in Deep Blue. In 1996, this permitted IBM’s Deep Blue, with the help 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 skilled systems

An essential element of the system architecture for all expert systems is the knowledge base, which stores realities and guidelines for problem-solving. [53] The easiest technique for a skilled system knowledge base is simply a collection or network of production rules. Production guidelines connect symbols in a relationship comparable to an If-Then declaration. The specialist system processes the rules to make reductions and to identify what additional info it requires, i.e. what questions to ask, using human-readable signs. For example, OPS5, CLIPS and their followers Jess and Drools operate in this fashion.

Expert systems can run in either a forward chaining – from evidence to conclusions – or backwards chaining – from objectives to needed data and prerequisites – manner. More sophisticated knowledge-based systems, such as Soar can likewise carry out meta-level reasoning, that is reasoning about their own thinking in regards to choosing how to resolve issues and keeping an eye on the success of problem-solving strategies.

Blackboard systems are a 2nd sort of knowledge-based or skilled system architecture. They model a neighborhood of specialists incrementally contributing, where they can, to fix an issue. The problem is represented in multiple levels of abstraction or alternate views. The experts (knowledge sources) volunteer their services whenever they recognize they can contribute. Potential analytical actions are represented on an agenda that is updated as the issue situation modifications. A controller chooses how useful each contribution is, and who must make the next analytical action. One example, the BB1 blackboard architecture [54] was initially influenced by research studies of how people plan to perform several jobs in a journey. [55] An innovation of BB1 was to use the exact same chalkboard model to fixing its control issue, i.e., its controller performed meta-level reasoning with knowledge sources that kept track of how well a plan or the problem-solving was proceeding and could change from one method to another as conditions – such as goals or times – changed. BB1 has actually been used in numerous domains: building website planning, intelligent tutoring systems, and real-time patient tracking.

The second AI winter, 1988-1993

At the height of the AI boom, business such as Symbolics, LMI, and Texas Instruments were offering LISP makers particularly targeted to speed up the advancement of AI applications and research study. In addition, a number of expert system business, such as Teknowledge and Inference Corporation, were selling professional system shells, training, and speaking with to corporations.

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

Many reasons can be used for the arrival of the second AI winter. The hardware business failed when much more affordable basic Unix workstations from Sun together with great compilers for LISP and Prolog came onto the marketplace. Many business deployments of specialist systems were stopped when they proved too expensive to preserve. Medical professional systems never captured on for numerous factors: the trouble in keeping them approximately date; the challenge for physician to discover how to use a bewildering variety of different expert systems for various medical conditions; and maybe most crucially, the hesitation of physicians to trust a computer-made diagnosis over their gut impulse, even for particular domains where the expert systems might surpass a typical physician. Equity capital cash deserted AI practically overnight. The world AI conference IJCAI hosted an enormous and extravagant exhibition and thousands of nonacademic attendees in 1987 in Vancouver; the primary AI conference the list below year, AAAI 1988 in St. Paul, was a small and strictly scholastic affair. [9]

Adding in more extensive structures, 1993-2011

Uncertain thinking

Both statistical approaches and extensions to reasoning were attempted.

One analytical approach, concealed Markov designs, had currently been promoted in the 1980s for speech acknowledgment work. [11] Subsequently, in 1988, Judea Pearl promoted using Bayesian Networks as a sound however efficient method of handling unpredictable reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian techniques were applied successfully in expert systems. [57] Even later on, in the 1990s, analytical relational knowing, a technique that integrates possibility with sensible formulas, permitted probability to be integrated with first-order reasoning, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.

Other, non-probabilistic extensions to first-order logic to assistance were also tried. For example, non-monotonic reasoning might be used with fact upkeep systems. A truth maintenance system tracked assumptions and justifications for all reasonings. It allowed reasonings to be withdrawn when presumptions were learnt to be inaccurate or a contradiction was obtained. Explanations could be attended to a reasoning by describing which guidelines were used to develop it and after that continuing through underlying inferences and guidelines all the way back to root presumptions. [58] Lofti Zadeh had actually presented a various sort of extension to handle the representation of vagueness. For instance, in choosing how “heavy” or “tall” a man is, there is frequently no clear “yes” or “no” response, and a predicate for heavy or high would rather return values between 0 and 1. Those worths represented to what degree the predicates were real. His fuzzy reasoning even more provided a method for propagating combinations of these worths through sensible solutions. [59]

Machine learning

Symbolic maker learning techniques were examined to attend to the knowledge acquisition traffic jam. Among the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test strategy to produce plausible rule hypotheses to evaluate versus spectra. Domain and task knowledge decreased the variety of prospects evaluated to a workable size. Feigenbaum described Meta-DENDRAL as

… the culmination of my imagine the early to mid-1960s relating to 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 utilized layers of knowledge to guide and prune the search. That knowledge got in there due to the fact that we talked to individuals. But how did individuals get the understanding? By taking a look at thousands of spectra. So we desired a program that would look at thousands of spectra and infer the knowledge of mass spectrometry that DENDRAL might utilize to fix individual hypothesis formation problems. We did it. We were even able to release brand-new knowledge of mass spectrometry in the Journal of the American Chemical Society, providing credit just in a footnote that a program, Meta-DENDRAL, actually did it. We had the ability to do something that had been a dream: to have a computer system program come up with a new and publishable piece of science. [51]

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

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

Symbolic maker finding out incorporated more than finding out by example. E.g., John Anderson provided a cognitive design of human knowing where skill practice results in a collection of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For example, a student may learn to use “Supplementary angles are 2 angles whose procedures sum 180 degrees” as a number of different procedural guidelines. E.g., one guideline might state that if X and Y are supplementary and you understand X, then Y will be 180 – X. He called his method “understanding compilation”. ACT-R has been utilized effectively to model elements of human cognition, such as learning and retention. ACT-R is likewise utilized in intelligent tutoring systems, called cognitive tutors, to successfully teach geometry, computer programs, and algebra to school kids. [64]

Inductive logic shows was another method to learning that enabled logic programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) could synthesize Prolog programs from examples. [65] John R. Koza applied hereditary algorithms to program synthesis to create genetic shows, which he used to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger supplied a more basic method to program synthesis that synthesizes a practical program in the course of showing its specifications to be appropriate. [66]

As an option to reasoning, Roger Schank introduced case-based thinking (CBR). The CBR technique laid out in his book, Dynamic Memory, [67] focuses first on keeping in mind essential problem-solving cases for future use and generalizing them where appropriate. When confronted with a new problem, CBR recovers the most similar previous case and adapts it to the specifics of the present issue. [68] Another option to reasoning, hereditary algorithms and genetic programming are based on an evolutionary design of knowing, where sets of guidelines are encoded into populations, the rules govern the behavior of people, and choice of the fittest prunes out sets of inappropriate guidelines over many generations. [69]

Symbolic artificial intelligence was used to learning ideas, guidelines, heuristics, and problem-solving. Approaches, other than those above, include:

1. Learning from instruction or advice-i.e., taking human direction, posed as recommendations, and determining how to operationalize it in particular situations. For example, in a game of Hearts, finding out exactly how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving performance by accepting subject-matter specialist (SME) feedback throughout training. When problem-solving stops working, querying the specialist to either find out a brand-new prototype for problem-solving or to discover a new explanation as to exactly why one prototype is more pertinent than another. For instance, the program Protos found out to detect tinnitus cases by interacting with an audiologist. [71] 3. Learning by analogy-constructing issue services based upon comparable issues seen in the past, and after that customizing their options to fit a new situation or domain. [72] [73] 4. Apprentice learning systems-learning unique solutions to problems by observing human analytical. Domain knowledge discusses why novel solutions are right 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 perform experiments and then finding out from the outcomes. Doug Lenat’s Eurisko, for instance, learned 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., looking for helpful macro-operators to be learned from series of fundamental problem-solving actions. Good macro-operators simplify problem-solving by allowing problems to be solved at a more abstract level. [76]
Deep learning and neuro-symbolic AI 2011-now

With the rise of deep learning, the symbolic AI method has actually been compared to deep knowing as complementary “… with parallels having been drawn sometimes by AI researchers in between Kahneman’s research on human reasoning and choice making – reflected in his book Thinking, Fast and Slow – and the so-called “AI systems 1 and 2″, which would in principle be modelled by deep knowing and symbolic thinking, respectively.” In this view, symbolic reasoning is more apt for deliberative reasoning, preparation, and description 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 approaches

Neuro-symbolic AI efforts to incorporate neural and symbolic architectures in a manner that addresses strengths and weaknesses of each, in a complementary fashion, in order to support robust AI efficient in reasoning, learning, and cognitive modeling. As argued by Valiant [77] and many others, [78] the effective building and construction of rich computational cognitive models requires the combination of sound symbolic thinking and effective (device) knowing designs. Gary Marcus, likewise, argues that: “We can not build rich cognitive designs in an adequate, automated method without the set of three of hybrid architecture, abundant prior knowledge, and sophisticated methods for thinking.”, [79] and in specific: “To build a robust, knowledge-driven approach to AI we should have the machinery of symbol-manipulation in our toolkit. Too much of useful understanding is abstract to make do without tools that represent and manipulate abstraction, and to date, the only machinery that we understand of that can manipulate such abstract understanding dependably is the apparatus of symbol manipulation. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based on a need to address the two type of believing talked about in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having 2 parts, System 1 and System 2. System 1 is quick, automated, user-friendly and unconscious. System 2 is slower, detailed, and explicit. System 1 is the kind used for pattern acknowledgment while System 2 is far much better matched for preparation, deduction, and deliberative thinking. In this view, deep knowing finest designs the very first sort of believing while symbolic thinking finest designs the second kind and both are required.

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

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 relatively little research community over the last 20 years and has actually yielded several considerable outcomes. Over the last years, neural symbolic systems have been shown capable of conquering 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 shown capable of representing modal and temporal reasonings (d’Avila Garcez and Lamb, 2006) and pieces of first-order reasoning (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have been applied to a variety of problems in the areas of bioinformatics, control engineering, software verification and adaptation, visual intelligence, ontology knowing, and video game. [78]

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

– Symbolic Neural symbolic-is the existing approach of numerous neural models 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 techniques are used to call neural strategies. In this case the symbolic approach is Monte Carlo tree search and the neural methods find out how to examine video game positions.
– Neural|Symbolic-uses a neural architecture to interpret affective data as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to create or label training data that is consequently found out by a deep knowing design, e.g., to train a neural design for symbolic computation by utilizing a Macsyma-like symbolic mathematics system to create or label examples.
– Neural _ Symbolic -uses a neural web that is produced from symbolic rules. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR evidence tree generated from knowledge base rules and terms. Logic Tensor Networks [86] likewise fall into this category.
– Neural [Symbolic] -allows a neural model to directly call a symbolic reasoning engine, e.g., to perform an action or evaluate a state.

Many key research study concerns 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 extracted from them?
– How should sensible knowledge be learned and reasoned about?
– How can abstract understanding that is difficult to encode logically be handled?

Techniques and contributions

This area provides an introduction of strategies and contributions in a general context leading to many other, more in-depth posts in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered earlier in the history area.

AI programs languages

The key AI programming language in the US throughout the last symbolic AI boom duration was LISP. LISP is the second earliest programming language after FORTRAN and was created in 1958 by John McCarthy. LISP offered the very first read-eval-print loop to support quick program advancement. Compiled functions could be freely mixed with analyzed functions. Program tracing, stepping, and breakpoints were also provided, together with the ability to alter worths or functions and continue from breakpoints or errors. It had the very first self-hosting compiler, indicating that the compiler itself was initially written in LISP and then ran interpretively to compile the compiler code.

Other essential developments originated by LISP that have actually spread out to other programming languages include:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

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

In contrast to the US, in Europe the key AI programs language throughout that exact same period was Prolog. Prolog provided a built-in shop of truths and stipulations that could be queried by a read-eval-print loop. The shop might act as an understanding base and the clauses might function as guidelines or a limited kind of reasoning. As a subset of first-order logic Prolog was based on Horn stipulations with a closed-world assumption-any truths not known were thought about false-and a special name presumption for primitive terms-e.g., the identifier barack_obama was thought about to refer to precisely one things. Backtracking and unification are integrated to Prolog.

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

Prolog is likewise a sort of declarative shows. The logic clauses that describe programs are directly translated to run the programs specified. No explicit series of actions is required, as is the case with imperative shows languages.

Japan promoted Prolog for its Fifth Generation Project, intending to develop unique hardware for high performance. Similarly, LISP makers were developed to run LISP, but as the second AI boom turned to bust these business could not compete with new workstations that might now run LISP or Prolog natively at comparable speeds. See the history area for more information.

Smalltalk was another prominent AI programs language. For instance, it presented metaclasses and, together with 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, hence offering a run-time meta-object protocol. [88]

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

Search

Search occurs in lots of type of problem solving, including planning, restriction fulfillment, and playing games such as checkers, chess, and go. The finest 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 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 thinking

Multiple different methods to represent knowledge and then factor with those representations have been examined. Below is a fast introduction of methods to understanding representation and automated thinking.

Knowledge representation

Semantic networks, conceptual charts, frames, and reasoning are all techniques to modeling understanding such as domain knowledge, analytical 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 used for any domain while WordNet is a lexical resource that can likewise be considered as an ontology. YAGO integrates WordNet as part of its ontology, to line up realities extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology presently being utilized.

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

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

Automatic theorem proving

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

Prover9.
ACL2.
Vampire.

Prover9 can be used 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 referred to as Nqthm.

Reasoning in knowledge-based systems

Knowledge-based systems have a specific understanding base, normally of rules, to enhance reusability across domains by separating procedural code and domain understanding. A different reasoning engine procedures rules and includes, deletes, or modifies an understanding store.

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

A more versatile kind of problem-solving happens when thinking about what to do next happens, rather than merely selecting one of the available actions. This sort of meta-level reasoning is used in Soar and in the BB1 blackboard architecture.

Cognitive architectures such as ACT-R may have extra abilities, such as the capability to compile often utilized knowledge into higher-level portions.

Commonsense reasoning

Marvin Minsky first proposed frames as a method of analyzing typical visual circumstances, such as a workplace, and Roger Schank extended this concept to scripts for typical regimens, such as dining out. Cyc has actually tried to capture useful common-sense knowledge and has “micro-theories” to handle particular kinds 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 range. We anticipate it to heat and potentially boil over, even though we may not know its temperature, its boiling point, or other information, such as air pressure.

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

Constraints and constraint-based reasoning

Constraint solvers perform a more minimal sort of reasoning than first-order reasoning. They can simplify sets of spatiotemporal constraints, such as those for RCC or Temporal Algebra, along with solving other sort of puzzle problems, such as Wordle, Sudoku, cryptarithmetic issues, and so on. Constraint reasoning shows can be used to solve scheduling problems, for example with restriction managing rules (CHR).

Automated planning

The General Problem Solver (GPS) cast preparation as analytical used means-ends analysis to develop strategies. STRIPS took a various method, viewing planning as theorem proving. Graphplan takes a least-commitment technique to preparation, rather than sequentially choosing actions from an initial state, working forwards, or an objective state if working in reverse. Satplan is an approach to planning where a planning problem is lowered to a Boolean satisfiability problem.

Natural language processing

Natural language processing focuses on treating language as information to perform jobs such as identifying topics without always comprehending the intended significance. Natural language understanding, in contrast, constructs a meaning representation and utilizes that for further processing, such as addressing concerns.

Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all aspects of natural language processing long handled by symbolic AI, but because improved by deep knowing methods. In symbolic AI, discourse representation theory and first-order reasoning have been used to represent sentence significances. Latent semantic analysis (LSA) and explicit semantic analysis likewise supplied vector representations of documents. In the latter case, vector components are interpretable as ideas named by Wikipedia short articles.

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

Agents and multi-agent systems

Agents are autonomous systems embedded in an environment they perceive and act upon in some sense. Russell and Norvig’s basic book on synthetic intelligence is arranged to reflect agent architectures of increasing elegance. [91] The sophistication of agents differs from easy reactive representatives, to those with a design of the world and automated planning abilities, potentially a BDI representative, i.e., one with beliefs, desires, and intents – or additionally a reinforcement finding out design learned in time to select actions – as much as 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 consists of numerous agents that communicate among themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The representatives require not all have the same internal architecture. Advantages of multi-agent systems consist of the ability to divide work among the agents and to increase fault tolerance when representatives are lost. Research issues include how representatives reach consensus, distributed issue fixing, multi-agent knowing, multi-agent preparation, and distributed constraint optimization.

Controversies emerged from at an early stage in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and between those who accepted AI but declined symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were primarily from theorists, on intellectual premises, however likewise from funding companies, particularly during the 2 AI winters.

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

Limitations were discovered in utilizing simple first-order logic to factor about dynamic domains. Problems were discovered both with concerns to mentioning the prerequisites for an action to prosper and in supplying axioms for what did not change after an action was carried out.

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

A comparable problem, called the Qualification Problem, takes place in trying to mention the prerequisites for an action to prosper. A limitless variety of pathological conditions can be imagined, e.g., a banana in a tailpipe could avoid an automobile from running correctly.

McCarthy’s technique to repair the frame problem was circumscription, a sort of non-monotonic logic where deductions could be made from actions that require just define what would alter while not having to clearly define everything that would not change. Other non-monotonic reasonings offered reality maintenance systems that modified beliefs leading to contradictions.

Other methods of handling more open-ended domains included probabilistic thinking systems and artificial intelligence to discover brand-new concepts and guidelines. McCarthy’s Advice Taker can be deemed an inspiration here, as it might incorporate brand-new knowledge supplied by a human in the form of assertions or guidelines. For instance, experimental symbolic machine finding out systems explored the capability to take top-level natural language guidance and to translate it into domain-specific actionable guidelines.

Similar to the issues in dealing with vibrant domains, sensible thinking is likewise hard to record in formal thinking. Examples of sensible reasoning consist of implicit reasoning about how individuals believe or basic understanding of daily occasions, objects, and living animals. This type of understanding is taken for given and not seen as noteworthy. Common-sense thinking is an open location of research study and challenging both for symbolic systems (e.g., Cyc has attempted to catch key parts of this understanding over more than a decade) and neural systems (e.g., self-driving cars that do not know not to drive into cones or not to hit pedestrians strolling a bicycle).

McCarthy viewed his Advice Taker as having sensible, but his definition of sensible was different than the one above. [94] He specified a program as having common sense “if it instantly deduces for itself a sufficiently wide class of instant effects of anything it is told and what it already understands. “

Connectionist AI: philosophical obstacles and sociological conflicts

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

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

1. Implementationism-where connectionist architectures carry out the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected completely, and connectionist architectures underlie intelligence and are completely sufficient 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 neighborhood, explained the moderate connectionism consider as basically suitable with existing research study in neuro-symbolic hybrids:

The 3rd and last position I wish to analyze here is what I call the moderate connectionist view, a more eclectic view of the existing dispute in between connectionism and symbolic AI. One of the researchers who has elaborated this position most explicitly is Andy Clark, a thinker from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark protected hybrid (partly symbolic, partly connectionist) systems. He declared that (a minimum of) two kinds of theories are required in order to study and design cognition. On the one hand, for some information-processing tasks (such as pattern acknowledgment) connectionism has benefits over symbolic designs. But on the other hand, for other cognitive processes (such as serial, deductive reasoning, and generative symbol adjustment procedures) the symbolic paradigm offers sufficient designs, and not only “approximations” (contrary to what extreme connectionists would declare). [97]

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

To think that we can merely abandon symbol-manipulation is to suspend disbelief.

And yet, for the most part, that’s how most current AI proceeds. Hinton and many others have actually striven to banish signs altogether. The deep learning hope-seemingly grounded not so much in science, however in a sort of historic grudge-is that smart behavior will emerge purely from the confluence of huge information and deep knowing. Where classical computers and software fix jobs by specifying sets of symbol-manipulating guidelines devoted to particular jobs, such as modifying a line in a word processor or performing an estimation in a spreadsheet, neural networks normally try to solve jobs by analytical approximation and learning from examples.

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

When deep knowing reemerged in 2012, it was with a kind of take-no-prisoners mindset that has defined many of the last years. By 2015, his hostility towards all things signs had fully crystallized. He offered a talk at an AI workshop at Stanford comparing symbols to aether, one of science’s greatest mistakes.

Ever since, his anti-symbolic project has only increased in strength. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep learning in among science’s essential journals, Nature. It closed with a direct attack on sign manipulation, calling not for reconciliation but for straight-out replacement. Later, Hinton informed an event of European Union leaders that investing any more cash in symbol-manipulating methods was “a huge error,” comparing it to investing in internal combustion engines in the period of electric cars and trucks. [98]

Part of these disagreements may be due to unclear terminology:

Turing award winner Judea Pearl provides a review of maker knowing which, regrettably, conflates the terms artificial intelligence and deep learning. Similarly, when Geoffrey Hinton refers to symbolic AI, the connotation of the term tends to be that of expert systems dispossessed of any ability to find out. Using the terminology requires information. Machine learning 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 sensible rather than dispersed, and the non-use of gradient-based knowing algorithms). Equally, symbolic AI is not almost production rules written by hand. A proper meaning of AI issues knowledge representation and thinking, self-governing multi-agent systems, preparation and argumentation, as well as knowing. [99]

Situated robotics: the world as a design

Another critique of symbolic AI is the embodied cognition technique:

The embodied cognition approach claims that it makes no sense to consider the brain independently: cognition happens 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, consisting of the rest of its body. Under the embodied cognition approach, robotics, vision, and other sensing units become central, not peripheral. [100]

Rodney Brooks created behavior-based robotics, one method to embodied cognition. Nouvelle AI, another name for this technique, is deemed an alternative to both symbolic AI and connectionist AI. His technique rejected representations, either symbolic or dispersed, as not only unneeded, but as detrimental. Instead, he developed the subsumption architecture, a layered architecture for embodied agents. Each layer accomplishes a different function and needs to work in the real life. For instance, the first robot he explains in Intelligence Without Representation, has 3 layers. The bottom layer interprets sonar sensors to avoid things. The middle layer triggers the robotic to roam around when there are no challenges. The top layer triggers the robot to go to more distant places for additional expedition. Each layer can temporarily hinder or reduce a lower-level layer. He slammed AI scientists for specifying AI problems for their systems, when: “There is no tidy department in between perception (abstraction) and thinking in the genuine world.” [101] He called his robotics “Creatures” and each layer was “composed of a fixed-topology network of simple finite state machines.” [102] In the Nouvelle AI approach, “First, it is extremely crucial to test the Creatures we develop in the real life; i.e., in the exact same world that we human beings occupy. It is devastating to fall into the temptation of testing them in a simplified world initially, even with the best intentions of later transferring activity to an unsimplified world.” [103] His focus on real-world screening was in contrast to “Early operate in AI concentrated on 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 benefits, however has actually been slammed by the other approaches. Symbolic AI has been criticized as disembodied, accountable to the credentials problem, and poor in managing the perceptual issues where deep discovering excels. In turn, connectionist AI has actually been criticized as inadequately matched for deliberative step-by-step problem resolving, including understanding, and managing planning. Finally, Nouvelle AI masters reactive and real-world robotics domains however has been slammed for difficulties in including learning and knowledge.

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

Overall, Dreyfus saw locations where AI did not have complete answers and said that Al is therefore impossible; we now see a lot of these very same locations undergoing continued research and advancement leading to increased capability, not impossibility. [100]

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

Notes

^ McCarthy as soon as stated: “This is AI, so we don’t care if it’s mentally genuine”. [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 significant branches of expert system: one aimed at producing intelligent behavior despite how it was accomplished, and the other targeted at modeling smart procedures discovered in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig composed “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 synthetic intelligence: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ 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 things 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 Zip Code Recognition”. Neural Computation. 1 (4 ): 541-551. doi:10.1162/ neco.1989.1.4.541. S2CID 41312633.
^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. “Thinking Fast and Slow in AI”. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. “AAAI Presidential Address: The State of AI”. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
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^ Russell & Norvig 2021, pp. 22-24.
^ McCorduck 2004, pp. 327-335, 434-435.
^ Crevier 1993, pp. 145-62, 197-203.
^ a b Russell & Norvig 2021, p. 23.
^ a b Clancey 1987.
^ a b Shustek, Len (2010 ). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-08-05.
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^ Garcez et al. 2002.
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