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Symbolic Artificial Intelligence
In expert system, symbolic artificial intelligence (also referred to as classical synthetic intelligence or logic-based expert system) [1] [2] is the term for the collection of all techniques in artificial intelligence research that are based upon high-level symbolic (human-readable) representations of problems, reasoning and search. [3] Symbolic AI used tools such as reasoning programs, production guidelines, semantic nets and frames, and it developed applications such as knowledge-based systems (in particular, professional systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to critical ideas in search, symbolic shows languages, agents, multi-agent systems, the semantic web, and the strengths and constraints of formal knowledge and thinking systems.
Symbolic AI was the dominant paradigm of AI research study from the mid-1950s up until the mid-1990s. [4] Researchers in the 1960s and the 1970s were encouraged that symbolic techniques would ultimately be successful in developing a device with synthetic basic intelligence and considered this the supreme objective of their field. [citation needed] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, resulted in impractical expectations and guarantees and was followed by the first AI Winter as funding dried up. [5] [6] A 2nd boom (1969-1986) occurred with the rise of specialist systems, their guarantee of catching business proficiency, and an enthusiastic business welcome. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later on frustration. [8] Problems with troubles in knowledge acquisition, keeping big understanding bases, and brittleness in dealing with out-of-domain issues emerged. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers focused on resolving hidden issues in managing unpredictability and in understanding acquisition. [10] Uncertainty was addressed with formal methods such as hidden Markov designs, Bayesian thinking, and statistical relational learning. [11] [12] Symbolic device discovering attended to the knowledge acquisition issue with contributions consisting of Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree knowing, case-based learning, and inductive reasoning programming to discover relations. [13]
Neural networks, a subsymbolic method, had actually been pursued from early days and reemerged highly in 2012. Early examples are Rosenblatt’s perceptron 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 effective till about 2012: “Until Big Data became commonplace, the general consensus in the Al neighborhood was that the so-called neural-network approach was helpless. Systems just didn’t work that well, compared to other methods. … A transformation was available in 2012, when a number of individuals, consisting of a team of researchers working with Hinton, worked out a way to use the power of GPUs to enormously increase the power of neural networks.” [16] Over the next numerous years, deep learning had incredible success in handling vision, speech recognition, speech synthesis, image generation, and machine translation. However, given that 2020, as intrinsic problems with bias, explanation, comprehensibility, and toughness ended up being more apparent with deep learning techniques; an increasing number of AI scientists have required combining the finest of both the symbolic and neural network techniques [17] [18] and resolving areas that both techniques have problem with, such as common-sense reasoning. [16]
A brief history of symbolic AI to the present day follows below. Period and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture [19] and the longer Wikipedia short article on the History of AI, with dates and titles differing slightly for increased clearness.
The very first AI summer: unreasonable vitality, 1948-1966
Success at early efforts in AI took place in 3 primary locations: artificial neural networks, understanding representation, and heuristic search, adding to high expectations. This section summarizes Kautz’s reprise of early AI history.
Approaches inspired by human or animal cognition or habits
Cybernetic methods attempted to replicate the feedback loops in between animals and their environments. A robotic turtle, with sensing units, motors for driving and steering, and 7 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 work in neural networks, reinforcement learning, and situated robotics. [20]
An important early symbolic AI program was the Logic theorist, written by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it was able to prove 38 primary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later generalized this work to create a domain-independent problem solver, GPS (General Problem Solver). GPS resolved problems represented with official operators by means of state-space search using means-ends analysis. [21]
During the 1960s, symbolic techniques attained great success at simulating smart habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was concentrated in 4 organizations in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Each one established its own style of research. Earlier techniques based upon cybernetics or artificial neural networks were deserted or pressed into the background.
Herbert Simon and Allen Newell studied human problem-solving abilities and tried to formalize them, and their work laid the foundations of the field of expert system, along with cognitive science, operations research and management science. Their research study team used the outcomes of mental experiments to establish programs that simulated the methods that people used to solve issues. [22] [23] This tradition, centered at Carnegie Mellon University would eventually culminate in the advancement of the Soar architecture in the middle 1980s. [24] [25]
Heuristic search
In addition to the extremely specialized domain-specific sort of understanding that we will see later on used in specialist systems, early symbolic AI researchers discovered another more basic application of knowledge. These were called heuristics, guidelines of thumb that direct a search in appealing instructions: “How can non-enumerative search be useful when the underlying issue is greatly difficult? The technique promoted by Simon and Newell is to use heuristics: quick algorithms that may fail on some inputs or output suboptimal solutions.” [26] Another crucial advance was to discover a method to apply these heuristics that ensures a service will be found, if there is one, not standing up to the occasional fallibility of heuristics: “The A * algorithm provided a basic frame for complete and optimal heuristically assisted search. A * is used as a subroutine within practically every AI algorithm today however is still no magic bullet; its guarantee of completeness is purchased at the expense of worst-case exponential time. [26]
Early work on knowledge representation and reasoning
Early work covered both applications of official reasoning highlighting first-order logic, along with efforts to deal with sensible reasoning in a less formal way.
Modeling official thinking with reasoning: the “neats”
Unlike Simon and Newell, John McCarthy felt that makers did not need to simulate the precise mechanisms of human thought, but might instead try to find the essence of abstract reasoning and analytical with reasoning, [27] no matter whether people utilized the same algorithms. [a] His laboratory at Stanford (SAIL) concentrated on using official reasoning to fix a variety of issues, consisting of understanding representation, planning and learning. [31] Logic was also the focus of the work at the University of Edinburgh and in other places in Europe which caused the development of the programming language Prolog and the science of reasoning 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 difficult problems in vision and natural language processing needed ad hoc solutions-they argued that no easy and basic concept (like logic) would record all the aspects of smart habits. Roger Schank explained 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 “scruffy” AI, since they must be built by hand, one complicated idea at a time. [38] [39] [40]
The very first AI winter season: crushed dreams, 1967-1977
The first AI winter season was a shock:
During the first AI summer, lots of people thought that machine intelligence might be attained in just a couple of years. The Defense Advance Research Projects Agency (DARPA) released programs to support AI research to utilize AI to fix issues of nationwide security; in particular, to automate the translation of Russian to English for intelligence operations and to develop autonomous tanks for the battlefield. Researchers had started to realize that achieving AI was going to be much harder than was supposed a years earlier, but a mix of hubris and disingenuousness led numerous university and think-tank researchers to accept financing with pledges of deliverables that they must have understood they could not satisfy. By the mid-1960s neither useful natural language translation systems nor autonomous tanks had been developed, and a significant backlash embeded in. New DARPA leadership canceled existing AI funding programs.
Beyond the United States, the most fertile ground for AI research was the United Kingdom. The AI winter season in the UK was stimulated on not a lot by disappointed military leaders as by rival academics who viewed AI researchers as charlatans and a drain on research study 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 mentioned that all of the issues being worked on in AI would be much better dealt with by researchers from other disciplines-such as applied mathematics. The report also declared that AI successes on toy issues might never scale to real-world applications due to combinatorial explosion. [41]
The 2nd AI summer season: knowledge is power, 1978-1987
Knowledge-based systems
As constraints with weak, domain-independent methods became more and more evident, [42] researchers from all 3 traditions began to construct understanding into AI applications. [43] [7] The understanding transformation was driven by the awareness that understanding underlies high-performance, domain-specific AI applications.
Edward Feigenbaum stated:
– “In the understanding lies the power.” [44]
to explain that high efficiency in a specific domain requires both general and extremely 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 know a good deal about the world in which it runs.
( 2) A possible extension of that concept, called the Breadth Hypothesis: there are two additional abilities required for smart behavior in unexpected situations: drawing on significantly basic understanding, and analogizing to specific but far-flung knowledge. [45]
Success with professional systems
This “understanding revolution” caused the development and deployment of professional systems (presented by Edward Feigenbaum), the first commercially effective kind of AI software application. [46] [47] [48]
Key professional systems were:
DENDRAL, which found the structure of natural particles from their chemical formula and mass spectrometer readings.
MYCIN, which detected bacteremia – and suggested further lab tests, when needed – by interpreting lab outcomes, patient history, and medical professional observations. “With about 450 rules, MYCIN had the ability to perform as well as some specialists, and considerably much better than junior medical professionals.” [49] INTERNIST and CADUCEUS which dealt with internal medicine diagnosis. Internist tried to catch the proficiency of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS might eventually detect up to 1000 various illness.
– GUIDON, which showed how a knowledge base developed for specialist issue solving could be repurposed for teaching. [50] XCON, to configure VAX computer systems, a then tiresome process that could take up to 90 days. XCON decreased the time to about 90 minutes. [9]
DENDRAL is thought about the very first professional system that depend on knowledge-intensive analytical. It is explained below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:
One of the people at Stanford thinking about computer-based models of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I told him I desired an induction “sandbox”, he said, “I have just the one for you.” His laboratory was doing mass spectrometry of amino acids. The question was: how do you go from taking a look at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we began the DENDRAL Project: I was proficient at heuristic search techniques, and he had an algorithm that was excellent at creating the chemical issue area.
We did not have a grand vision. We worked bottom up. Our chemist was Carl Djerassi, inventor of the chemical behind the contraceptive pill, and also one of the world’s most appreciated mass spectrometrists. Carl and his postdocs were world-class specialists in mass spectrometry. We began to contribute to their knowledge, creating understanding of engineering as we went along. These experiments amounted to titrating DENDRAL more and more understanding. The more you did that, the smarter the program ended up being. We had great results.
The generalization was: in the knowledge lies the power. That was the huge concept. In my career that is the substantial, “Ah ha!,” and it wasn’t the way AI was being done formerly. Sounds simple, however it’s most likely AI’s most effective generalization. [51]
The other professional systems mentioned above followed DENDRAL. MYCIN exemplifies the traditional professional system architecture of a knowledge-base of rules coupled to a symbolic reasoning mechanism, consisting of using certainty aspects to manage unpredictability. GUIDON reveals how an explicit knowledge base can be repurposed for a second application, tutoring, and is an example of an intelligent tutoring system, a particular kind of knowledge-based application. Clancey showed that it was not adequate simply to utilize MYCIN’s rules for direction, however that he also required to add rules for dialogue management and student modeling. [50] XCON is considerable because of the millions of dollars it saved DEC, which triggered the professional system boom where most all significant corporations in the US had skilled systems groups, to capture corporate expertise, protect it, and automate it:
By 1988, DEC’s AI group had 40 expert systems deployed, with more en route. DuPont had 100 in usage and 500 in advancement. Nearly every major U.S. corporation had its own Al group and was either utilizing or investigating 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 skilled systems
An essential element of the system architecture for all professional systems is the understanding base, which shops realities and guidelines for problem-solving. [53] The easiest technique for an expert system understanding base is just a collection or network of production guidelines. Production rules link signs in a relationship comparable to an If-Then declaration. The professional system processes the guidelines to make reductions and to determine what additional info it needs, i.e. what questions to ask, using human-readable signs. For example, OPS5, CLIPS and their successors Jess and Drools run in this fashion.
Expert systems can run in either a forward chaining – from proof to conclusions – or backwards chaining – from goals to required data and requirements – way. More advanced knowledge-based systems, such as Soar can likewise carry out meta-level reasoning, that is reasoning about their own reasoning in regards to deciding how to resolve issues and keeping an eye on the success of analytical strategies.
Blackboard systems are a 2nd kind of knowledge-based or expert system architecture. They model a neighborhood of professionals incrementally contributing, where they can, to solve a problem. The issue is represented in multiple levels of abstraction or alternate views. The specialists (knowledge sources) volunteer their services whenever they acknowledge they can contribute. Potential analytical actions are represented on a program that is updated as the problem situation changes. A controller chooses how helpful each contribution is, and who ought to make the next analytical action. One example, the BB1 chalkboard architecture [54] was originally inspired by research studies of how human beings plan to carry out several jobs in a trip. [55] A development of BB1 was to use the exact same blackboard model to resolving its control issue, i.e., its controller performed meta-level thinking with understanding sources that kept an eye on how well a plan or the problem-solving was proceeding and might change from one method to another as conditions – such as goals or times – altered. BB1 has been applied in numerous domains: construction site planning, smart 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 specifically targeted to accelerate the development of AI applications and research study. In addition, numerous expert system companies, such as Teknowledge and Inference Corporation, were offering skilled system shells, training, and seeking advice from to corporations.
Unfortunately, the AI boom did not last and Kautz best explains the second AI winter that followed:
Many reasons can be used for the arrival of the 2nd AI winter season. The hardware business stopped working when a lot more economical general Unix workstations from Sun together with good compilers for LISP and Prolog came onto the marketplace. Many business releases of specialist systems were ceased when they showed too expensive to maintain. Medical professional systems never captured on for several reasons: the trouble in keeping them up to date; the difficulty for medical specialists to learn how to utilize a bewildering variety of different specialist systems for various medical conditions; and maybe most crucially, the reluctance of doctors to trust a computer-made medical diagnosis over their gut impulse, even for particular domains where the specialist systems could outshine an average doctor. Venture capital money deserted AI almost overnight. The world AI conference IJCAI hosted an enormous and luxurious trade program and countless nonacademic participants in 1987 in Vancouver; the primary AI conference the list below year, AAAI 1988 in St. Paul, was a little and strictly scholastic affair. [9]
Adding in more extensive structures, 1993-2011
Uncertain reasoning
Both statistical approaches and extensions to logic were tried.
One analytical approach, concealed Markov designs, had already been promoted in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized the use of Bayesian Networks as a sound however effective method of managing uncertain reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian techniques were used successfully in professional systems. [57] Even later, in the 1990s, statistical relational learning, an approach that integrates likelihood with sensible solutions, 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 support were also attempted. For example, non-monotonic thinking might be utilized with fact maintenance systems. A fact maintenance system tracked assumptions and reasons for all reasonings. It enabled reasonings to be withdrawn when presumptions were discovered to be inaccurate or a contradiction was obtained. Explanations could be offered for an inference by explaining which rules were used to produce it and then continuing through underlying inferences and guidelines all the way back to root presumptions. [58] Lofti Zadeh had introduced a various kind of extension to manage the representation of ambiguity. For example, in choosing how “heavy” or “high” a guy is, there is regularly no clear “yes” or “no” answer, and a predicate for heavy or tall would rather return values in between 0 and 1. Those values represented to what degree the predicates held true. His fuzzy logic even more provided a means for propagating mixes of these values through sensible solutions. [59]
Artificial intelligence
Symbolic device finding out methods were examined to deal with the understanding acquisition bottleneck. One of the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test strategy to create possible rule hypotheses to evaluate against spectra. Domain and job understanding reduced the number of prospects tested to a workable size. Feigenbaum described Meta-DENDRAL as
… the culmination of my imagine the early to mid-1960s pertaining 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 steer and prune the search. That understanding acted due to the fact that we spoke with individuals. But how did the individuals get the understanding? By taking a look at thousands of spectra. So we wanted a program that would look at thousands of spectra and infer the knowledge of mass spectrometry that DENDRAL might use to resolve specific hypothesis development issues. We did it. We were even able to release new understanding of mass spectrometry in the Journal of the American Chemical Society, giving credit only in a footnote that a program, Meta-DENDRAL, really did it. We were able to do something that had actually been a dream: to have a computer system program created a new and publishable piece of science. [51]
In contrast to the knowledge-intensive technique of Meta-DENDRAL, Ross Quinlan invented a domain-independent approach to analytical category, choice tree knowing, beginning first with ID3 [60] and then later on extending its abilities to C4.5. [61] The choice trees created are glass box, interpretable classifiers, with human-interpretable classification rules.
Advances were made in understanding artificial intelligence theory, too. Tom Mitchell presented variation space learning which describes knowing as an explore an area of hypotheses, with upper, more basic, and lower, more particular, limits encompassing all feasible hypotheses consistent with the examples seen so far. [62] More officially, Valiant introduced Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of artificial intelligence. [63]
Symbolic maker learning included more than discovering by example. E.g., John Anderson supplied a cognitive model of human knowing where ability practice results in a compilation of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For example, a trainee may learn to apply “Supplementary angles are 2 angles whose measures sum 180 degrees” as a number of different procedural rules. E.g., one guideline might state that if X and Y are extra and you understand X, then Y will be 180 – X. He called his approach “knowledge compilation”. ACT-R has been utilized effectively to design aspects of human cognition, such as discovering and retention. ACT-R is also utilized in intelligent tutoring systems, called cognitive tutors, to successfully teach geometry, computer programs, and algebra to school children. [64]
Inductive logic shows was another method to finding out that permitted reasoning 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 genetic algorithms to program synthesis to produce genetic programming, which he used to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger supplied a more general approach to program synthesis that synthesizes a functional program in the course of showing its specs to be appropriate. [66]
As an alternative to logic, Roger Schank presented case-based reasoning (CBR). The CBR approach detailed in his book, Dynamic Memory, [67] focuses first on remembering key analytical cases for future usage and generalizing them where appropriate. When confronted with a new issue, CBR retrieves the most comparable previous case and adapts it to the specifics of the existing issue. [68] Another alternative to reasoning, genetic algorithms and genetic shows are based on an evolutionary model of knowing, where sets of rules are encoded into populations, the rules govern the habits of individuals, and selection of the fittest prunes out sets of unsuitable rules over numerous generations. [69]
Symbolic machine learning was used to learning principles, rules, heuristics, and problem-solving. Approaches, other than those above, consist of:
1. Learning from instruction or advice-i.e., taking human guideline, impersonated guidance, and figuring out how to operationalize it in particular situations. For example, in a video game of Hearts, finding out exactly how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving efficiency by accepting subject-matter expert (SME) feedback during training. When analytical fails, querying the professional to either learn a new prototype for analytical or to learn a brand-new explanation as to precisely why one prototype is more relevant than another. For example, the program Protos learned to identify tinnitus cases by interacting with an audiologist. [71] 3. Learning by analogy-constructing problem services based on comparable problems seen in the past, and then customizing their services to fit a new situation or domain. [72] [73] 4. Apprentice learning systems-learning unique services to issues by observing human analytical. Domain knowledge describes why unique options are proper and how the service can be generalized. LEAP learned how to create VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., developing tasks to carry out experiments and then discovering from the outcomes. Doug Lenat’s Eurisko, for instance, found out heuristics to beat human players at the Traveller role-playing game for 2 years in a row. [75] 6. Learning macro-operators-i.e., looking for useful macro-operators to be gained from series of standard analytical actions. Good macro-operators simplify problem-solving by enabling issues 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 technique has been compared to deep knowing as complementary “… with parallels having actually been drawn many times by AI researchers between Kahneman’s research study on human reasoning and choice making – shown in his book Thinking, Fast and Slow – and the so-called “AI systems 1 and 2″, which would in principle be designed by deep learning and symbolic thinking, respectively.” In this view, symbolic reasoning is more apt for deliberative thinking, planning, and description while deep learning is more apt for fast pattern acknowledgment in perceptual applications with noisy information. [17] [18]
Neuro-symbolic AI: integrating neural and symbolic methods
Neuro-symbolic AI efforts to incorporate neural and symbolic architectures in a way that addresses strengths and weak points of each, in a complementary style, in order to support robust AI efficient in thinking, finding out, and cognitive modeling. As argued by Valiant [77] and many others, [78] the reliable construction of abundant computational cognitive models requires the combination of sound symbolic reasoning and effective (maker) knowing models. Gary Marcus, similarly, argues that: “We can not build abundant cognitive designs in an appropriate, automated way without the triune of hybrid architecture, abundant anticipation, and advanced methods for thinking.”, [79] and in particular: “To construct a robust, knowledge-driven technique to AI we need to have the equipment of symbol-manipulation in our toolkit. Excessive of helpful understanding is abstract to make do without tools that represent and control abstraction, and to date, the only machinery that we understand of that can manipulate such abstract knowledge dependably is the device of symbol manipulation. ” [80]
Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have likewise argued for a synthesis. Their arguments are based upon a requirement to deal with the 2 type of believing talked about in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having two components, System 1 and System 2. System 1 is fast, automated, user-friendly and unconscious. System 2 is slower, step-by-step, and specific. System 1 is the kind utilized for pattern recognition while System 2 is far much better fit for planning, reduction, and deliberative thinking. In this view, deep learning best designs the very first sort of thinking while symbolic thinking best designs the second kind and both are required.
Garcez and Lamb explain research study in this location as being ongoing 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 reasoning has been held every year since 2005, see http://www.neural-symbolic.org/ for details.
In their 2015 paper, Neural-Symbolic Learning and Reasoning: Contributions and Challenges, Garcez et al. argue that:
The integration of the symbolic and connectionist paradigms of AI has actually been pursued by a fairly small research neighborhood over the last 2 years and has yielded numerous substantial results. Over the last decade, neural symbolic systems have been shown efficient in getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in reaction to Smolensky (1988 ); see also (Hinton, 1990). Neural networks were revealed capable of representing modal and temporal logics (d’Avila Garcez and Lamb, 2006) and fragments of first-order reasoning (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have actually been used to a number of issues in the locations of bioinformatics, control engineering, software confirmation and adaptation, visual intelligence, ontology learning, and video game. [78]
Approaches for combination are varied. Henry Kautz’s taxonomy of neuro-symbolic architectures, together with some examples, follows:
– Symbolic Neural symbolic-is the current approach of lots of neural models in natural language processing, where words or subword tokens are both the supreme input and output of big language models. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic strategies are utilized to call neural strategies. In this case the symbolic approach is Monte Carlo tree search and the neural techniques find out how to evaluate game positions.
– Neural|Symbolic-uses a neural architecture to analyze affective data as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to produce or label training information that is subsequently found out by a deep knowing design, e.g., to train a neural design for symbolic calculation by utilizing a Macsyma-like symbolic mathematics system to develop or label examples.
– Neural _ Symbolic -utilizes a neural web that is generated from symbolic rules. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR proof tree produced from knowledge base guidelines and terms. Logic Tensor Networks [86] likewise fall under this classification.
– Neural [Symbolic] -allows a neural model to directly call a symbolic reasoning engine, e.g., to perform an action or examine a state.
Many essential research questions stay, such as:
– What is the very best way to incorporate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and drawn out from them?
– How should common-sense knowledge be learned and reasoned about?
– How can abstract understanding that is hard to encode logically be dealt with?
Techniques and contributions
This area supplies an introduction of techniques and contributions in an overall context leading to lots of other, more detailed articles in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered previously in the history area.
AI programming languages
The essential AI programs language in the US during the last symbolic AI boom duration was LISP. LISP is the 2nd oldest programming language after FORTRAN and was developed in 1958 by John McCarthy. LISP offered the first read-eval-print loop to support fast program advancement. Compiled functions might be easily blended with interpreted functions. Program tracing, stepping, and breakpoints were also offered, in addition to the ability to change values or functions and continue from breakpoints or errors. It had the very first self-hosting compiler, implying that the compiler itself was originally written in LISP and after that ran interpretively to assemble the compiler code.
Other crucial innovations originated by LISP that have actually infected other programming languages consist of:
Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals
Programs were themselves data structures that other programs might operate on, enabling the simple definition of higher-level languages.
In contrast to the US, in Europe the crucial AI shows language throughout that same duration was Prolog. Prolog offered a built-in shop of facts and provisions that could be queried by a read-eval-print loop. The store could act as an understanding base and the clauses could act as guidelines or a restricted kind of logic. As a subset of first-order reasoning Prolog was based upon Horn stipulations with a closed-world assumption-any facts not understood were thought about false-and an unique name assumption for primitive terms-e.g., the identifier barack_obama was considered to refer to precisely one item. Backtracking and unification are integrated to Prolog.
Alain Colmerauer and Philippe Roussel are credited as the creators of Prolog. Prolog is a form of logic shows, which was created by Robert Kowalski. Its history was also affected by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of methods. For more information see the area on the origins of Prolog in the PLANNER post.
Prolog is also a kind of declarative programs. The logic stipulations that describe programs are straight analyzed to run the programs defined. No specific series of actions is needed, as is the case with vital programming languages.
Japan promoted Prolog for its Fifth Generation Project, planning to construct special hardware for high efficiency. Similarly, LISP machines were built to run LISP, however as the second AI boom turned to bust these business could not take on brand-new workstations that could now run LISP or Prolog natively at comparable speeds. See the history area for more information.
Smalltalk was another influential AI shows language. For instance, it introduced metaclasses and, along 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 allows multiple inheritance, in addition to incremental extensions to both classes and metaclasses, thus supplying a run-time meta-object procedure. [88]
For other AI programs languages see this list of programs languages for expert system. Currently, Python, a multi-paradigm shows language, is the most popular shows language, partially due to its extensive plan library that supports data science, natural language processing, and deep learning. Python includes a read-eval-print loop, functional elements such as higher-order functions, and object-oriented shows that includes metaclasses.
Search
Search occurs in lots of sort of problem fixing, consisting of planning, restriction fulfillment, and playing games such as checkers, chess, and go. The very best understood AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven clause knowing, and the DPLL algorithm. For adversarial search when playing games, alpha-beta pruning, branch and bound, and minimax were early contributions.
Knowledge representation and reasoning
Multiple different methods to represent knowledge and after that reason with those representations have been investigated. Below is a fast summary of techniques to knowledge representation and automated thinking.
Knowledge representation
Semantic networks, conceptual charts, frames, and reasoning are all approaches to modeling knowledge such as domain understanding, analytical knowledge, and the semantic meaning of language. Ontologies model crucial ideas and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be utilized for any domain while WordNet is a lexical resource that can also be deemed an ontology. YAGO integrates WordNet as part of its ontology, to line up facts extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being used.
Description logic is a logic for automated category of ontologies and for finding inconsistent classification information. OWL is a language utilized to represent ontologies with description reasoning. Protégé is an ontology editor that can read in OWL ontologies and after that check consistency with deductive classifiers such as such as HermiT. [89]
First-order reasoning is more general than description reasoning. The automated theorem provers gone over below can show theorems in first-order logic. Horn clause reasoning is more limited than first-order logic and is utilized in reasoning programs languages such as Prolog. Extensions to first-order reasoning include temporal logic, to handle time; epistemic logic, to reason about representative knowledge; modal reasoning, to manage possibility and requirement; and probabilistic reasonings to manage 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 conjunction with the Mace4 design checker. ACL2 is a theorem prover that can handle evidence by induction and is a descendant of the Boyer-Moore Theorem Prover, likewise understood as Nqthm.
Reasoning in knowledge-based systems
Knowledge-based systems have a specific knowledge base, typically of rules, to boost reusability throughout domains by separating procedural code and domain knowledge. A different inference engine processes guidelines and adds, deletes, or modifies a knowledge shop.
Forward chaining reasoning engines are the most common, and are seen in CLIPS and OPS5. Backward chaining happens in Prolog, where a more restricted sensible representation is used, Horn Clauses. Pattern-matching, particularly marriage, is used in Prolog.
A more flexible kind of analytical takes place when thinking about what to do next happens, rather than merely selecting one of the offered actions. This type of meta-level thinking is used in Soar and in the BB1 chalkboard architecture.
Cognitive architectures such as ACT-R may have extra capabilities, such as the ability to put together often used knowledge into higher-level chunks.
Commonsense thinking
Marvin Minsky initially proposed frames as a way of translating common visual situations, such as a workplace, and Roger Schank extended this concept to scripts for common regimens, such as dining out. Cyc has tried to capture helpful common-sense knowledge and has “micro-theories” to deal with particular sort of domain-specific reasoning.
Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human thinking about ignorant physics, such as what happens when we warm a liquid in a pot on the range. We expect it to heat and potentially boil over, despite the fact that we may not understand its temperature level, 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 resolved with constraint solvers.
Constraints and constraint-based thinking
Constraint solvers perform a more limited kind of inference than first-order logic. They can streamline sets of spatiotemporal restrictions, such as those for RCC or Temporal Algebra, in addition to fixing other type of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic programs can be used to solve scheduling problems, for example with constraint managing rules (CHR).
Automated planning
The General Problem Solver (GPS) cast preparation as problem-solving used means-ends analysis to produce plans. STRIPS took a various method, seeing planning as theorem proving. Graphplan takes a least-commitment technique to planning, instead of sequentially selecting actions from an initial state, working forwards, or an objective state if working backwards. Satplan is a method to preparing where a planning problem is decreased to a Boolean satisfiability problem.
Natural language processing
Natural language processing concentrates on treating language as data to perform tasks such as recognizing subjects without always understanding the designated significance. Natural language understanding, on the other hand, constructs a significance representation and utilizes that for further processing, such as answering concerns.
Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all elements of natural language processing long dealt with by symbolic AI, but since improved by deep knowing methods. In symbolic AI, discourse representation theory and first-order logic have been utilized to represent sentence meanings. Latent semantic analysis (LSA) and specific semantic analysis also provided vector representations of files. In the latter case, vector elements are interpretable as ideas named by Wikipedia short articles.
New deep learning approaches based upon Transformer designs have actually now eclipsed these earlier symbolic AI methods and attained advanced efficiency 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 components is nontransparent.
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 standard textbook on artificial intelligence is arranged to show agent architectures of increasing elegance. [91] The sophistication of agents differs from easy reactive representatives, to those with a model of the world and automated planning capabilities, potentially a BDI representative, i.e., one with beliefs, desires, and intentions – or additionally a support finding out model discovered gradually to select actions – up to a mix of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep learning for understanding. [92]
On the other hand, a multi-agent system consists of numerous agents that communicate among themselves with some inter-agent interaction language such as Knowledge Query and Manipulation Language (KQML). The agents require not all have the same internal architecture. Advantages of multi-agent systems include the ability to divide work among the agents and to increase fault tolerance when agents are lost. Research issues include how agents reach consensus, distributed issue fixing, multi-agent knowing, multi-agent preparation, and distributed constraint optimization.
Controversies developed from early in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who welcomed AI however rejected symbolic approaches-primarily connectionists-and those outside the field. Critiques from beyond the field were mainly from philosophers, on intellectual premises, however also from financing companies, particularly throughout the 2 AI winters.
The Frame Problem: knowledge representation difficulties for first-order reasoning
Limitations were found in using simple first-order reasoning to reason about dynamic domains. Problems were found both with regards to enumerating the prerequisites for an action to prosper 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 “showing that a person person 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 prosper. Similar axioms would be needed for other domain actions to define what did not change.
A comparable problem, called the Qualification Problem, happens in trying to identify the prerequisites for an action to prosper. A boundless number of pathological conditions can be imagined, e.g., a banana in a tailpipe might prevent an automobile from operating correctly.
McCarthy’s approach to repair the frame issue was circumscription, a sort of non-monotonic logic where deductions might be made from actions that require just define what would alter while not needing to explicitly define whatever that would not alter. Other non-monotonic logics supplied fact maintenance systems that revised beliefs leading to contradictions.
Other ways of handling more open-ended domains included probabilistic thinking systems and machine learning to learn brand-new principles and rules. McCarthy’s Advice Taker can be seen as a motivation here, as it could include brand-new understanding offered by a human in the type of assertions or guidelines. For instance, experimental symbolic maker discovering systems explored the ability to take high-level natural language recommendations and to translate it into domain-specific actionable guidelines.
Similar to the issues in dealing with vibrant domains, sensible reasoning is likewise tough to capture in official reasoning. Examples of common-sense thinking consist of implicit reasoning about how people believe or basic understanding of everyday occasions, things, and living creatures. This type of knowledge is taken for approved and not viewed as noteworthy. Common-sense thinking is an open location of research and challenging both for symbolic systems (e.g., Cyc has actually tried to capture essential parts of this understanding over more than a years) and neural systems (e.g., self-driving cars that do not understand not to drive into cones or not to strike pedestrians walking a bike).
McCarthy saw his Advice Taker as having sensible, but his meaning of sensible was different than the one above. [94] He defined a program as having sound judgment “if it immediately deduces for itself an adequately broad class of immediate repercussions of anything it is informed and what it already knows. “
Connectionist AI: philosophical difficulties and sociological conflicts
Connectionist techniques consist of earlier deal with neural networks, [95] such as perceptrons; operate in the mid to late 80s, such as Danny Hillis’s Connection Machine and Yann LeCun’s advances in convolutional neural networks; to today’s advanced techniques, such as Transformers, GANs, and other work in deep knowing.
Three philosophical positions [96] have been outlined amongst connectionists:
1. Implementationism-where connectionist architectures implement the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected completely, and connectionist architectures underlie intelligence and are totally sufficient to describe it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are viewed as complementary and both are needed for intelligence
Olazaran, in his sociological history of the debates within the neural network neighborhood, described the moderate connectionism view as basically compatible with present research study in neuro-symbolic hybrids:
The third and last position I wish to analyze here is what I call the moderate connectionist view, a more eclectic view of the present debate in between connectionism and symbolic AI. One of the scientists who has actually elaborated this position most explicitly is Andy Clark, a thinker from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark defended hybrid (partly symbolic, partially connectionist) systems. He declared that (at least) two type of theories are needed in order to study and model cognition. On the one hand, for some information-processing tasks (such as pattern recognition) connectionism has advantages over symbolic models. But on the other hand, for other cognitive processes (such as serial, deductive reasoning, and generative sign manipulation processes) the symbolic paradigm offers adequate models, and not just “approximations” (contrary to what extreme connectionists would declare). [97]
Gary Marcus has actually declared that the animus in the deep knowing community against symbolic techniques now may be more sociological than philosophical:
To believe that we can merely desert symbol-manipulation is to suspend shock.
And yet, for the many part, that’s how most current AI proceeds. Hinton and lots of others have striven to eradicate signs completely. The deep knowing hope-seemingly grounded not a lot in science, however in a sort of historical grudge-is that intelligent habits will emerge simply from the confluence of huge information and deep learning. Where classical computer systems and software solve jobs by specifying sets of symbol-manipulating guidelines devoted to particular jobs, such as modifying a line in a word processor or performing a calculation in a spreadsheet, neural networks typically attempt to solve tasks by analytical approximation and gaining from examples.
According to Marcus, Geoffrey Hinton and his coworkers have actually been emphatically “anti-symbolic”:
When deep knowing reemerged in 2012, it was with a sort of take-no-prisoners attitude that has actually characterized the majority of the last years. By 2015, his hostility towards all things symbols had fully taken shape. He lectured at an AI workshop at Stanford comparing signs to aether, one of science’s biggest errors.
…
Ever since, his anti-symbolic project has just increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep knowing in among science’s essential journals, Nature. It closed with a direct attack on symbol manipulation, calling not for reconciliation however for outright replacement. Later, Hinton informed a gathering of European Union leaders that investing any more cash in symbol-manipulating techniques was “a big error,” likening it to purchasing internal combustion engines in the age of electric vehicles. [98]
Part of these conflicts may be due to uncertain terms:
Turing award winner Judea Pearl provides a critique of artificial intelligence which, unfortunately, conflates the terms device knowing and deep learning. Similarly, when Geoffrey Hinton refers to symbolic AI, the undertone of the term tends to be that of professional systems dispossessed of any capability to learn. Using the terminology is in need of information. Machine learning is not confined to association guideline mining, c.f. the body of work on symbolic ML and relational knowing (the differences to deep knowing being the choice of representation, localist sensible instead of dispersed, and the non-use of gradient-based knowing algorithms). Equally, symbolic AI is not just about production guidelines written by hand. A proper definition of AI concerns understanding representation and thinking, self-governing multi-agent systems, preparation and argumentation, as well as knowing. [99]
Situated robotics: the world as a design
Another review of symbolic AI is the embodied cognition technique:
The embodied cognition method declares that it makes no sense to consider the brain independently: cognition happens within a body, which is embedded in an environment. We need to study the system as a whole; the brain’s working exploits regularities in its environment, consisting of the rest of its body. Under the embodied cognition method, robotics, vision, and other sensors become central, not peripheral. [100]
Rodney Brooks created behavior-based robotics, one method to embodied cognition. Nouvelle AI, another name for this approach, is considered as an alternative to both symbolic AI and connectionist AI. His technique turned down representations, either symbolic or distributed, as not just unnecessary, however as detrimental. Instead, he developed the subsumption architecture, a layered architecture for embodied agents. Each layer achieves a various purpose and needs to work in the real world. For instance, the first robotic he describes in Intelligence Without Representation, has three layers. The bottom layer interprets finder sensors to prevent items. The middle layer triggers the robotic to wander around when there are no obstacles. The leading layer triggers the robot to go to more remote places for additional expedition. Each layer can temporarily prevent or suppress a lower-level layer. He criticized AI scientists for defining AI problems for their systems, when: “There is no tidy division in between perception (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 easy limited state devices.” [102] In the Nouvelle AI method, “First, it is critically important to evaluate the Creatures we integrate in the genuine world; i.e., in the exact same world that we human beings inhabit. It is dreadful to fall under the temptation of checking them in a streamlined world initially, even with the very best intentions of later transferring activity to an unsimplified world.” [103] His focus on real-world testing was in contrast to “Early operate in AI focused on games, geometrical issues, symbolic algebra, theorem proving, and other formal systems” [104] and the usage of the blocks world in symbolic AI systems such as SHRDLU.
Current views
Each approach-symbolic, connectionist, and behavior-based-has benefits, however has actually been criticized by the other methods. Symbolic AI has been slammed as disembodied, liable to the qualification problem, and bad in managing the perceptual problems where deep discovering excels. In turn, connectionist AI has actually been criticized as improperly fit for deliberative detailed problem fixing, integrating knowledge, and handling preparation. Finally, Nouvelle AI stands out in reactive and real-world robotics domains but has been criticized for troubles in integrating learning and knowledge.
Hybrid AIs including one or more of these approaches are presently considered as the path forward. [19] [81] [82] Russell and Norvig conclude that:
Overall, Dreyfus saw locations where AI did not have total answers and said that Al is for that reason impossible; we now see a lot of these very same areas going through continued research study and development leading to increased capability, not impossibility. [100]
Expert system.
Automated planning and scheduling
Automated theorem proving
Belief modification
Case-based thinking
Cognitive architecture
Cognitive science
Connectionism
Constraint programming
Deep knowing
First-order reasoning
GOFAI
History of artificial intelligence
Inductive reasoning programming
Knowledge-based systems
Knowledge representation and reasoning
Logic programming
Artificial intelligence
Model monitoring
Model-based reasoning
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of expert system
Physical sign systems hypothesis
Semantic Web
Sequential pattern mining
Statistical relational knowing
Symbolic mathematics
YAGO ontology
WordNet
Notes
^ McCarthy as soon as said: “This is AI, so we don’t care if it’s emotionally 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 targeted at producing intelligent behavior despite how it was achieved, and the other focused on modeling intelligent procedures discovered in nature, particularly human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not specify the goal of their field as making ‘machines that fly so exactly like pigeons that they can deceive even other pigeons.'” [30] Citations
^ Garnelo, Marta; Shanahan, Murray (October 2019). “Reconciling deep learning with symbolic expert system: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). “Logic-Based Artificial Intelligence”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep knowing with expert system: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating mistakes”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten Postal Code Recognition”. Neural Computation. 1 (4 ): 541-551. doi:10.1162/ neco.1989.1.4.541. S2CID 41312633.
^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. “Thinking Fast and Slow in AI”. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. “AAAI Presidential Address: The State of AI”. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
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^ Russell & Norvig 2021, pp. 22-24.
^ McCorduck 2004, pp. 327-335, 434-435.
^ Crevier 1993, pp. 145-62, 197-203.
^ a b Russell & Norvig 2021, p. 23.
^ a b Clancey 1987.
^ a b Shustek, Len (2010 ). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-08-05.
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^ Garcez et al. 2002.
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