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Symbolic Artificial Intelligence
In artificial intelligence, symbolic expert system (likewise called classical expert system or logic-based artificial intelligence) [1] [2] is the term for the collection of all approaches in synthetic intelligence research study that are based upon top-level symbolic (human-readable) representations of problems, reasoning and search. [3] Symbolic AI utilized tools such as reasoning programs, production rules, semantic internet and frames, and it established applications such as knowledge-based systems (in specific, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to influential concepts in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and constraints of formal knowledge and reasoning systems.
Symbolic AI was the dominant paradigm of AI research study from the mid-1950s until the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic approaches would eventually be successful in producing a machine with synthetic basic intelligence and considered this the supreme goal of their field. [citation required] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, caused unrealistic expectations and promises and was followed by the very first AI Winter as funding dried up. [5] [6] A second boom (1969-1986) accompanied the rise of expert systems, their guarantee of capturing corporate know-how, and a passionate business welcome. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later on disappointment. [8] Problems with problems in knowledge acquisition, keeping large knowledge bases, and brittleness in dealing with out-of-domain issues emerged. Another, 2nd, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists focused on resolving hidden problems in handling unpredictability and in knowledge acquisition. [10] Uncertainty was attended to with formal approaches such as surprise Markov designs, Bayesian thinking, and analytical relational knowing. [11] [12] Symbolic machine learning attended to the understanding acquisition issue with contributions consisting of Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree learning, case-based learning, and inductive reasoning programming to find out relations. [13]
Neural networks, a subsymbolic approach, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt’s perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and work in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not deemed successful until about 2012: “Until Big Data ended up being commonplace, the general agreement 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 people, consisting of a team of researchers dealing with Hinton, exercised a way to utilize the power of GPUs to tremendously increase the power of neural networks.” [16] Over the next several years, deep knowing had amazing success in managing vision, speech acknowledgment, speech synthesis, image generation, and machine translation. However, since 2020, as inherent troubles with predisposition, description, coherence, and robustness ended up being more evident with deep learning techniques; an increasing number of AI researchers have called for combining the best of both the symbolic and neural network approaches [17] [18] and dealing with areas that both techniques have difficulty with, such as common-sense reasoning. [16]
A brief history of symbolic AI to the present day follows listed below. Time durations and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture [19] and the longer Wikipedia article on the History of AI, with dates and titles varying a little for increased clearness.
The first AI summer: unreasonable enthusiasm, 1948-1966
Success at early efforts in AI took place in three main locations: artificial neural networks, knowledge representation, and heuristic search, contributing to high expectations. This area summarizes Kautz’s reprise of early AI history.
Approaches inspired by human or animal cognition or behavior
Cybernetic methods attempted to replicate the feedback loops in between animals and their environments. A robotic turtle, with sensors, motors for driving and guiding, and 7 vacuum tubes for control, based on a preprogrammed neural web, was developed as early as 1948. This work can be viewed as an early precursor to later work in neural networks, reinforcement knowing, 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 elementary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later generalized this work to develop a domain-independent issue solver, GPS (General Problem Solver). GPS solved issues represented with formal operators via state-space search using means-ends analysis. [21]
During the 1960s, symbolic methods achieved fantastic success at mimicing 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 on) University of Edinburgh. Each one developed its own design of research. Earlier approaches based on cybernetics or synthetic neural networks were abandoned 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, in addition to cognitive science, operations research study and management science. Their research study team used the outcomes of psychological experiments to develop programs that simulated the strategies that individuals utilized to solve problems. [22] [23] This tradition, focused at Carnegie Mellon University would eventually culminate in the advancement of the Soar architecture in the center 1980s. [24] [25]
Heuristic search
In addition to the extremely specialized domain-specific type of knowledge that we will see later used in specialist systems, early symbolic AI scientists found another more basic application of understanding. These were called heuristics, guidelines that guide a search in promising directions: “How can non-enumerative search be practical when the underlying problem is exponentially difficult? The technique promoted by Simon and Newell is to employ heuristics: fast algorithms that may fail on some inputs or output suboptimal solutions.” [26] Another essential advance was to discover a method to use these heuristics that guarantees a service will be discovered, if there is one, not standing up to the periodic fallibility of heuristics: “The A * algorithm supplied a general frame for total and optimal heuristically directed search. A * is utilized as a subroutine within almost every AI algorithm today however is still no magic bullet; its assurance of efficiency is bought at the cost of worst-case exponential time. [26]
Early work on understanding representation and thinking
Early work covered both applications of formal thinking emphasizing first-order logic, in addition to attempts to handle sensible thinking in a less formal manner.
Modeling formal reasoning with logic: the “neats”
Unlike Simon and Newell, John McCarthy felt that devices did not need to simulate the precise mechanisms of human idea, however might rather look for the essence of abstract reasoning and analytical with logic, [27] regardless of whether individuals used the very same algorithms. [a] His lab at Stanford (SAIL) concentrated on utilizing formal reasoning to solve a broad range of problems, including understanding representation, planning and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and elsewhere in Europe which led to the advancement of the programs 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] found that resolving difficult issues in vision and natural language processing required ad hoc solutions-they argued that no basic and general principle (like logic) would record all the elements of smart habits. Roger Schank described their “anti-logic” approaches as “shabby” (as opposed to the “cool” paradigms at CMU and Stanford). [36] [37] Commonsense understanding bases (such as Doug Lenat’s Cyc) are an example of “scruffy” AI, because they need to be constructed by hand, one complicated idea at a time. [38] [39] [40]
The first AI winter season: crushed dreams, 1967-1977
The first AI winter season was a shock:
During the first AI summertime, lots of people thought that device intelligence might be achieved in just a couple of years. The Defense Advance Research Projects Agency (DARPA) introduced programs to support AI research to use AI to solve issues of nationwide security; in particular, to automate the translation of Russian to English for intelligence operations and to produce autonomous tanks for the battlefield. Researchers had begun to understand that achieving AI was going to be much more difficult than was expected a decade previously, but a mix of hubris and disingenuousness led numerous university and think-tank researchers to accept funding with promises of deliverables that they should have known they might not fulfill. By the mid-1960s neither useful natural language translation systems nor autonomous tanks had actually been produced, and a remarkable reaction set in. New DARPA management canceled existing AI financing programs.
Beyond the United States, the most fertile ground for AI research study was the UK. The AI winter in the United Kingdom was spurred on not a lot by dissatisfied military leaders as by rival academics who saw AI scientists as charlatans and a drain on research funding. A teacher of used mathematics, Sir James Lighthill, was commissioned by Parliament to examine the state of AI research study in the nation. The report mentioned that all of the problems being dealt with in AI would be much better dealt with by researchers from other disciplines-such as applied mathematics. The report likewise declared that AI successes on toy issues could never ever scale to real-world applications due to combinatorial surge. [41]
The second AI summer: understanding is power, 1978-1987
Knowledge-based systems
As limitations with weak, domain-independent methods ended up being increasingly more evident, [42] scientists from all three customs started to construct knowledge into AI applications. [43] [7] The knowledge revolution was driven by the realization that understanding underlies high-performance, domain-specific AI applications.
Edward Feigenbaum said:
– “In the knowledge lies the power.” [44]
to explain that high performance in a particular domain needs 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 perform a complex job well, it should understand an excellent offer about the world in which it operates.
( 2) A possible extension of that principle, called the Breadth Hypothesis: there are two extra capabilities essential for intelligent habits in unforeseen circumstances: falling back on significantly general understanding, and analogizing to specific however distant knowledge. [45]
Success with professional systems
This “understanding transformation” caused the advancement and deployment of expert systems (introduced by Edward Feigenbaum), the very first commercially effective type of AI software. [46] [47] [48]
Key specialist systems were:
DENDRAL, which found the structure of natural particles from their chemical formula and mass spectrometer readings.
MYCIN, which detected bacteremia – and suggested more laboratory tests, when essential – by interpreting laboratory outcomes, patient history, and doctor observations. “With about 450 rules, MYCIN had the ability to perform along with some professionals, and considerably better than junior physicians.” [49] INTERNIST and CADUCEUS which dealt with internal medicine diagnosis. Internist attempted to record the knowledge of the chairman of internal medicine at the University of Pittsburgh School of Medicine while CADUCEUS could eventually identify approximately 1000 different illness.
– GUIDON, which demonstrated how an understanding base developed for specialist problem fixing could be repurposed for mentor. [50] XCON, to set up VAX computer systems, a then laborious procedure that could use up to 90 days. XCON decreased the time to about 90 minutes. [9]
DENDRAL is considered the very first specialist system that depend on knowledge-intensive problem-solving. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:
Among individuals at Stanford interested in computer-based models of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I desired an induction “sandbox”, he said, “I have simply the one for you.” His lab was doing mass spectrometry of amino acids. The question was: how do you go from looking at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we started the DENDRAL Project: I was proficient at heuristic search approaches, and he had an algorithm that was great at generating the chemical issue space.
We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, developer of the chemical behind the birth control tablet, and also among the world’s most respected mass spectrometrists. Carl and his postdocs were first-rate professionals in mass spectrometry. We started to include to their understanding, developing knowledge of engineering as we went along. These experiments amounted to titrating DENDRAL a growing number of understanding. The more you did that, the smarter the program ended up being. We had very good results.
The generalization was: in the knowledge lies the power. That was the big idea. In my profession that is the huge, “Ah ha!,” and it wasn’t the method AI was being done formerly. Sounds simple, but it’s most likely AI’s most effective generalization. [51]
The other professional systems pointed out above came after DENDRAL. MYCIN exhibits the timeless expert system architecture of a knowledge-base of guidelines combined to a symbolic thinking system, consisting of the use of certainty elements to manage uncertainty. GUIDON shows how an explicit knowledge 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 sufficient just to use MYCIN’s guidelines for direction, however that he also required to include rules for discussion management and trainee modeling. [50] XCON is significant since of the countless dollars it saved DEC, which set off the specialist system boom where most all significant corporations in the US had skilled systems groups, to catch corporate expertise, maintain it, and automate it:
By 1988, DEC’s AI group had 40 specialist systems deployed, with more en route. DuPont had 100 in use and 500 in development. Nearly every major U.S. corporation had its own Al group and was either utilizing or examining professional systems. [49]
Chess professional knowledge was encoded in Deep Blue. In 1996, this allowed IBM’s Deep Blue, with the assistance of symbolic AI, to win in a game of chess against the world champion at that time, Garry Kasparov. [52]
Architecture of knowledge-based and skilled systems
An essential part of the system architecture for all specialist systems is the understanding base, which stores realities and guidelines for analytical. [53] The simplest approach for a professional system knowledge base is just a collection or network of production rules. Production guidelines link symbols in a relationship comparable to an If-Then statement. The expert system processes the guidelines to make deductions and to determine what additional info it requires, i.e. what concerns to ask, using human-readable signs. For example, OPS5, CLIPS and their followers Jess and Drools run in this fashion.
Expert systems can run in either a forward chaining – from evidence to conclusions – or backward chaining – from goals to needed information and prerequisites – manner. More innovative knowledge-based systems, such as Soar can likewise perform meta-level reasoning, that is reasoning about their own reasoning in regards to deciding how to fix issues and keeping an eye on the success of problem-solving techniques.
Blackboard systems are a second kind of knowledge-based or professional system architecture. They design a neighborhood of specialists incrementally contributing, where they can, to resolve an issue. The issue is represented in several levels of abstraction or alternate views. The professionals (understanding sources) volunteer their services whenever they acknowledge they can contribute. Potential problem-solving actions are represented on an agenda that is upgraded as the issue circumstance changes. A controller decides how beneficial each contribution is, and who should make the next analytical action. One example, the BB1 blackboard architecture [54] was initially motivated by research studies of how people prepare to carry out several jobs in a journey. [55] An innovation of BB1 was to apply the exact same chalkboard model to fixing its control issue, i.e., its controller carried out meta-level thinking with understanding sources that monitored how well a plan or the problem-solving was continuing and might change from one technique to another as conditions – such as goals or times – altered. BB1 has actually been applied in numerous domains: building and construction website planning, intelligent tutoring systems, and real-time patient monitoring.
The 2nd AI winter, 1988-1993
At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were offering LISP machines particularly targeted to speed up the advancement of AI applications and research. In addition, a number of expert system companies, such as Teknowledge and Inference Corporation, were selling expert system shells, training, and consulting to corporations.
Unfortunately, the AI boom did not last and Kautz finest describes the 2nd AI winter that followed:
Many reasons can be used for the arrival of the second AI winter season. The hardware companies failed when a lot more economical basic Unix workstations from Sun together with good compilers for LISP and Prolog came onto the marketplace. Many commercial implementations of specialist systems were stopped when they proved too costly to preserve. Medical expert systems never ever caught on for several reasons: the difficulty in keeping them up to date; the challenge for doctor to learn how to utilize an overwelming range of various specialist systems for various medical conditions; and maybe most crucially, the unwillingness of medical professionals to trust a computer-made medical diagnosis over their gut impulse, even for particular domains where the specialist systems might exceed an average doctor. Equity capital money deserted AI almost over night. The world AI conference IJCAI hosted a huge and extravagant exhibition and thousands of nonacademic attendees in 1987 in Vancouver; the primary AI conference the following year, AAAI 1988 in St. Paul, was a little and strictly scholastic affair. [9]
Adding in more extensive structures, 1993-2011
Uncertain thinking
Both statistical techniques and extensions to logic were attempted.
One analytical approach, concealed Markov designs, had actually currently been popularized in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized using Bayesian Networks as a sound however efficient method of dealing with unsure reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian methods were used effectively in professional systems. [57] Even later on, in the 1990s, analytical relational learning, a technique that integrates possibility with logical formulas, enabled possibility to be combined with first-order logic, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.
Other, non-probabilistic extensions to first-order logic to support were also tried. For instance, non-monotonic reasoning might be utilized with fact upkeep systems. A fact upkeep system tracked assumptions and reasons for all inferences. It permitted inferences to be withdrawn when assumptions were discovered out to be incorrect or a contradiction was derived. Explanations could be attended to a reasoning by discussing which rules were applied to develop it and then continuing through underlying inferences and guidelines all the way back to root assumptions. [58] Lofti Zadeh had actually presented a different kind of extension to deal with the representation of uncertainty. For example, in deciding how “heavy” or “high” a male is, there is frequently no clear “yes” or “no” answer, and a predicate for heavy or high would instead return values between 0 and 1. Those worths represented to what degree the predicates were true. His fuzzy reasoning even more offered a way for propagating mixes of these worths through rational formulas. [59]
Machine learning
Symbolic maker finding out techniques were examined to deal with the knowledge acquisition bottleneck. Among the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test method to produce possible rule hypotheses to check against spectra. Domain and task understanding reduced the number of prospects checked to a workable size. Feigenbaum explained Meta-DENDRAL as
… the conclusion of my imagine the early to mid-1960s pertaining to theory development. The conception was that you had an issue solver like DENDRAL that took some inputs and produced an output. In doing so, it utilized layers of understanding to steer and prune the search. That understanding got in there due to the fact that we spoke with people. But how did individuals get the knowledge? By looking at thousands of spectra. So we wanted a program that would take a look at thousands of spectra and presume the knowledge of mass spectrometry that DENDRAL could use to fix private hypothesis formation problems. We did it. We were even able to publish brand-new knowledge of mass spectrometry in the Journal of the American Chemical Society, giving credit only in a footnote that a program, Meta-DENDRAL, actually did it. We were able to do something that had actually been a dream: to have a computer program come up with a brand-new and publishable piece of science. [51]
In contrast to the knowledge-intensive method of Meta-DENDRAL, Ross Quinlan created a domain-independent method to statistical category, decision tree knowing, starting first with ID3 [60] and then later extending its capabilities to C4.5. [61] The choice trees created are glass box, interpretable classifiers, with human-interpretable classification guidelines.
Advances were made in comprehending artificial intelligence theory, too. Tom Mitchell presented variation space learning which describes learning as a search through an area of hypotheses, with upper, more basic, and lower, more particular, boundaries encompassing all feasible hypotheses constant with the examples seen up until now. [62] More formally, Valiant presented Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of device learning. [63]
Symbolic machine discovering incorporated more than finding out by example. E.g., John Anderson offered a cognitive design of human learning where skill practice leads to a collection of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a trainee may learn to use “Supplementary angles are two angles whose steps sum 180 degrees” as numerous various procedural rules. E.g., one guideline might state that if X and Y are additional and you know X, then Y will be 180 – X. He called his approach “knowledge compilation”. ACT-R has been utilized successfully to design aspects of human cognition, such as learning and retention. ACT-R is likewise utilized in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer shows, and algebra to school kids. [64]
Inductive reasoning programming was another approach to finding out that enabled logic programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) might synthesize Prolog programs from examples. [65] John R. Koza applied genetic algorithms to program synthesis to create hereditary shows, which he used to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger supplied a more basic approach to program synthesis that synthesizes a functional program in the course of showing its specifications to be correct. [66]
As an alternative to reasoning, Roger Schank introduced case-based thinking (CBR). The CBR technique detailed in his book, Dynamic Memory, [67] focuses initially on remembering essential problem-solving cases for future usage and generalizing them where proper. When faced with a new problem, CBR retrieves the most similar previous case and adapts it to the specifics of the present problem. [68] Another alternative to reasoning, genetic algorithms and genetic programs are based upon an evolutionary design of learning, where sets of guidelines are encoded into populations, the guidelines govern the habits of people, and choice of the fittest prunes out sets of unsuitable guidelines over lots of generations. [69]
Symbolic machine learning was used to learning ideas, rules, heuristics, and problem-solving. Approaches, besides those above, consist of:
1. Learning from instruction or advice-i.e., taking human guideline, postured as guidance, and figuring out how to operationalize it in specific circumstances. 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 performance by accepting subject-matter specialist (SME) feedback during training. When analytical fails, querying the professional to either discover a new exemplar for analytical or to learn a new explanation regarding precisely why one exemplar is more appropriate than another. For instance, the program Protos learned to diagnose tinnitus cases by connecting with an audiologist. [71] 3. Learning by analogy-constructing issue services based upon similar issues seen in the past, and then customizing their services to fit a new scenario or domain. [72] [73] 4. Apprentice knowing systems-learning unique options to issues by observing human problem-solving. Domain understanding describes why unique services are right and how the option can be generalized. LEAP learned how to create VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., creating tasks to perform experiments and after that gaining from the results. Doug Lenat’s Eurisko, for instance, learned heuristics to beat human gamers at the Traveller role-playing video game for 2 years in a row. [75] 6. Learning macro-operators-i.e., looking for useful macro-operators to be discovered from sequences of basic problem-solving actions. Good macro-operators streamline problem-solving by enabling problems to be resolved at a more abstract level. [76]
Deep knowing 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 having been drawn often times by AI researchers in between Kahneman’s research on human thinking and choice making – reflected in his book Thinking, Fast and Slow – and the so-called “AI systems 1 and 2″, which would in concept be designed by deep knowing and symbolic reasoning, respectively.” In this view, symbolic reasoning is more apt for deliberative thinking, planning, and explanation while deep knowing is more apt for quick pattern recognition in affective applications with loud information. [17] [18]
Neuro-symbolic AI: incorporating neural and symbolic approaches
Neuro-symbolic AI efforts to integrate neural and symbolic architectures in a manner that addresses strengths and weak points of each, in a complementary style, in order to support robust AI efficient in reasoning, finding out, and cognitive modeling. As argued by Valiant [77] and lots of others, [78] the reliable building and construction of rich computational cognitive designs demands the combination of sound symbolic thinking and effective (machine) knowing models. Gary Marcus, similarly, argues that: “We can not construct abundant cognitive designs in an adequate, automatic way without the triune of hybrid architecture, rich anticipation, and sophisticated techniques for reasoning.”, [79] and in specific: “To develop a robust, knowledge-driven method to AI we must 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 equipment that we understand of that can control such abstract knowledge reliably is the device of sign adjustment. ” [80]
Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based upon a need to attend to the two sort of believing talked about in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having two elements, System 1 and System 2. System 1 is fast, automated, instinctive and unconscious. System 2 is slower, detailed, and specific. System 1 is the kind utilized for pattern acknowledgment while System 2 is far better fit for planning, deduction, and deliberative thinking. In this view, deep learning finest models the first sort of thinking while symbolic reasoning finest designs the 2nd 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 considering 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 reasonably small research neighborhood over the last 2 years and has yielded a number of significant results. Over the last decade, neural symbolic systems have been revealed efficient in getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in action to Smolensky (1988 ); see likewise (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 actually been applied to a variety of issues in the locations of bioinformatics, control engineering, software verification and adaptation, visual intelligence, ontology learning, and video game. [78]
Approaches for combination are varied. Henry Kautz’s taxonomy of neuro-symbolic architectures, along with some examples, follows:
– Symbolic Neural symbolic-is the existing approach of many neural models in natural language processing, where words or subword tokens are both the ultimate input and output of big language models. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic methods are used to call neural techniques. In this case the symbolic technique is Monte Carlo tree search and the neural methods learn how to examine game positions.
– Neural|Symbolic-uses a neural architecture to translate perceptual information as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic thinking to create or label training information that is subsequently found out by a deep knowing design, e.g., to train a neural model for symbolic calculation by utilizing a Macsyma-like symbolic mathematics system to produce or label examples.
– Neural _ Symbolic -utilizes a neural internet that is created from symbolic rules. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR proof tree generated from knowledge base rules and terms. Logic Tensor Networks [86] also fall into this classification.
– Neural [Symbolic] -permits a neural model to straight call a symbolic thinking engine, e.g., to perform an action or assess a state.
Many essential research concerns remain, such as:
– What is the best way 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 hard to encode realistically be managed?
Techniques and contributions
This area provides a summary of methods and contributions in a general context leading to many other, more in-depth posts in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered earlier in the history section.
AI shows languages
The essential AI shows language in the US during the last symbolic AI boom period was LISP. LISP is the second oldest shows language after FORTRAN and was produced in 1958 by John McCarthy. LISP provided the first read-eval-print loop to support fast program advancement. Compiled functions could be easily blended with translated functions. Program tracing, stepping, and breakpoints were likewise provided, along with the capability 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 initially composed in LISP and then ran interpretively to compile the compiler code.
Other crucial innovations pioneered by LISP that have spread out to other programs languages consist of:
Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals
Programs were themselves data structures that other programs could run on, permitting the simple meaning of higher-level languages.
In contrast to the US, in Europe the key AI programming language throughout that exact same duration was Prolog. Prolog offered a built-in shop of truths and provisions that could be queried by a read-eval-print loop. The shop could serve as an understanding base and the provisions might function as guidelines or a limited form of reasoning. As a subset of first-order logic Prolog was based on Horn provisions with a closed-world assumption-any facts not understood were thought about false-and a special name assumption for primitive terms-e.g., the identifier barack_obama was considered to refer to exactly one things. Backtracking and marriage are built-in to Prolog.
Alain Colmerauer and Philippe Roussel are credited as the creators of Prolog. Prolog is a type of reasoning shows, which was created 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 article.
Prolog is likewise a kind of declarative shows. The reasoning clauses that explain programs are directly translated to run the programs defined. No specific series of actions is needed, as holds true with crucial programming languages.
Japan promoted Prolog for its Fifth Generation Project, planning to develop special hardware for high efficiency. Similarly, LISP devices were built to run LISP, however as the second AI boom turned to bust these business could not contend with new workstations that might now run LISP or Prolog natively at comparable speeds. See the history area for more detail.
Smalltalk was another prominent AI programming language. For instance, it presented metaclasses and, together with Flavors and CommonLoops, affected the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the present basic Lisp dialect. CLOS is a Lisp-based object-oriented system that allows several inheritance, in addition to incremental extensions to both classes and metaclasses, therefore offering a run-time meta-object protocol. [88]
For other AI shows languages see this list of shows languages for expert system. Currently, Python, a multi-paradigm shows language, is the most popular programming language, partially due to its comprehensive package library that supports data science, natural language processing, and deep knowing. Python consists of a read-eval-print loop, functional components such as higher-order functions, and object-oriented programs that consists of metaclasses.
Search
Search occurs in many type of issue fixing, consisting of planning, constraint satisfaction, and playing video games such as checkers, chess, and go. The very best known AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven provision knowing, and the DPLL algorithm. For adversarial search when playing video games, alpha-beta pruning, branch and bound, and minimax were early contributions.
Knowledge representation and thinking
Multiple various techniques to represent understanding and after that reason with those representations have been investigated. Below is a fast summary of methods to knowledge representation and automated thinking.
Knowledge representation
Semantic networks, conceptual graphs, frames, and logic are all methods to modeling knowledge such as domain knowledge, problem-solving understanding, and the semantic meaning of language. Ontologies model essential 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 likewise be deemed an ontology. YAGO incorporates WordNet as part of its ontology, to line up facts drawn out from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being used.
Description reasoning is a reasoning for automated classification of ontologies and for identifying inconsistent category information. OWL is a language utilized to represent ontologies with description reasoning. Protégé is an ontology editor that can read in OWL ontologies and then examine consistency with deductive classifiers such as such as HermiT. [89]
First-order logic is more basic than description reasoning. The automated theorem provers gone over below can prove theorems in first-order logic. Horn clause reasoning is more restricted than first-order reasoning and is used in reasoning shows languages such as Prolog. Extensions to first-order reasoning consist of temporal logic, to deal with time; epistemic reasoning, to reason about agent understanding; modal reasoning, to manage possibility and necessity; and probabilistic logics to handle logic and possibility together.
Automatic theorem showing
Examples of automated theorem provers for first-order reasoning are:
Prover9.
ACL2.
Vampire.
Prover9 can be used in conjunction with the Mace4 model checker. ACL2 is a theorem prover that can manage proofs by induction and is a descendant of the Boyer-Moore Theorem Prover, also referred to as Nqthm.
Reasoning in knowledge-based systems
Knowledge-based systems have an explicit knowledge base, generally of guidelines, to boost reusability across domains by separating procedural code and domain knowledge. A different inference engine procedures rules and adds, deletes, or modifies a knowledge shop.
Forward chaining inference engines are the most common, and are seen in CLIPS and OPS5. Backward chaining happens in Prolog, where a more restricted logical representation is utilized, Horn Clauses. Pattern-matching, specifically unification, is used in Prolog.
A more flexible kind of problem-solving occurs when reasoning about what to do next happens, rather than simply choosing among the offered actions. This sort of meta-level thinking is used in Soar and in the BB1 blackboard architecture.
Cognitive architectures such as ACT-R may have extra capabilities, such as the ability to assemble regularly utilized knowledge into higher-level pieces.
Commonsense thinking
Marvin Minsky first proposed frames as a way of analyzing typical visual situations, such as an office, and Roger Schank extended this idea to scripts for common routines, such as eating in restaurants. Cyc has actually attempted to catch useful common-sense knowledge and has “micro-theories” to manage specific type of domain-specific thinking.
Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human thinking about ignorant physics, such as what takes place when we warm a liquid in a pot on the range. We anticipate it to heat and potentially boil over, although we may not know its temperature, its boiling point, or other information, such as atmospheric pressure.
Similarly, Allen’s temporal interval algebra is a simplification of thinking about time and Region Connection Calculus is a simplification of thinking about spatial relationships. Both can be fixed with constraint solvers.
Constraints and constraint-based reasoning
Constraint solvers carry out a more minimal type of inference than first-order reasoning. They can streamline sets of spatiotemporal constraints, 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 reasoning programs can be utilized to solve scheduling issues, for example with constraint handling rules (CHR).
Automated preparation
The General Problem Solver (GPS) cast planning as problem-solving utilized means-ends analysis to develop plans. STRIPS took a different approach, viewing planning as theorem proving. Graphplan takes a least-commitment technique to planning, instead of sequentially selecting actions from a preliminary state, working forwards, or a goal state if working in reverse. Satplan is an approach to preparing where a planning problem is lowered to a Boolean satisfiability problem.
Natural language processing
Natural language processing concentrates on treating language as information to perform tasks such as determining subjects without necessarily understanding the intended meaning. Natural language understanding, on the other hand, constructs a meaning representation and uses that for more 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 considering that enhanced by deep learning approaches. In symbolic AI, discourse representation theory and first-order logic have actually been utilized to represent sentence meanings. Latent semantic analysis (LSA) and specific semantic analysis also offered vector representations of documents. In the latter case, vector parts are interpretable as concepts called by Wikipedia articles.
New deep learning techniques based on Transformer models have now eclipsed these earlier symbolic AI approaches and attained state-of-the-art efficiency in natural language processing. However, Transformer models are nontransparent and do not yet produce human-interpretable semantic representations for sentences and documents. Instead, they produce task-specific vectors where the meaning of the vector parts is nontransparent.
Agents and multi-agent systems
Agents are autonomous systems embedded in an environment they view and act upon in some sense. Russell and Norvig’s basic book on expert system is arranged to show agent architectures of increasing sophistication. [91] The sophistication of agents varies from simple reactive representatives, to those with a design of the world and automated planning abilities, perhaps a BDI agent, i.e., one with beliefs, desires, and intents – or additionally a reinforcement discovering model discovered over time to choose actions – approximately a mix of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep knowing for understanding. [92]
On the other hand, a multi-agent system consists of several representatives that interact amongst themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The agents need not all have the exact same internal architecture. Advantages of multi-agent systems include the ability to divide work among the representatives and to increase fault tolerance when representatives are lost. Research issues consist of how agents reach consensus, distributed problem solving, multi-agent knowing, multi-agent planning, and dispersed restraint optimization.
Controversies occurred from early on in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and between those who welcomed AI but rejected symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were mostly from thinkers, on intellectual premises, however also from funding agencies, especially throughout the 2 AI winter seasons.
The Frame Problem: understanding representation difficulties for first-order reasoning
Limitations were discovered in utilizing basic first-order reasoning to factor about vibrant domains. Problems were discovered both with concerns to identifying the prerequisites for an action to prosper and in offering 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 Artificial Intelligence.” [93] A simple example happens in “showing that a person individual could get into conversation with another”, as an axiom asserting “if an individual has a telephone he still has it after searching for a number in the telephone directory” would be needed for the reduction to prosper. Similar axioms would be needed for other domain actions to specify what did not alter.
A similar problem, called the Qualification Problem, occurs in attempting to identify the prerequisites for an action to prosper. A boundless number of pathological conditions can be envisioned, e.g., a banana in a tailpipe might avoid a vehicle from operating correctly.
McCarthy’s approach to fix the frame problem was circumscription, a type of non-monotonic reasoning where reductions might be made from actions that require only specify what would alter while not needing to explicitly define whatever that would not change. Other non-monotonic logics offered fact upkeep systems that revised beliefs leading to contradictions.
Other methods of handling more open-ended domains included probabilistic thinking systems and device learning to find out brand-new ideas and rules. McCarthy’s Advice Taker can be deemed an inspiration here, as it might incorporate brand-new understanding provided by a human in the form of assertions or rules. For instance, experimental symbolic maker learning systems checked out the capability to take top-level natural language advice and to analyze it into domain-specific actionable guidelines.
Similar to the issues in handling dynamic domains, common-sense thinking is likewise difficult to catch in formal thinking. Examples of sensible thinking consist of implicit reasoning about how people think or general understanding of day-to-day events, items, and living creatures. This sort of understanding is taken for given and not considered as noteworthy. Common-sense thinking is an open location of research study and challenging both for symbolic systems (e.g., Cyc has attempted to capture essential parts of this understanding over more than a decade) and neural systems (e.g., self-driving vehicles that do not know not to drive into cones or not to hit pedestrians walking a bike).
McCarthy viewed his Advice Taker as having sensible, but his meaning of common-sense was different than the one above. [94] He specified a program as having sound judgment “if it immediately deduces for itself an adequately large class of immediate consequences of anything it is told and what it currently knows. “
Connectionist AI: philosophical challenges and sociological conflicts
Connectionist techniques include 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 approaches, such as Transformers, GANs, and other operate in deep knowing.
Three philosophical positions [96] have actually been detailed among connectionists:
1. Implementationism-where connectionist architectures carry out the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is declined absolutely, and connectionist architectures underlie intelligence and are completely enough to discuss 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, described the moderate connectionism view as basically compatible with present 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 diverse view of the existing argument between connectionism and symbolic AI. One of the researchers who has elaborated this position most explicitly is Andy Clark, a theorist from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark safeguarded hybrid (partially symbolic, partially connectionist) systems. He declared that (a minimum of) 2 kinds of theories are required in order to study and design cognition. On the one hand, for some information-processing tasks (such as pattern recognition) connectionism has advantages over symbolic designs. But on the other hand, for other cognitive procedures (such as serial, deductive reasoning, and generative symbol manipulation procedures) the symbolic paradigm provides sufficient designs, and not only “approximations” (contrary to what extreme connectionists would claim). [97]
Gary Marcus has actually declared that the animus in the deep knowing neighborhood versus symbolic approaches now might be more sociological than philosophical:
To think that we can simply abandon symbol-manipulation is to suspend shock.
And yet, for the many part, that’s how most current AI proceeds. Hinton and numerous others have actually attempted difficult to eliminate signs altogether. The deep knowing hope-seemingly grounded not so much in science, but in a sort of historic grudge-is that smart behavior will emerge simply from the confluence of enormous data and deep knowing. Where classical computer systems and software application solve jobs by specifying sets of symbol-manipulating guidelines devoted to particular jobs, such as editing a line in a word processor or performing an estimation in a spreadsheet, neural networks normally try to solve jobs by statistical approximation and finding out from examples.
According to Marcus, Geoffrey Hinton and his colleagues have been emphatically “anti-symbolic”:
When deep learning reemerged in 2012, it was with a type of take-no-prisoners mindset that has defined many of the last years. By 2015, his hostility toward all things symbols had actually completely crystallized. He offered a talk at an AI workshop at Stanford comparing symbols to aether, among science’s biggest errors.
…
Ever since, his anti-symbolic campaign has actually just increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep knowing in one of science’s crucial journals, Nature. It closed with a direct attack on sign manipulation, calling not for reconciliation but for straight-out replacement. Later, Hinton told a gathering of European Union leaders that investing any additional money in symbol-manipulating methods was “a huge mistake,” likening it to purchasing internal combustion engines in the period of electrical cars and trucks. [98]
Part of these disputes may be due to uncertain terminology:
Turing award winner Judea Pearl offers a critique of artificial intelligence which, sadly, conflates the terms device knowing and deep learning. Similarly, when Geoffrey Hinton describes symbolic AI, the connotation of the term tends to be that of specialist systems dispossessed of any capability to find out. Using the terms needs explanation. Artificial intelligence is not confined to association rule mining, c.f. the body of work on symbolic ML and relational learning (the differences to deep knowing being the choice of representation, localist logical rather than dispersed, and the non-use of gradient-based knowing algorithms). Equally, symbolic AI is not almost production guidelines composed by hand. A proper definition of AI issues knowledge representation and reasoning, autonomous multi-agent systems, planning and argumentation, in addition to learning. [99]
Situated robotics: the world as a model
Another critique of symbolic AI is the embodied cognition technique:
The embodied cognition approach declares that it makes no sense to consider the brain separately: cognition occurs within a body, which is embedded in an environment. We require to study the system as a whole; the brain’s operating exploits consistencies in its environment, consisting of the rest of its body. Under the embodied cognition approach, robotics, vision, and other sensors end up being central, not peripheral. [100]
Rodney Brooks created behavior-based robotics, one technique to embodied cognition. Nouvelle AI, another name for this method, is deemed an alternative to both symbolic AI and connectionist AI. His approach turned down representations, either symbolic or dispersed, as not only unneeded, but as damaging. Instead, he developed the subsumption architecture, a layered architecture for embodied representatives. Each layer accomplishes a various purpose and should function in the real life. For example, the very first robotic he explains in Intelligence Without Representation, has 3 layers. The bottom layer interprets sonar sensing units to avoid things. The middle layer causes the robotic to wander around when there are no obstacles. The leading layer causes the robotic to go to more far-off locations for further exploration. Each layer can momentarily inhibit or reduce a lower-level layer. He criticized AI researchers for specifying AI issues for their systems, when: “There is no tidy department in between understanding (abstraction) and reasoning in the real life.” [101] He called his robotics “Creatures” and each layer was “made up of a fixed-topology network of easy limited state machines.” [102] In the Nouvelle AI technique, “First, it is essential to test the Creatures we build in the real world; i.e., in the very same world that we human beings inhabit. It is dreadful to fall into the temptation of checking them in a simplified world initially, even with the finest objectives of later moving activity to an unsimplified world.” [103] His emphasis on real-world testing remained in contrast to “Early operate in AI focused on video games, geometrical problems, symbolic algebra, theorem proving, and other formal systems” [104] and the use of the blocks world in symbolic AI systems such as SHRDLU.
Current views
Each approach-symbolic, connectionist, and behavior-based-has advantages, however has actually been criticized by the other techniques. Symbolic AI has been slammed as disembodied, accountable to the credentials problem, and poor in dealing with the affective issues where deep finding out excels. In turn, connectionist AI has been criticized as badly suited for deliberative step-by-step issue resolving, incorporating understanding, and dealing with preparation. Finally, Nouvelle AI stands out in reactive and real-world robotics domains but has been slammed for difficulties in integrating knowing and knowledge.
Hybrid AIs including several of these techniques are presently viewed as the course forward. [19] [81] [82] Russell and Norvig conclude that:
Overall, Dreyfus saw areas where AI did not have total responses and said that Al is therefore difficult; we now see numerous of these exact same locations going through ongoing research and advancement leading to increased capability, not impossibility. [100]
Artificial intelligence.
Automated planning and scheduling
Automated theorem proving
Belief modification
Case-based thinking
Cognitive architecture
Cognitive science
Connectionism
Constraint shows
Deep learning
First-order reasoning
GOFAI
History of expert system
Inductive logic shows
Knowledge-based systems
Knowledge representation and thinking
Logic shows
Machine knowing
Model checking
Model-based thinking
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of artificial intelligence
Physical symbol systems hypothesis
Semantic Web
Sequential pattern mining
Statistical relational knowing
Symbolic mathematics
YAGO ontology
WordNet
Notes
^ McCarthy once stated: “This is AI, so we do not care if it’s emotionally real”. [4] McCarthy reiterated his position in 2006 at the AI@50 conference where he stated “Expert system is not, by meaning, simulation of human intelligence”. [28] Pamela McCorduck writes that there are “2 significant branches of expert system: one aimed at producing intelligent behavior no matter how it was accomplished, and the other targeted at modeling smart procedures found 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 precisely 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 things 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 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 errors”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten 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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^ Marcus 2020, p. 17.
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^ Garcez et al. 2002.
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