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Symbolic Artificial Intelligence
In synthetic intelligence, symbolic expert system (likewise known as classical expert system or logic-based expert system) [1] [2] is the term for the collection of all methods in expert system research study that are based upon high-level symbolic (human-readable) representations of issues, reasoning and search. [3] Symbolic AI used tools such as logic programming, production rules, semantic webs and frames, and it developed applications such as knowledge-based systems (in specific, skilled systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated preparation and scheduling systems. The Symbolic AI paradigm caused influential ideas in search, symbolic programming languages, representatives, multi-agent systems, the semantic web, and the strengths and restrictions of official 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 persuaded that symbolic approaches would eventually prosper in developing a device with synthetic general intelligence and considered this the ultimate objective of their field. [citation needed] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, led to unrealistic expectations and guarantees and was followed by the very first AI Winter as moneying dried up. [5] [6] A second boom (1969-1986) happened with the rise of professional systems, their guarantee of capturing business competence, and an enthusiastic corporate embrace. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later frustration. [8] Problems with problems in understanding acquisition, maintaining large knowledge bases, and brittleness in managing out-of-domain problems occurred. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers concentrated on attending to hidden problems in managing uncertainty and in knowledge acquisition. [10] Uncertainty was resolved with formal techniques such as surprise Markov models, Bayesian thinking, and statistical relational knowing. [11] [12] Symbolic device learning attended to the understanding acquisition problem with contributions consisting of Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree learning, case-based knowing, and inductive logic programs to discover relations. [13]
Neural networks, a subsymbolic method, had actually 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 operate 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 prevalent, the basic agreement in the Al neighborhood was that the so-called neural-network approach was helpless. Systems simply didn’t work that well, compared to other methods. … A revolution came in 2012, when a number of people, consisting of a team of scientists dealing with Hinton, exercised a way to use the power of GPUs to enormously increase the power of neural networks.” [16] Over the next a number of years, deep learning had spectacular success in dealing with vision, speech acknowledgment, speech synthesis, image generation, and machine translation. However, given that 2020, as intrinsic problems with bias, description, coherence, and effectiveness became more evident with deep knowing methods; an increasing variety of AI researchers have required combining the very best of both the symbolic and neural network approaches [17] [18] and addressing locations that both methods have difficulty with, such as common-sense reasoning. [16]
A brief history of symbolic AI to the present day follows listed below. Period and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture [19] and the longer Wikipedia post on the History of AI, with dates and titles differing a little for increased clarity.
The very first AI summer season: irrational exuberance, 1948-1966
Success at early efforts in AI took place in 3 main areas: artificial neural networks, understanding representation, and heuristic search, contributing to high expectations. This section sums up Kautz’s reprise of early AI history.
Approaches inspired by human or animal cognition or behavior
Cybernetic techniques tried to reproduce the feedback loops between animals and their environments. A robotic turtle, with sensing units, motors for driving and steering, and 7 vacuum tubes for control, based upon a preprogrammed neural net, was built as early as 1948. This work can be viewed as an early precursor to later work in neural networks, reinforcement knowing, and located robotics. [20]
An essential early symbolic AI program was the Logic theorist, composed by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it was able to prove 38 primary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later on generalized this work to create a domain-independent problem solver, GPS (General Problem Solver). GPS solved problems represented with official operators via state-space search using means-ends analysis. [21]
During the 1960s, symbolic methods achieved excellent success at replicating intelligent behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was concentrated in 4 institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of . Each one established its own design of research study. Earlier methods based on cybernetics or synthetic neural networks were abandoned or pushed into the background.
Herbert Simon and Allen Newell studied human analytical skills and tried to formalize them, and their work laid the structures of the field of expert system, in addition to cognitive science, operations research and management science. Their research study team used the outcomes of psychological experiments to establish programs that simulated the methods that individuals utilized to fix problems. [22] [23] This custom, centered at Carnegie Mellon University would eventually culminate in the advancement of the Soar architecture in the center 1980s. [24] [25]
Heuristic search
In addition to the extremely specialized domain-specific type of understanding that we will see later used in specialist systems, early symbolic AI researchers discovered another more general application of knowledge. These were called heuristics, guidelines that direct a search in promising instructions: “How can non-enumerative search be useful when the underlying issue is greatly tough? The approach advocated by Simon and Newell is to use heuristics: fast algorithms that might stop working on some inputs or output suboptimal services.” [26] Another essential advance was to discover a method to use these heuristics that guarantees an option will be found, if there is one, not holding up against the occasional fallibility of heuristics: “The A * algorithm offered a general frame for complete and optimum heuristically assisted search. A * is utilized as a subroutine within practically every AI algorithm today however is still no magic bullet; its warranty of efficiency 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 thinking stressing first-order logic, along with attempts to deal with common-sense reasoning in a less formal manner.
Modeling formal reasoning with reasoning: the “neats”
Unlike Simon and Newell, John McCarthy felt that makers did not require to mimic the specific mechanisms of human thought, however could instead look for the essence of abstract thinking and analytical with logic, [27] regardless of whether people used the same algorithms. [a] His laboratory at Stanford (SAIL) concentrated on utilizing official logic to resolve a variety of issues, including understanding representation, preparation and knowing. [31] Logic was also the focus of the work at the University of Edinburgh and somewhere else in Europe which caused the advancement of the shows language Prolog and the science of reasoning programs. [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 challenging problems in vision and natural language processing required advertisement hoc solutions-they argued that no easy and general concept (like reasoning) would catch all the elements of intelligent behavior. Roger Schank described their “anti-logic” methods as “scruffy” (rather than the “cool” paradigms at CMU and Stanford). [36] [37] Commonsense knowledge bases (such as Doug Lenat’s Cyc) are an example of “scruffy” AI, since they should be built by hand, one complicated principle at a time. [38] [39] [40]
The very first AI winter season: crushed dreams, 1967-1977
The first AI winter was a shock:
During the first AI summer season, many individuals believed that maker intelligence might be attained in simply a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research study to use AI to solve issues of nationwide security; in specific, to automate the translation of Russian to English for intelligence operations and to create self-governing tanks for the battlefield. Researchers had actually begun to recognize that attaining AI was going to be much more difficult than was expected a decade previously, but a combination of hubris and disingenuousness led many university and think-tank researchers to accept financing with guarantees of deliverables that they need to have known they might not meet. By the mid-1960s neither useful natural language translation systems nor self-governing tanks had actually been produced, and a dramatic backlash embeded in. New DARPA leadership canceled existing AI funding programs.
Beyond the United States, the most fertile ground for AI research study was the United Kingdom. The AI winter in the United Kingdom was spurred on not so much by dissatisfied military leaders as by rival academics who saw AI researchers as charlatans and a drain on research study financing. A teacher of used mathematics, Sir James Lighthill, was commissioned by Parliament to assess the state of AI research study in the nation. The report stated that all of the issues being worked on in AI would be better dealt with by researchers from other disciplines-such as used mathematics. The report also declared that AI successes on toy issues could never ever scale to real-world applications due to combinatorial surge. [41]
The second AI summer season: knowledge is power, 1978-1987
Knowledge-based systems
As limitations with weak, domain-independent methods ended up being increasingly more evident, [42] researchers from all 3 traditions started to construct knowledge into AI applications. [43] [7] The knowledge transformation was driven by the awareness that understanding underlies high-performance, domain-specific AI applications.
Edward Feigenbaum said:
– “In the understanding lies the power.” [44]
to describe that high performance in a specific domain requires both basic and highly domain-specific knowledge. Ed Feigenbaum and Doug Lenat called this The Knowledge Principle:
( 1) The Knowledge Principle: if a program is to perform an intricate job well, it should know a lot about the world in which it runs.
( 2) A possible extension of that principle, called the Breadth Hypothesis: there are 2 additional capabilities essential for smart habits in unanticipated circumstances: drawing on progressively general knowledge, and analogizing to particular but remote knowledge. [45]
Success with specialist systems
This “knowledge transformation” caused the advancement and deployment of expert systems (introduced by Edward Feigenbaum), the first commercially effective type of AI software. [46] [47] [48]
Key professional systems were:
DENDRAL, which discovered the structure of natural molecules from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and suggested more laboratory tests, when necessary – by analyzing lab results, patient history, and doctor observations. “With about 450 guidelines, MYCIN had the ability to perform along with some specialists, and substantially better than junior physicians.” [49] INTERNIST and CADUCEUS which tackled internal medication diagnosis. Internist tried to capture the competence of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS could eventually detect approximately 1000 different diseases.
– GUIDON, which showed how an understanding base built for expert problem solving could be repurposed for teaching. [50] XCON, to set up VAX computer systems, a then tiresome procedure that could use up to 90 days. XCON lowered the time to about 90 minutes. [9]
DENDRAL is considered the very first specialist system that relied on knowledge-intensive analytical. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:
One of individuals at Stanford interested in computer-based models of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genetics. When I informed him I wanted an induction “sandbox”, he stated, “I have simply the one for you.” His laboratory was doing mass spectrometry of amino acids. The 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 excellent at heuristic search methods, and he had an algorithm that was great at creating the chemical problem area.
We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, creator of the chemical behind the birth control tablet, and likewise one of the world’s most appreciated mass spectrometrists. Carl and his postdocs were world-class experts in mass spectrometry. We started to contribute to their knowledge, developing knowledge of engineering as we went along. These experiments amounted to titrating DENDRAL increasingly more knowledge. The more you did that, the smarter the program ended up being. We had extremely excellent outcomes.
The generalization was: in the understanding lies the power. That was the big concept. In my career that is the big, “Ah ha!,” and it wasn’t the method AI was being done previously. Sounds simple, however it’s most likely AI’s most effective generalization. [51]
The other expert systems discussed above followed DENDRAL. MYCIN exhibits the traditional expert system architecture of a knowledge-base of rules paired to a symbolic reasoning mechanism, including the usage of certainty factors to handle uncertainty. GUIDON reveals how an explicit understanding base can be repurposed for a 2nd application, tutoring, and is an example of a smart tutoring system, a particular sort of knowledge-based application. Clancey revealed that it was not sufficient simply to utilize MYCIN’s guidelines for guideline, however that he also needed to add guidelines for dialogue management and trainee modeling. [50] XCON is significant since of the countless dollars it saved DEC, which triggered the specialist system boom where most all significant corporations in the US had professional systems groups, to record corporate know-how, protect it, and automate it:
By 1988, DEC’s AI group had 40 expert systems released, with more en route. DuPont had 100 in use and 500 in development. Nearly every major U.S. corporation had its own Al group and was either using or examining expert systems. [49]
Chess specialist understanding was encoded in Deep Blue. In 1996, this allowed IBM’s Deep Blue, with the assistance of symbolic AI, to win in a video game of chess versus the world champion at that time, Garry Kasparov. [52]
Architecture of knowledge-based and expert systems
A key part of the system architecture for all expert systems is the knowledge base, which shops realities and rules for problem-solving. [53] The simplest technique for a skilled system understanding base is simply a collection or network of production rules. Production guidelines connect symbols in a relationship similar to an If-Then statement. The professional system processes the guidelines to make deductions and to determine what extra information it requires, i.e. what questions to ask, utilizing human-readable signs. For instance, OPS5, CLIPS and their followers Jess and Drools run in this style.
Expert systems can run in either a forward chaining – from proof to conclusions – or backwards chaining – from objectives to required information and requirements – way. More advanced knowledge-based systems, such as Soar can also carry out meta-level thinking, that is reasoning about their own thinking in terms of choosing 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 skilled system architecture. They design a neighborhood of professionals incrementally contributing, where they can, to fix an issue. The problem is represented in multiple levels of abstraction or alternate views. The professionals (knowledge sources) volunteer their services whenever they acknowledge they can contribute. Potential analytical actions are represented on an agenda that is updated as the issue situation modifications. A controller chooses how helpful each contribution is, and who must make the next analytical action. One example, the BB1 chalkboard architecture [54] was initially inspired by research studies of how humans prepare to perform multiple jobs in a trip. [55] An innovation of BB1 was to apply the exact same chalkboard design to fixing its control issue, i.e., its controller carried out meta-level reasoning with knowledge sources that kept an eye on how well a plan or the analytical was continuing and might switch from one method to another as conditions – such as goals or times – changed. BB1 has been applied in numerous domains: building and construction website planning, intelligent tutoring systems, and real-time client monitoring.
The second AI winter, 1988-1993
At the height of the AI boom, business such as Symbolics, LMI, and Texas Instruments were selling LISP makers specifically targeted to speed up the advancement of AI applications and research study. 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 second AI winter that followed:
Many factors can be offered for the arrival of the 2nd AI winter. The hardware business stopped working when a lot more economical general Unix workstations from Sun together with great compilers for LISP and Prolog came onto the market. Many business implementations of professional systems were ceased when they proved too costly to maintain. Medical specialist systems never caught on for a number of reasons: the trouble in keeping them as much as date; the difficulty for physician to find out how to utilize a bewildering range of different expert systems for different medical conditions; and possibly most crucially, the unwillingness of medical professionals to trust a computer-made diagnosis over their gut instinct, even for specific domains where the professional systems could exceed an average medical professional. Equity capital money deserted AI almost overnight. The world AI conference IJCAI hosted a huge and extravagant trade show and countless nonacademic attendees in 1987 in Vancouver; the main AI conference the list below year, AAAI 1988 in St. Paul, was a small and strictly academic affair. [9]
Including more strenuous structures, 1993-2011
Uncertain thinking
Both analytical techniques and extensions to logic were attempted.
One analytical approach, hidden Markov models, had already been popularized in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized using Bayesian Networks as a noise however effective method of managing unpredictable reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian methods were applied successfully in specialist systems. [57] Even later on, in the 1990s, analytical relational learning, a method that combines possibility with logical solutions, enabled likelihood to be combined with first-order reasoning, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.
Other, non-probabilistic extensions to first-order reasoning to support were also tried. For example, non-monotonic thinking might be utilized with reality upkeep systems. A truth upkeep system tracked presumptions and reasons for all reasonings. It permitted inferences to be withdrawn when presumptions were discovered to be inaccurate or a contradiction was obtained. Explanations could be offered an inference by explaining which guidelines were applied to produce it and then continuing through underlying reasonings and rules all the method back to root assumptions. [58] Lofti Zadeh had introduced a various sort of extension to handle the representation of ambiguity. For example, in choosing how “heavy” or “high” a male is, there is often no clear “yes” or “no” response, and a predicate for heavy or high would rather return values between 0 and 1. Those worths represented to what degree the predicates were true. His fuzzy reasoning even more supplied a means for propagating combinations of these worths through rational formulas. [59]
Machine knowing
Symbolic maker learning techniques were examined to deal with the understanding acquisition traffic jam. One of the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test method to create possible guideline hypotheses to test against spectra. Domain and job understanding minimized the variety of candidates checked to a manageable size. Feigenbaum described Meta-DENDRAL as
… the conclusion of my dream of the early to mid-1960s having to do with 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 guide and prune the search. That understanding got in there because we interviewed people. But how did the people get the knowledge? By looking at thousands of spectra. So we desired a program that would take a look at countless spectra and infer the knowledge of mass spectrometry that DENDRAL could utilize to fix individual hypothesis development issues. We did it. We were even able to release new knowledge of mass spectrometry in the Journal of the American Chemical Society, providing credit just in a footnote that a program, Meta-DENDRAL, actually did it. We had the ability to do something that had been a dream: to have a computer program developed a new and publishable piece of science. [51]
In contrast to the knowledge-intensive approach of Meta-DENDRAL, Ross Quinlan developed a domain-independent method to statistical category, decision tree learning, starting initially 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 category guidelines.
Advances were made in comprehending artificial intelligence theory, too. Tom Mitchell introduced variation space knowing which explains learning as an explore a space of hypotheses, with upper, more basic, and lower, more specific, limits incorporating all viable hypotheses constant with the examples seen so far. [62] More officially, Valiant introduced Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of device learning. [63]
Symbolic device learning encompassed more than discovering by example. E.g., John Anderson offered a cognitive design of human knowing where skill practice leads to a compilation of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a student may find out to apply “Supplementary angles are two angles whose steps sum 180 degrees” as a number of different procedural rules. E.g., one rule may state that if X and Y are additional and you know X, then Y will be 180 – X. He called his method “understanding compilation”. ACT-R has actually been utilized successfully to design aspects of human cognition, such as discovering and retention. ACT-R is likewise used in smart tutoring systems, called cognitive tutors, to effectively teach geometry, computer shows, and algebra to school kids. [64]
Inductive reasoning programs was another approach to learning that enabled reasoning programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) could synthesize Prolog programs from examples. [65] John R. Koza applied genetic algorithms to program synthesis to produce genetic shows, which he used to synthesize LISP programs. Finally, Zohar Manna and Richard Waldinger supplied a more general method to program synthesis that synthesizes a functional program in the course of showing its specs to be proper. [66]
As an option to reasoning, Roger Schank introduced case-based thinking (CBR). The CBR approach described in his book, Dynamic Memory, [67] focuses initially on keeping in mind key analytical cases for future usage and generalizing them where suitable. When confronted with a brand-new issue, CBR obtains the most similar previous case and adjusts it to the specifics of the existing issue. [68] Another option to logic, genetic algorithms and hereditary programs are based on an evolutionary design of knowing, where sets of guidelines are encoded into populations, the guidelines govern the habits of individuals, and selection of the fittest prunes out sets of inappropriate rules over many generations. [69]
Symbolic artificial intelligence was used to discovering principles, rules, heuristics, and problem-solving. Approaches, other than those above, include:
1. Learning from guideline or advice-i.e., taking human guideline, impersonated recommendations, and determining how to operationalize it in specific scenarios. For example, in a game of Hearts, discovering precisely how to play a hand to “prevent taking points.” [70] 2. Learning from exemplars-improving performance by accepting subject-matter expert (SME) feedback throughout training. When problem-solving stops working, querying the professional to either find out a brand-new exemplar for analytical or to discover a brand-new explanation regarding exactly why one prototype is more relevant than another. For instance, the program Protos learned to identify tinnitus cases by engaging with an audiologist. [71] 3. Learning by analogy-constructing problem solutions based on similar problems seen in the past, and after that modifying their solutions to fit a new situation or domain. [72] [73] 4. Apprentice knowing systems-learning unique options to problems by observing human problem-solving. Domain understanding explains why novel options are proper and how the option can be generalized. LEAP found out how to create VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., developing jobs to perform experiments and after that gaining from the results. Doug Lenat’s Eurisko, for example, discovered heuristics to beat human players at the Traveller role-playing video game for two years in a row. [75] 6. Learning macro-operators-i.e., searching for helpful macro-operators to be gained from sequences of basic problem-solving actions. Good macro-operators streamline problem-solving by allowing issues to be fixed at a more abstract level. [76]
Deep knowing and neuro-symbolic AI 2011-now
With the rise of deep knowing, the symbolic AI method has been compared to deep learning as complementary “… with parallels having actually been drawn sometimes by AI scientists between Kahneman’s research study on human thinking and decision making – reflected in his book Thinking, Fast and Slow – and the so-called “AI systems 1 and 2″, which would in concept be modelled by deep knowing and symbolic thinking, respectively.” In this view, symbolic reasoning is more apt for deliberative thinking, preparation, and explanation while deep knowing is more apt for fast pattern acknowledgment in affective applications with noisy information. [17] [18]
Neuro-symbolic AI: integrating neural and symbolic techniques
Neuro-symbolic AI attempts to incorporate 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 capable of thinking, learning, and cognitive modeling. As argued by Valiant [77] and numerous others, [78] the efficient building and construction of abundant computational cognitive designs demands the mix of sound symbolic reasoning and effective (device) learning models. Gary Marcus, likewise, argues that: “We can not construct abundant cognitive designs in a sufficient, automated way without the set of three of hybrid architecture, rich anticipation, and sophisticated techniques for thinking.”, [79] and in particular: “To construct a robust, knowledge-driven approach to AI we must have the machinery of symbol-manipulation in our toolkit. Excessive of useful knowledge is abstract to make do without tools that represent and control abstraction, and to date, the only machinery that we understand of that can control such abstract understanding dependably is the device of sign adjustment. ” [80]
Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have likewise argued for a synthesis. Their arguments are based on a need to address the 2 kinds of thinking discussed in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having two elements, System 1 and System 2. System 1 is quickly, automatic, instinctive and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is the kind used for pattern recognition while System 2 is far better suited for preparation, reduction, and deliberative thinking. In this view, deep knowing finest models the first sort of believing while symbolic reasoning finest models the 2nd kind and both are needed.
Garcez and Lamb explain research in this location as being continuous for at least the previous twenty years, [83] dating from their 2002 book on neurosymbolic learning systems. [84] A series of workshops on neuro-symbolic thinking has actually been held every year given that 2005, see http://www.neural-symbolic.org/ for details.
In their 2015 paper, Neural-Symbolic Learning and Reasoning: Contributions and Challenges, Garcez et al. argue that:
The combination of the symbolic and connectionist paradigms of AI has actually been pursued by a reasonably little research study neighborhood over the last 20 years and has yielded several significant results. Over the last decade, neural symbolic systems have actually been revealed capable of 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 revealed capable of representing modal and temporal logics (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 used to a variety of problems in the locations of bioinformatics, control engineering, software verification and adaptation, visual intelligence, ontology learning, and computer games. [78]
Approaches for combination are differed. Henry Kautz’s taxonomy of neuro-symbolic architectures, together with some examples, follows:
– Symbolic Neural symbolic-is the current approach of numerous neural designs in natural language processing, where words or subword tokens are both the supreme input and output of large language designs. Examples include BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic strategies are utilized to call neural methods. In this case the symbolic method is Monte Carlo tree search and the neural strategies find out how to assess game positions.
– Neural|Symbolic-uses a neural architecture to translate perceptual information as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to create or label training data that is subsequently found out by a deep learning design, e.g., to train a neural model for symbolic calculation by using a Macsyma-like symbolic mathematics system to produce or identify examples.
– Neural _ Symbolic -uses a neural internet that is generated from symbolic guidelines. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR evidence tree produced from knowledge base rules and terms. Logic Tensor Networks [86] likewise fall under this classification.
– Neural [Symbolic] -allows a neural design to directly call a symbolic thinking engine, e.g., to carry out an action or examine a state.
Many key research concerns remain, such as:
– What is the very best method to incorporate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and drawn out from them?
– How should sensible understanding be found out and reasoned about?
– How can abstract understanding that is difficult to encode realistically be dealt with?
Techniques and contributions
This section provides a summary of techniques and contributions in a general context leading to numerous other, more in-depth articles in Wikipedia. Sections on Artificial Intelligence and Uncertain Reasoning are covered earlier in the history area.
AI shows languages
The crucial AI shows language in the US during the last symbolic AI boom duration was LISP. LISP is the second oldest shows language after FORTRAN and was produced in 1958 by John McCarthy. LISP supplied the first read-eval-print loop to support rapid program advancement. Compiled functions could be easily blended with analyzed functions. Program tracing, stepping, and breakpoints were likewise supplied, in addition to the ability to alter values or functions and continue from breakpoints or mistakes. It had the first self-hosting compiler, implying that the compiler itself was originally composed in LISP and after that ran interpretively to compile the compiler code.
Other essential innovations pioneered by LISP that have actually infected other shows languages include:
Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals
Programs were themselves data structures that other programs might operate on, allowing the easy definition of higher-level languages.
In contrast to the US, in Europe the crucial AI programming language throughout that very same duration was Prolog. Prolog provided an integrated store of realities and provisions that could be queried by a read-eval-print loop. The shop might serve as an understanding base and the clauses could act as rules or a restricted kind of logic. As a subset of first-order reasoning Prolog was based on Horn clauses with a closed-world assumption-any facts not known were considered false-and a distinct name assumption for primitive terms-e.g., the identifier barack_obama was considered to refer to exactly one things. Backtracking and marriage are integrated to Prolog.
Alain Colmerauer and Philippe Roussel are credited as the innovators of Prolog. Prolog is a kind of reasoning shows, which was invented by Robert Kowalski. Its history was also affected 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 post.
Prolog is also a type of declarative shows. The reasoning clauses that describe programs are straight translated to run the programs specified. No specific series of actions is needed, as holds true with essential shows languages.
Japan championed Prolog for its Fifth Generation Project, intending to build special hardware for high performance. Similarly, LISP makers were constructed to run LISP, but as the second AI boom turned to bust these business might not compete with new workstations that might now run LISP or Prolog natively at equivalent speeds. See the history area for more detail.
Smalltalk was another prominent AI shows language. For instance, it introduced metaclasses and, together with Flavors and CommonLoops, influenced the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the current basic Lisp dialect. CLOS is a Lisp-based object-oriented system that allows numerous inheritance, in addition to incremental extensions to both classes and metaclasses, therefore providing a run-time meta-object protocol. [88]
For other AI programming languages see this list of shows languages for artificial intelligence. Currently, Python, a multi-paradigm shows language, is the most popular shows 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 aspects such as higher-order functions, and object-oriented shows that includes metaclasses.
Search
Search emerges in lots of type of issue solving, including preparation, restraint fulfillment, and playing games such as checkers, chess, and go. The very best known AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven stipulation knowing, and the DPLL algorithm. For adversarial search when playing video games, alpha-beta pruning, branch and bound, and minimax were early contributions.
Knowledge representation and reasoning
Multiple different methods to represent understanding and after that reason with those representations have been examined. Below is a fast summary of approaches to knowledge representation and automated thinking.
Knowledge representation
Semantic networks, conceptual charts, frames, and logic are all approaches to modeling knowledge such as domain knowledge, analytical knowledge, and the semantic meaning of language. Ontologies design 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 used for any domain while WordNet is a lexical resource that can likewise be seen as an ontology. YAGO incorporates WordNet as part of its ontology, to align realities drawn out from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology presently being used.
Description logic is a reasoning for automated classification of ontologies and for spotting irregular classification information. OWL is a language utilized to represent ontologies with description reasoning. Protégé is an ontology editor that can check out in OWL ontologies and after that examine consistency with deductive classifiers such as such as HermiT. [89]
First-order logic is more basic than description reasoning. The automated theorem provers discussed below can show theorems in first-order reasoning. Horn clause reasoning is more restricted than first-order reasoning and is used in reasoning shows languages such as Prolog. Extensions to first-order logic include temporal reasoning, to deal with time; epistemic logic, to reason about agent understanding; modal logic, to handle possibility and requirement; and probabilistic reasonings 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 utilized in conjunction with the Mace4 design checker. ACL2 is a theorem prover that can deal with evidence by induction and is a descendant of the Boyer-Moore Theorem Prover, also called Nqthm.
Reasoning in knowledge-based systems
Knowledge-based systems have an explicit knowledge base, usually of guidelines, to enhance reusability throughout domains by separating procedural code and domain understanding. A different inference engine procedures guidelines and includes, deletes, or modifies a knowledge store.
Forward chaining reasoning engines are the most typical, and are seen in CLIPS and OPS5. Backward chaining takes place in Prolog, where a more limited sensible representation is used, Horn Clauses. Pattern-matching, specifically unification, is used in Prolog.
A more flexible sort of analytical happens when reasoning about what to do next takes place, rather than just picking one of the readily available actions. This kind of meta-level reasoning 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 frequently utilized knowledge into higher-level pieces.
Commonsense reasoning
Marvin Minsky initially proposed frames as a way of translating common visual situations, such as a workplace, and Roger Schank extended this idea to scripts for typical regimens, such as dining out. Cyc has actually tried to catch beneficial common-sense understanding and has “micro-theories” to deal with specific sort of domain-specific reasoning.
Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] estimates human thinking about naive physics, such as what occurs when we warm a liquid in a pot on the range. We anticipate it to heat and potentially boil over, despite the fact that we might not understand its temperature level, its boiling point, or other information, such as atmospheric pressure.
Similarly, Allen’s temporal interval algebra is a simplification of reasoning about time and Region Connection Calculus is a simplification of reasoning about spatial relationships. Both can be solved with constraint solvers.
Constraints and constraint-based reasoning
Constraint solvers carry out a more minimal sort of inference than first-order reasoning. They can streamline sets of spatiotemporal restraints, such as those for RCC or Temporal Algebra, along with fixing other sort of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic programming can be utilized to resolve scheduling issues, for example with restriction managing guidelines (CHR).
Automated planning
The General Problem Solver (GPS) cast planning as analytical utilized means-ends analysis to develop plans. STRIPS took a various method, seeing preparation as theorem proving. Graphplan takes a least-commitment method to preparation, rather than sequentially picking actions from an initial state, working forwards, or a goal state if working backwards. Satplan is a technique to preparing where a preparation issue is lowered to a Boolean satisfiability problem.
Natural language processing
Natural language processing focuses on treating language as information to carry out tasks such as recognizing subjects without necessarily understanding the desired meaning. Natural language understanding, in contrast, constructs a meaning representation and utilizes that for additional processing, such as answering questions.
Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb expression chunking are all elements of natural language processing long dealt with by symbolic AI, but since improved by deep learning methods. In symbolic AI, discourse representation theory and first-order reasoning have been utilized to represent sentence meanings. Latent semantic analysis (LSA) and specific semantic analysis likewise supplied vector representations of documents. In the latter case, vector components are interpretable as concepts called by Wikipedia posts.
New deep learning methods based on Transformer designs have now eclipsed these earlier symbolic AI methods and attained cutting edge performance in natural language processing. However, Transformer models are opaque and do not yet produce human-interpretable semantic representations for sentences and documents. Instead, they produce task-specific vectors where the meaning of the vector elements is opaque.
Agents and multi-agent systems
Agents are self-governing systems embedded in an environment they view and act on in some sense. Russell and Norvig’s standard book on expert system is arranged to show agent architectures of increasing elegance. [91] The sophistication of representatives varies from easy reactive agents, to those with a model of the world and automated preparation capabilities, perhaps a BDI representative, i.e., one with beliefs, desires, and intentions – or additionally a reinforcement finding out design found out gradually to choose actions – up to a mix of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep knowing for perception. [92]
On the other hand, a multi-agent system consists of multiple agents that communicate among themselves with some inter-agent interaction language such as Knowledge Query and Manipulation Language (KQML). The representatives require not all have the very same internal architecture. Advantages of multi-agent systems include the ability to divide work amongst the agents and to increase fault tolerance when representatives are lost. Research issues include how representatives reach agreement, dispersed issue fixing, multi-agent knowing, multi-agent planning, and distributed restraint optimization.
Controversies occurred from at an early stage in symbolic AI, both within the field-e.g., in between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who embraced AI but declined symbolic approaches-primarily connectionists-and those outside the field. Critiques from outside of the field were mainly from philosophers, on intellectual premises, however likewise from funding firms, particularly throughout the two AI winters.
The Frame Problem: knowledge representation challenges for first-order reasoning
Limitations were discovered in utilizing simple first-order logic to factor about dynamic domains. Problems were discovered both with concerns to specifying the prerequisites for an action to succeed and in offering axioms for what did not change after an action was performed.
McCarthy and Hayes presented the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Expert System.” [93] A basic example occurs in “proving that one person might enter discussion with another”, as an axiom asserting “if an individual has a telephone he still has it after searching for a number in the telephone book” would be required for the reduction to be successful. Similar axioms would be needed for other domain actions to specify what did not change.
A comparable issue, called the Qualification Problem, takes place in attempting to enumerate the preconditions for an action to succeed. A boundless variety of pathological conditions can be pictured, e.g., a banana in a tailpipe could prevent a car from running correctly.
McCarthy’s method to fix the frame issue was circumscription, a type of non-monotonic reasoning where deductions might be made from actions that require only specify what would alter while not needing to explicitly define everything that would not alter. Other non-monotonic reasonings provided truth maintenance systems that revised beliefs leading to contradictions.
Other ways of managing more open-ended domains included probabilistic thinking systems and artificial intelligence to learn brand-new principles and guidelines. McCarthy’s Advice Taker can be considered as an inspiration here, as it might include new knowledge provided by a human in the kind of assertions or guidelines. For example, speculative symbolic device discovering systems checked out the ability to take top-level natural language advice and to analyze it into domain-specific actionable guidelines.
Similar to the issues in handling dynamic domains, sensible reasoning is likewise tough to record in formal reasoning. Examples of sensible reasoning consist of implicit reasoning about how individuals believe or general knowledge of day-to-day events, objects, and living creatures. This sort of understanding is taken for granted and not deemed noteworthy. Common-sense thinking is an open area of research study and challenging both for symbolic systems (e.g., Cyc has attempted to catch essential parts of this understanding over more than a decade) and neural systems (e.g., self-driving cars and trucks that do not know not to drive into cones or not to hit pedestrians walking a bicycle).
McCarthy saw his Advice Taker as having sensible, however his meaning of common-sense was different than the one above. [94] He specified a program as having common sense “if it instantly deduces for itself a sufficiently wide class of instant effects of anything it is told and what it currently understands. “
Connectionist AI: philosophical obstacles and sociological disputes
Connectionist methods consist of earlier work on neural networks, [95] such as perceptrons; operate in the mid to late 80s, such as Danny Hillis’s Connection Machine and Yann LeCun’s advances in convolutional neural networks; to today’s more sophisticated techniques, such as Transformers, GANs, and other work in deep learning.
Three philosophical positions [96] have been outlined among connectionists:
1. Implementationism-where connectionist architectures implement the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is declined completely, and connectionist architectures underlie intelligence and are completely enough to discuss it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are viewed as complementary and both are required for intelligence
Olazaran, in his sociological history of the controversies within the neural network community, explained the moderate connectionism consider as basically suitable with existing research in neuro-symbolic hybrids:
The 3rd and last position I want to examine here is what I call the moderate connectionist view, a more diverse view of the present debate in between connectionism and symbolic AI. Among the researchers who has actually 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 protected hybrid (partly symbolic, partly connectionist) systems. He declared that (at least) 2 kinds of theories are required in order to study and model cognition. On the one hand, for some information-processing jobs (such as pattern acknowledgment) connectionism has advantages over symbolic designs. But on the other hand, for other cognitive procedures (such as serial, deductive thinking, and generative symbol manipulation processes) the symbolic paradigm uses sufficient models, and not only “approximations” (contrary to what radical connectionists would declare). [97]
Gary Marcus has actually claimed that the animus in the deep knowing community versus symbolic techniques now may be more sociological than philosophical:
To think that we can just abandon symbol-manipulation is to suspend disbelief.
And yet, for the many part, that’s how most present AI earnings. Hinton and lots of others have actually attempted tough to get rid of signs completely. The deep learning hope-seemingly grounded not a lot in science, however in a sort of historical grudge-is that smart behavior will emerge purely from the confluence of enormous information and deep learning. Where classical computers and software resolve tasks by specifying sets of symbol-manipulating guidelines dedicated to particular jobs, such as modifying a line in a word processor or performing a computation in a spreadsheet, neural networks usually attempt to fix jobs by statistical approximation and gaining from examples.
According to Marcus, Geoffrey Hinton and his colleagues have actually been emphatically “anti-symbolic”:
When deep learning reemerged in 2012, it was with a type of take-no-prisoners attitude that has characterized the majority of the last decade. By 2015, his hostility toward all things signs had actually completely crystallized. He offered a talk at an AI workshop at Stanford comparing symbols to aether, among science’s greatest mistakes.
…
Since then, his anti-symbolic project has actually just increased in intensity. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep learning in among science’s essential journals, Nature. It closed with a direct attack on sign adjustment, calling not for reconciliation but for straight-out replacement. Later, Hinton told a gathering of European Union leaders that investing any further cash in symbol-manipulating techniques was “a big error,” comparing it to purchasing internal combustion engines in the era of electrical vehicles. [98]
Part of these conflicts may be due to uncertain terms:
Turing award winner Judea Pearl provides a critique of device learning which, sadly, conflates the terms device knowing and deep learning. Similarly, when Geoffrey Hinton describes symbolic AI, the undertone of the term tends to be that of expert systems dispossessed of any capability to learn. The usage of the terms is in need of clarification. Artificial intelligence is not restricted to association guideline mining, c.f. the body of work on symbolic ML and relational knowing (the distinctions to deep knowing being the choice of representation, localist rational rather than dispersed, and the non-use of gradient-based knowing algorithms). Equally, symbolic AI is not almost production rules composed by hand. A correct definition of AI concerns knowledge representation and reasoning, self-governing multi-agent systems, planning and argumentation, along with knowing. [99]
Situated robotics: the world as a design
Another review of symbolic AI is the embodied cognition method:
The embodied cognition technique declares that it makes no sense to consider the brain individually: cognition happens within a body, which is embedded in an environment. We require to study the system as a whole; the brain’s functioning exploits consistencies in its environment, consisting of the rest of its body. Under the embodied cognition method, robotics, vision, and other sensing units become main, not peripheral. [100]
Rodney Brooks invented 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 method turned down representations, either symbolic or dispersed, as not just unneeded, but as harmful. Instead, he produced the subsumption architecture, a layered architecture for embodied representatives. Each layer attains a different purpose and should operate in the real life. For example, the very first robot he describes in Intelligence Without Representation, has three layers. The bottom layer interprets sonar sensing units to avoid items. The middle layer triggers the robot to wander around when there are no barriers. The leading layer triggers the robot to go to more far-off places for more expedition. Each layer can briefly prevent or suppress a lower-level layer. He criticized AI researchers for specifying AI problems for their systems, when: “There is no clean department in between perception (abstraction) and reasoning in the real life.” [101] He called his robotics “Creatures” and each layer was “composed of a fixed-topology network of easy limited state makers.” [102] In the Nouvelle AI technique, “First, it is essential to check the Creatures we build in the real life; i.e., in the same world that we humans live in. It is disastrous to fall under the temptation of testing them in a simplified world first, even with the very best objectives of later moving activity to an unsimplified world.” [103] His focus on real-world screening was in contrast to “Early work in AI focused on video games, geometrical problems, symbolic algebra, theorem proving, and other formal systems” [104] and making use of the blocks world in symbolic AI systems such as SHRDLU.
Current views
Each approach-symbolic, connectionist, and behavior-based-has benefits, however has actually been slammed by the other techniques. Symbolic AI has actually been criticized as disembodied, liable to the qualification issue, and bad in managing the affective problems where deep discovering excels. In turn, connectionist AI has been criticized as poorly suited for deliberative step-by-step problem resolving, incorporating understanding, and managing planning. Finally, Nouvelle AI excels in reactive and real-world robotics domains but has been slammed for difficulties in including knowing and knowledge.
Hybrid AIs incorporating several of these approaches are currently deemed the course forward. [19] [81] [82] Russell and Norvig conclude that:
Overall, Dreyfus saw locations where AI did not have complete responses and said that Al is for that reason difficult; we now see a number of these exact same areas going through ongoing research and development causing increased ability, not impossibility. [100]
Artificial intelligence.
Automated planning and scheduling
Automated theorem proving
Belief revision
Case-based thinking
Cognitive architecture
Cognitive science
Connectionism
Constraint programs
Deep learning
First-order logic
GOFAI
History of synthetic intelligence
Inductive logic shows
Knowledge-based systems
Knowledge representation and thinking
Logic programs
Machine knowing
Model checking
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 learning
Symbolic mathematics
YAGO ontology
WordNet
Notes
^ McCarthy as soon as said: “This is AI, so we don’t care if it’s psychologically genuine”. [4] McCarthy repeated 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 writes that there are “2 major branches of synthetic intelligence: one focused on producing intelligent habits regardless of how it was achieved, and the other aimed at modeling smart procedures discovered in nature, particularly human ones.”, [29] Stuart Russell and Peter Norvig composed “Aeronautical engineering texts do not specify the goal of their field as making ‘makers that fly so exactly like pigeons that they can deceive even other pigeons.'” [30] Citations
^ Garnelo, Marta; Shanahan, Murray (October 2019). “Reconciling deep knowing with symbolic synthetic intelligence: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). “Logic-Based Artificial Intelligence”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep knowing with symbolic synthetic intelligence: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. 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.
^ Lenat, Douglas B; Feigenbaum, Edward A (1988 ). “On the limits of knowledge”. Proceedings of the International Workshop on Artificial Intelligence for Industrial Applications: 291-300. doi:10.1109/ AIIA.1988.13308. S2CID 11778085.
^ 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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^ Russell & Norvig 2021, pp. 335-337.
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^ Shapiro, Ehud Y (1981 ). “The Model Inference System”. Proceedings of the 7th international joint conference on Artificial intelligence. IJCAI. Vol. 2. p. 1064.
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^ Bareiss, Ray; Porter, Bruce; Wier, Craig. “Chapter 4: Protos: An Exemplar-Based Learning Apprentice”. In Michalski, Carbonell & Mitchell (1986 ), pp. 112-139.
^ Carbonell, Jaime. “Chapter 5: Learning by Analogy: Formulating and Generalizing Plans from Past Experience”. In Michalski, Carbonell & Mitchell (1983 ), pp. 137-162.
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^ Marcus 2020, p. 17.
^ a b Rossi 2022.
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^ Garcez & Lamb 2020, p. 2.
^ Garcez et al. 2002.
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