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Symbolic Artificial Intelligence
In artificial intelligence, symbolic expert system (likewise called classical expert system or logic-based expert system) [1] [2] is the term for the collection of all techniques in expert system research study that are based upon high-level symbolic (human-readable) representations of issues, reasoning and search. [3] Symbolic AI utilized tools such as logic shows, production rules, semantic nets 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 preparation and scheduling systems. The Symbolic AI paradigm resulted in seminal concepts in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and restrictions of official 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 encouraged that symbolic approaches would eventually be successful in creating a maker with synthetic basic intelligence and considered this the ultimate objective of their field. [citation required] 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 first AI Winter as funding dried up. [5] [6] A second boom (1969-1986) accompanied the increase of expert systems, their guarantee of catching business know-how, and a passionate corporate accept. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later dissatisfaction. [8] Problems with problems in knowledge acquisition, keeping large knowledge bases, and brittleness in handling out-of-domain problems developed. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI researchers concentrated on addressing underlying problems in managing uncertainty and in knowledge acquisition. [10] Uncertainty was attended to with formal methods such as hidden Markov models, Bayesian reasoning, and analytical relational learning. [11] [12] Symbolic machine finding out dealt with the knowledge acquisition issue with contributions including Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree learning, case-based learning, and inductive reasoning shows to find out relations. [13]
Neural networks, a subsymbolic method, had actually been pursued from early days and reemerged highly in 2012. Early examples are Rosenblatt’s perceptron 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 became commonplace, the basic agreement in the Al neighborhood was that the so-called neural-network method was helpless. Systems just didn’t work that well, compared to other approaches. … A revolution was available in 2012, when a variety of individuals, consisting of a team of researchers dealing with Hinton, exercised a method to use the power of GPUs to enormously increase the power of neural networks.” [16] Over the next numerous years, deep knowing had incredible success in dealing with vision, speech recognition, speech synthesis, image generation, and device translation. However, considering that 2020, as fundamental difficulties with bias, explanation, coherence, and robustness became more apparent with deep learning approaches; an increasing variety of AI researchers have actually required integrating the finest of both the symbolic and neural network approaches [17] [18] and dealing with locations that both approaches have trouble with, such as sensible thinking. [16]
A short history of symbolic AI to today 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 short article on the History of AI, with dates and titles varying somewhat for increased clarity.
The very first AI summertime: irrational liveliness, 1948-1966
Success at early attempts in AI occurred in 3 main locations: synthetic neural networks, understanding representation, and heuristic search, contributing to high expectations. This area sums up Kautz’s reprise of early AI history.
Approaches motivated 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 steering, and seven vacuum tubes for control, based upon a preprogrammed neural net, was constructed as early as 1948. This work can be seen as an early precursor to later work in neural networks, support knowing, and located robotics. [20]
A crucial early symbolic AI program was the Logic theorist, written by Allen Newell, Herbert Simon and Cliff Shaw in 1955-56, as it had the ability to prove 38 elementary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later on generalized this work to develop a domain-independent problem solver, GPS (General Problem Solver). GPS resolved issues represented with official operators through state-space search utilizing means-ends analysis. [21]
During the 1960s, symbolic approaches achieved fantastic success at imitating intelligent behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was focused in 4 organizations in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Every one developed its own design of research study. Earlier techniques based upon cybernetics or synthetic neural networks were abandoned or pushed into the background.
Herbert Simon and Allen Newell studied human problem-solving skills and attempted to formalize them, and their work laid the structures of the field of expert system, along with cognitive science, operations research study and management science. Their research group used the outcomes of mental experiments to develop programs that simulated the techniques that people utilized to fix issues. [22] [23] This tradition, focused at Carnegie Mellon University would ultimately culminate in the development of the Soar architecture in the middle 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 general application of knowledge. These were called heuristics, rules of thumb that guide a search in promising instructions: “How can non-enumerative search be practical when the underlying problem is exponentially difficult? The approach promoted by Simon and Newell is to use heuristics: quick algorithms that might stop working on some inputs or output suboptimal services.” [26] Another essential advance was to find a method to apply these heuristics that ensures a solution will be discovered, if there is one, not withstanding the periodic fallibility of heuristics: “The A * algorithm offered a basic frame for complete and ideal heuristically directed search. A * is utilized as a subroutine within practically every AI algorithm today but is still no magic bullet; its guarantee of efficiency is bought at the cost of worst-case rapid time. [26]
Early deal with understanding representation and reasoning
Early work covered both applications of official thinking stressing first-order reasoning, in addition to attempts to manage sensible reasoning in a less formal way.
Modeling formal thinking with reasoning: the “neats”
Unlike Simon and Newell, John McCarthy felt that makers did not require to simulate the precise mechanisms of human thought, however might instead look for the essence of abstract thinking and problem-solving with reasoning, [27] no matter whether individuals used the very same algorithms. [a] His laboratory at Stanford (SAIL) focused on utilizing formal reasoning to fix a wide array of problems, including knowledge representation, planning and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and in other places in Europe which resulted in the advancement of the programming language Prolog and the science of reasoning shows. [32] [33]
Modeling implicit sensible understanding with frames and scripts: the “scruffies”
Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] found that fixing challenging issues in vision and natural language processing needed advertisement hoc solutions-they argued that no basic and basic concept (like logic) would catch all the elements of intelligent habits. Roger Schank explained their “anti-logic” approaches 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, considering that they must be built by hand, one complex principle at a time. [38] [39] [40]
The first AI winter season: crushed dreams, 1967-1977
The very first AI winter was a shock:
During the first AI summer season, numerous people thought that machine intelligence might be achieved in just a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research study to use AI to resolve problems of nationwide security; in specific, 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 years previously, but a mix of hubris and disingenuousness led many university and think-tank scientists to accept financing with guarantees of deliverables that they need to have known they could not fulfill. By the mid-1960s neither useful natural language translation systems nor autonomous tanks had actually been developed, and a remarkable backlash embeded in. New DARPA management canceled existing AI financing programs.
Beyond the United States, the most fertile ground for AI research was the United Kingdom. The AI winter season in the UK was stimulated on not so much by disappointed military leaders as by competing academics who viewed AI researchers as charlatans and a drain on research financing. A professor of applied mathematics, Sir James Lighthill, was commissioned by Parliament to examine the state of AI research in the country. The report mentioned that all of the issues being dealt with 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 might never ever scale to real-world applications due to combinatorial explosion. [41]
The 2nd AI summer season: understanding is power, 1978-1987
Knowledge-based systems
As constraints with weak, domain-independent techniques ended up being more and more obvious, [42] researchers from all 3 traditions began to develop knowledge into AI applications. [43] [7] The knowledge transformation was driven by the realization that knowledge underlies high-performance, domain-specific AI applications.
Edward Feigenbaum said:
– “In the knowledge lies the power.” [44]
to describe that high performance in a particular domain needs 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 a complex job well, it must understand a lot about the world in which it operates.
( 2) A plausible extension of that principle, called the Breadth Hypothesis: there are two additional capabilities needed for smart habits in unforeseen scenarios: falling back on increasingly basic understanding, and analogizing to specific however far-flung understanding. [45]
Success with expert systems
This “understanding revolution” resulted in the development and release of specialist systems (presented by Edward Feigenbaum), the first commercially effective type of AI software application. [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 detected bacteremia – and suggested additional laboratory tests, when essential – by translating laboratory results, client history, and physician observations. “With about 450 rules, MYCIN was able to carry out along with some experts, and considerably much better than junior medical professionals.” [49] INTERNIST and CADUCEUS which dealt with internal medication diagnosis. Internist tried to catch the proficiency of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS could ultimately identify approximately 1000 different illness.
– GUIDON, which demonstrated how an understanding base built for professional problem solving could be repurposed for mentor. [50] XCON, to configure VAX computers, a then tiresome process that might use up to 90 days. XCON decreased the time to about 90 minutes. [9]
DENDRAL is thought about the very first professional system that depend on knowledge-intensive analytical. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:
Among individuals at Stanford interested in computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I informed him I wanted an induction “sandbox”, he stated, “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 began the DENDRAL Project: I was good at heuristic search techniques, and he had an algorithm that was great at creating the chemical issue space.
We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, inventor of the chemical behind the birth control pill, and also among the world’s most appreciated mass spectrometrists. Carl and his postdocs were world-class professionals in mass spectrometry. We began to contribute to their knowledge, creating knowledge of engineering as we went along. These experiments totaled up to titrating DENDRAL a growing number of knowledge. The more you did that, the smarter the program ended up being. We had extremely great results.
The generalization was: in the knowledge lies the power. That was the big idea. 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 probably AI’s most effective generalization. [51]
The other specialist systems mentioned above came after DENDRAL. MYCIN exemplifies the classic professional system architecture of a knowledge-base of rules combined to a symbolic reasoning system, consisting of making use of certainty factors to manage unpredictability. GUIDON demonstrates how an explicit knowledge base can be repurposed for a 2nd application, tutoring, and is an example of an intelligent tutoring system, a specific kind of knowledge-based application. Clancey showed that it was not sufficient just to utilize MYCIN’s guidelines for instruction, but that he likewise needed to include guidelines for dialogue management and student modeling. [50] XCON is substantial because of the millions of dollars it conserved DEC, which triggered the expert system boom where most all major corporations in the US had professional systems groups, to catch business expertise, protect it, and automate it:
By 1988, DEC’s AI group had 40 professional systems deployed, with more on the method. DuPont had 100 in usage and 500 in development. Nearly every major U.S. corporation had its own Al group and was either using or investigating professional systems. [49]
Chess expert understanding was encoded in Deep Blue. In 1996, this allowed IBM’s Deep Blue, with the help of symbolic AI, to win in a game of chess versus the world champ at that time, Garry Kasparov. [52]
Architecture of knowledge-based and skilled systems
A crucial element of the system architecture for all professional systems is the understanding base, which shops truths and guidelines for problem-solving. [53] The easiest method for an expert system understanding base is simply a collection or network of production rules. Production guidelines link symbols in a relationship similar to an If-Then statement. The expert system processes the rules to make reductions and to identify what additional details it requires, i.e. what questions to ask, utilizing human-readable signs. For example, OPS5, CLIPS and their successors Jess and Drools run in this fashion.
Expert systems can operate in either a forward chaining – from evidence to conclusions – or backwards chaining – from objectives to required information and requirements – way. More advanced knowledge-based systems, such as Soar can likewise carry out meta-level thinking, that is thinking about their own reasoning in terms of choosing how to solve problems and keeping an eye on the success of analytical methods.
Blackboard systems are a second type of knowledge-based or skilled system architecture. They model a neighborhood of professionals incrementally contributing, where they can, to fix an issue. The issue is represented in several levels of abstraction or alternate views. The professionals (understanding sources) volunteer their services whenever they recognize they can contribute. Potential problem-solving actions are represented on a program that is updated as the issue circumstance changes. A controller decides how beneficial each contribution is, and who need to make the next analytical action. One example, the BB1 blackboard architecture [54] was initially inspired by research studies of how people plan to perform numerous tasks in a trip. [55] A development of BB1 was to apply the exact same blackboard design to resolving its control issue, i.e., its controller performed meta-level reasoning with understanding sources that kept track of how well a strategy or the analytical was proceeding and might change from one strategy to another as conditions – such as goals or times – changed. BB1 has actually been applied in multiple domains: building and construction site planning, smart tutoring systems, and real-time client tracking.
The 2nd AI winter season, 1988-1993
At the height of the AI boom, companies such as Symbolics, LMI, and Texas Instruments were offering LISP machines particularly targeted to accelerate the advancement of AI applications and research. In addition, a number of artificial intelligence business, such as Teknowledge and Inference Corporation, were selling professional system shells, training, and speaking with to corporations.
Unfortunately, the AI boom did not last and Kautz finest explains the second AI winter season that followed:
Many reasons can be provided for the arrival of the second AI winter season. The hardware business failed when a lot more economical basic Unix workstations from Sun together with great compilers for LISP and Prolog came onto the marketplace. Many industrial deployments of professional systems were discontinued when they showed too costly to keep. Medical professional systems never captured on for numerous reasons: the trouble in keeping them up to date; the obstacle for medical professionals to find out how to use a bewildering range of different professional systems for various medical conditions; and maybe most crucially, the unwillingness of medical professionals to rely on a computer-made medical diagnosis over their gut impulse, even for particular domains where the expert systems might surpass a typical physician. Venture capital money deserted AI almost over night. The world AI conference IJCAI hosted a massive and extravagant trade show and thousands of nonacademic guests in 1987 in Vancouver; the main AI conference the following year, AAAI 1988 in St. Paul, was a small and strictly scholastic affair. [9]
Including more extensive foundations, 1993-2011
Uncertain reasoning
Both statistical approaches and extensions to reasoning were tried.
One statistical approach, concealed Markov models, had already been popularized in the 1980s for speech acknowledgment work. [11] Subsequently, in 1988, Judea Pearl promoted using Bayesian Networks as a noise but effective method of dealing with unpredictable thinking with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian techniques were used effectively in specialist systems. [57] Even later, in the 1990s, statistical relational learning, an approach that combines probability with logical formulas, allowed 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 reasoning to assistance were likewise tried. For example, non-monotonic thinking could be utilized with truth upkeep systems. A reality maintenance system tracked assumptions and justifications for all reasonings. It allowed reasonings to be withdrawn when assumptions were learnt to be inaccurate or a contradiction was obtained. Explanations could be offered an inference by describing which rules were used to produce it and then continuing through underlying reasonings and guidelines all the method back to root assumptions. [58] Lofti Zadeh had presented a various type of extension to deal with the representation of ambiguity. For example, in deciding how “heavy” or “tall” a man is, there is regularly no clear “yes” or “no” response, and a predicate for heavy or high would rather return worths in between 0 and 1. Those values represented to what degree the predicates held true. His fuzzy reasoning further provided a means for propagating combinations of these values through sensible solutions. [59]
Machine learning
Symbolic device finding out methods were examined to deal with the understanding acquisition traffic jam. Among the earliest is Meta-DENDRAL. Meta-DENDRAL utilized a generate-and-test technique to generate plausible rule hypotheses to evaluate versus spectra. Domain and job understanding minimized the number 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 formation. The conception was that you had a problem solver like DENDRAL that took some inputs and produced an output. In doing so, it used layers of knowledge to guide and prune the search. That understanding acted due to the fact that we spoke with individuals. But how did individuals get the understanding? By looking at countless spectra. So we desired a program that would look at thousands of spectra and infer the understanding of mass spectrometry that DENDRAL could utilize to resolve private hypothesis development issues. We did it. We were even able to release brand-new knowledge of mass spectrometry in the Journal of the American Chemical Society, offering credit just in a footnote that a program, Meta-DENDRAL, in fact did it. We were able to do something that had actually been a dream: to have a computer program come up with a new and publishable piece of science. [51]
In contrast to the knowledge-intensive technique of Meta-DENDRAL, Ross Quinlan created a domain-independent technique to statistical category, choice tree knowing, beginning first with ID3 [60] and after that later extending its capabilities to C4.5. [61] The choice trees created are glass box, interpretable classifiers, with human-interpretable classification guidelines.
Advances were made in comprehending artificial intelligence theory, too. Tom Mitchell introduced version area knowing which describes knowing as a search through an area of hypotheses, with upper, more basic, and lower, more particular, boundaries encompassing all practical hypotheses constant with the examples seen up until now. [62] More officially, Valiant introduced Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of device knowing. [63]
Symbolic machine finding out encompassed more than learning by example. E.g., John Anderson offered a cognitive design of human learning where ability practice results in a collection of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a trainee may learn to apply “Supplementary angles are two angles whose procedures sum 180 degrees” as numerous various procedural rules. E.g., one guideline might say that if X and Y are extra and you understand X, then Y will be 180 – X. He called his approach “knowledge compilation”. ACT-R has been used successfully to design elements of human cognition, such as finding out and retention. ACT-R is likewise used in intelligent tutoring systems, called cognitive tutors, to successfully teach geometry, computer programs, and algebra to school kids. [64]
Inductive logic shows was another approach to learning that allowed reasoning programs to be manufactured from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) could manufacture Prolog programs from examples. [65] John R. Koza used genetic algorithms to program synthesis to produce genetic programs, which he utilized to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger supplied a more basic approach to program synthesis that manufactures a practical program in the course of showing its requirements to be proper. [66]
As an option to reasoning, Roger Schank introduced case-based thinking (CBR). The CBR technique described in his book, Dynamic Memory, [67] focuses initially on keeping in mind essential problem-solving cases for future use and generalizing them where appropriate. When confronted with a new issue, CBR obtains the most similar previous case and adjusts it to the specifics of the existing problem. [68] Another option to logic, genetic algorithms and hereditary programming are based upon an evolutionary model of knowing, where sets of guidelines are encoded into populations, the rules govern the habits of people, and choice of the fittest prunes out sets of unsuitable rules over lots of generations. [69]
Symbolic maker knowing was applied to discovering principles, rules, heuristics, and analytical. Approaches, besides those above, include:
1. Learning from direction or advice-i.e., taking human instruction, presented as advice, and determining how to operationalize it in particular circumstances. For example, in a video game of Hearts, discovering exactly how to play a hand to “prevent taking points.” [70] 2. Learning from exemplars-improving performance by accepting subject-matter professional (SME) feedback during training. When problem-solving fails, querying the professional to either discover a new prototype for analytical or to learn a new explanation as to precisely why one prototype is more pertinent than another. For instance, the program Protos learned to diagnose tinnitus cases by interacting with an audiologist. [71] 3. Learning by analogy-constructing problem solutions based upon comparable issues seen in the past, and then modifying their services to fit a new situation or domain. [72] [73] 4. Apprentice knowing systems-learning unique options to problems by observing human analytical. Domain understanding discusses why unique options are correct and how the solution can be generalized. LEAP found out how to develop VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing tasks to bring out experiments and then finding out from the results. Doug Lenat’s Eurisko, for example, discovered heuristics to beat human players at the Traveller role-playing video game for 2 years in a row. [75] 6. Learning macro-operators-i.e., browsing for useful macro-operators to be learned from series of fundamental analytical actions. Good macro-operators streamline problem-solving by enabling issues to be resolved at a more abstract level. [76]
Deep knowing and neuro-symbolic AI 2011-now
With the increase of deep learning, the symbolic AI method has actually been compared to deep learning as complementary “… with parallels having been drawn lot of times by AI researchers 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 principle be modelled by deep knowing and symbolic reasoning, respectively.” In this view, symbolic thinking is more apt for deliberative reasoning, preparation, and explanation while deep learning is more apt for quick pattern recognition in perceptual applications with noisy information. [17] [18]
Neuro-symbolic AI: integrating neural and symbolic methods
Neuro-symbolic AI efforts to integrate neural and symbolic architectures in a way that addresses strengths and weak points of each, in a complementary fashion, in order to support robust AI capable of thinking, discovering, and cognitive modeling. As argued by Valiant [77] and numerous others, [78] the efficient construction of abundant computational cognitive models demands the combination of sound symbolic reasoning and effective (machine) knowing designs. Gary Marcus, likewise, argues that: “We can not construct rich cognitive models in an adequate, automated way without the triumvirate of hybrid architecture, abundant prior understanding, and sophisticated methods for thinking.”, [79] and in specific: “To build a robust, knowledge-driven approach to AI we should have the equipment of symbol-manipulation in our toolkit. Excessive of beneficial understanding is abstract to make do without tools that represent and manipulate abstraction, and to date, the only machinery that we understand of that can control such abstract understanding dependably is the apparatus of sign manipulation. ” [80]
Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have also argued for a synthesis. Their arguments are based on a requirement to deal with the two type of thinking talked about in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having two components, System 1 and System 2. System 1 is quickly, automated, instinctive and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is the kind utilized for pattern recognition while System 2 is far much better suited for planning, deduction, and deliberative thinking. In this view, deep knowing finest models the very first kind of believing while symbolic thinking best designs the 2nd kind and both are required.
Garcez and Lamb explain research study in this area as being ongoing for a minimum of the previous twenty years, [83] dating from their 2002 book on neurosymbolic learning systems. [84] A series of workshops on neuro-symbolic reasoning 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 been pursued by a relatively small research study community over the last 20 years and has actually yielded a number of substantial results. Over the last decade, neural symbolic systems have been shown efficient in getting rid of the so-called propositional fixation of neural networks, as McCarthy (1988) put it in response to Smolensky (1988 ); see likewise (Hinton, 1990). Neural networks were revealed efficient in 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 areas of bioinformatics, control engineering, software confirmation and adaptation, visual intelligence, ontology learning, and video game. [78]
Approaches for integration are differed. Henry Kautz’s taxonomy of neuro-symbolic architectures, along with some examples, follows:
– Symbolic Neural symbolic-is the current technique of numerous neural designs in natural language processing, where words or subword tokens are both the supreme input and output of big language models. Examples consist of BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exhibited by AlphaGo, where symbolic techniques are utilized to call neural strategies. In this case the symbolic approach is Monte Carlo tree search and the neural strategies discover how to assess video game positions.
– Neural|Symbolic-uses a neural architecture to interpret perceptual data as signs and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to generate or identify training data that is consequently found out by a deep knowing design, e.g., to train a neural model for symbolic computation by utilizing a Macsyma-like symbolic mathematics system to develop or identify examples.
– Neural _ Symbolic -utilizes a neural internet that is produced from symbolic rules. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR proof tree created from understanding base guidelines and terms. Logic Tensor Networks [86] likewise fall under this category.
– Neural [Symbolic] -enables a neural design to directly call a symbolic reasoning engine, e.g., to perform an action or evaluate a state.
Many crucial research study concerns remain, such as:
– What is the 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 discovered and reasoned about?
– How can abstract knowledge that is difficult to encode rationally be handled?
Techniques and contributions
This area offers an introduction of methods and contributions in a total context leading to lots of other, more in-depth articles in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered previously in the history section.
AI programming languages
The key AI programming language in the US during the last symbolic AI boom duration was LISP. LISP is the second earliest programming language after FORTRAN and was created in 1958 by John McCarthy. LISP offered the first read-eval-print loop to support rapid program development. Compiled functions might be easily combined with analyzed functions. Program tracing, stepping, and breakpoints were also provided, together with the ability to change worths or functions and continue from breakpoints or mistakes. It had the very first self-hosting compiler, implying that the compiler itself was initially composed in LISP and then ran interpretively to assemble the compiler code.
Other essential developments originated by LISP that have infected other programs languages consist of:
Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals
Programs were themselves data structures that other programs could operate on, allowing the easy meaning of higher-level languages.
In contrast to the US, in Europe the crucial AI shows language during that same duration was Prolog. Prolog provided an integrated shop of facts and provisions that could be queried by a read-eval-print loop. The shop might serve as an understanding base and the clauses might act as guidelines or a limited form of logic. As a subset of first-order logic Prolog was based on Horn clauses with a closed-world assumption-any realities not understood were considered false-and an unique name assumption for primitive terms-e.g., the identifier barack_obama was thought about to describe precisely one things. Backtracking and marriage are integrated to Prolog.
Alain Colmerauer and Philippe Roussel are credited as the creators of Prolog. Prolog is a kind of reasoning programs, which was created by Robert Kowalski. Its history was also affected by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of approaches. For more information see the area on the origins of Prolog in the PLANNER article.
Prolog is likewise a kind of declarative programming. The reasoning clauses that explain programs are straight translated to run the programs specified. No specific series of actions is needed, as is the case with imperative programming languages.
Japan championed Prolog for its Fifth Generation Project, planning to build special hardware for high performance. Similarly, LISP makers were developed to run LISP, however as the 2nd AI boom turned to bust these companies might not take on new workstations that might now run LISP or Prolog natively at similar speeds. See the history section for more detail.
Smalltalk was another prominent AI programs language. For instance, it presented metaclasses and, along with Flavors and CommonLoops, affected the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the current basic Lisp dialect. CLOS is a Lisp-based object-oriented system that permits numerous inheritance, in addition to incremental extensions to both classes and metaclasses, thus offering a run-time meta-object protocol. [88]
For other AI shows languages see this list of programming languages for expert system. Currently, Python, a multi-paradigm programs language, is the most popular shows language, partly due to its substantial plan library that supports information science, natural language processing, and deep learning. Python consists of a read-eval-print loop, practical aspects such as higher-order functions, and object-oriented programming that includes metaclasses.
Search
Search develops in lots of type of problem resolving, consisting of planning, restraint fulfillment, and playing games such as checkers, chess, and go. The 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 thinking
Multiple different methods to represent understanding and then reason with those representations have actually been investigated. Below is a fast introduction of methods to understanding representation and automated thinking.
Knowledge representation
Semantic networks, conceptual graphs, frames, and logic are all approaches to modeling understanding such as domain knowledge, problem-solving knowledge, and the semantic significance of language. Ontologies model key principles and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be utilized for any domain while WordNet is a lexical resource that can likewise be considered as an ontology. YAGO integrates WordNet as part of its ontology, to align truths extracted 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 category of ontologies and for discovering inconsistent category data. OWL is a language used to represent ontologies with description logic. Protégé is an ontology editor that can read in OWL ontologies and then inspect consistency with deductive classifiers such as such as HermiT. [89]
First-order logic is more general than description reasoning. The automated theorem provers discussed listed below can show theorems in first-order reasoning. Horn stipulation reasoning is more limited than first-order reasoning and is utilized in reasoning programs languages such as Prolog. Extensions to first-order logic include temporal logic, to handle time; epistemic logic, to reason about agent understanding; modal logic, to manage possibility and requirement; and probabilistic logics to manage reasoning and probability together.
Automatic theorem showing
Examples of automated theorem provers for first-order logic are:
Prover9.
ACL2.
Vampire.
Prover9 can be utilized in combination with the Mace4 design checker. ACL2 is a theorem prover that can handle proofs by induction and is a descendant of the Boyer-Moore Theorem Prover, also called Nqthm.
Reasoning in knowledge-based systems
Knowledge-based systems have a specific understanding base, typically of rules, to boost reusability across domains by separating procedural code and domain understanding. A different inference engine procedures rules and includes, deletes, or customizes a knowledge store.
Forward chaining inference engines are the most typical, and are seen in CLIPS and OPS5. Backward chaining takes place in Prolog, where a more minimal logical representation is used, Horn Clauses. Pattern-matching, particularly unification, is used in Prolog.
A more flexible kind of analytical takes place when thinking about what to do next occurs, instead of just choosing one of the readily available actions. This type of meta-level reasoning is utilized in Soar and in the BB1 blackboard architecture.
Cognitive architectures such as ACT-R might have additional abilities, such as the ability to compile regularly utilized knowledge into higher-level chunks.
Commonsense thinking
Marvin Minsky initially proposed frames as a way of translating typical visual scenarios, such as a workplace, and Roger Schank extended this idea to scripts for common regimens, such as eating in restaurants. Cyc has actually tried to record useful common-sense knowledge and has “micro-theories” to deal with specific type of domain-specific reasoning.
Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] estimates human thinking about ignorant physics, such as what happens when we heat a liquid in a pot on the stove. We anticipate it to heat and perhaps boil over, despite the fact that we might not know its temperature, its boiling point, or other details, such as air 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 resolved with constraint solvers.
Constraints and constraint-based thinking
Constraint solvers perform a more restricted type of reasoning than first-order logic. They can streamline sets of spatiotemporal constraints, such as those for RCC or Temporal Algebra, in addition to solving other sort of puzzle problems, such as Wordle, Sudoku, cryptarithmetic issues, and so on. Constraint reasoning shows can be utilized to fix scheduling issues, for instance with restraint managing rules (CHR).
Automated planning
The General Problem Solver (GPS) cast planning as analytical utilized means-ends analysis to produce strategies. STRIPS took a different approach, viewing preparation as theorem proving. Graphplan takes a least-commitment method to planning, instead of sequentially selecting actions from a preliminary state, working forwards, or a goal state if working backwards. Satplan is an approach to planning where a preparation issue is reduced to a Boolean satisfiability issue.
Natural language processing
Natural language processing focuses on treating language as information to perform jobs such as determining subjects without necessarily understanding the desired meaning. Natural language understanding, in contrast, constructs a significance representation and uses that for additional processing, such as addressing questions.
Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb phrase chunking are all aspects of natural language processing long dealt with by symbolic AI, but given that enhanced by deep learning techniques. In symbolic AI, discourse representation theory and first-order reasoning have actually been used to represent sentence significances. Latent semantic analysis (LSA) and specific semantic analysis likewise provided vector representations of documents. In the latter case, vector elements are interpretable as ideas called by Wikipedia articles.
New deep knowing approaches based upon Transformer designs have actually now eclipsed these earlier symbolic AI approaches and attained modern performance in natural language processing. However, Transformer designs 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 parts is nontransparent.
Agents and multi-agent systems
Agents are autonomous systems embedded in an environment they perceive and act on in some sense. Russell and Norvig’s standard textbook on expert system is organized to show agent architectures of increasing elegance. [91] The sophistication of agents varies from easy reactive agents, to those with a model of the world and automated preparation abilities, possibly a BDI agent, i.e., one with beliefs, desires, and objectives – or additionally a reinforcement learning design discovered with time to select actions – up to a mix of alternative architectures, such as a neuro-symbolic architecture [87] that includes deep learning for perception. [92]
In contrast, a multi-agent system consists of numerous representatives that communicate among themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The agents need not all have the same internal architecture. Advantages of multi-agent systems include the ability to divide work among the agents and to increase fault tolerance when agents are lost. Research problems consist of how agents reach consensus, dispersed problem resolving, multi-agent knowing, multi-agent preparation, and dispersed restriction optimization.
Controversies developed from early on in symbolic AI, both within the field-e.g., between logicists (the pro-logic “neats”) and non-logicists (the anti-logic “scruffies”)- and in between those who embraced AI however declined symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were mainly from thinkers, on intellectual grounds, but likewise from funding agencies, specifically throughout the two AI winter seasons.
The Frame Problem: understanding representation obstacles for first-order reasoning
Limitations were discovered in using easy first-order logic to factor about vibrant domains. Problems were found both with regards to specifying the prerequisites for an action to be successful and in offering axioms for what did not alter after an action was carried out.
McCarthy and Hayes presented the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Expert System.” [93] A simple example takes place in “proving that one individual might get into conversation with another”, as an axiom asserting “if a person has a telephone he still has it after searching for a number in the telephone book” would be required for the reduction to prosper. Similar axioms would be needed for other domain actions to specify what did not alter.
A comparable issue, called the Qualification Problem, takes place in attempting to specify the preconditions for an action to succeed. An infinite number of pathological conditions can be imagined, e.g., a banana in a tailpipe could avoid an automobile from operating properly.
McCarthy’s technique to fix the frame issue was circumscription, a sort of non-monotonic logic where reductions could be made from actions that need only define what would change while not having to explicitly define everything that would not change. Other non-monotonic reasonings provided truth maintenance systems that revised beliefs resulting in contradictions.
Other methods of handling more open-ended domains consisted of probabilistic thinking systems and artificial intelligence to learn new concepts and rules. McCarthy’s Advice Taker can be viewed as a motivation here, as it could include brand-new understanding provided by a human in the type of assertions or rules. For example, experimental symbolic device discovering systems checked out the ability to take top-level natural language suggestions and to analyze it into domain-specific actionable rules.
Similar to the problems in dealing with vibrant domains, common-sense reasoning is also hard to record in formal reasoning. Examples of common-sense reasoning consist of implicit thinking about how individuals think or general understanding of everyday occasions, items, and living animals. This sort of knowledge is considered given and not deemed noteworthy. Common-sense reasoning is an open area of research study and challenging both for symbolic systems (e.g., Cyc has tried to capture crucial parts of this understanding over more than a decade) and neural systems (e.g., self-driving automobiles that do not understand not to drive into cones or not to hit pedestrians walking a bike).
McCarthy viewed his Advice Taker as having common-sense, however his definition of common-sense was various than the one above. [94] He defined a program as having sound judgment “if it automatically deduces for itself an adequately wide class of instant repercussions of anything it is told and what it currently knows. “
Connectionist AI: philosophical challenges and sociological disputes
Connectionist approaches include earlier deal with neural networks, [95] such as perceptrons; work in the mid to late 80s, such as Danny Hillis’s Connection Machine and Yann LeCun’s advances in convolutional neural networks; to today’s advanced techniques, such as Transformers, GANs, and other operate in deep learning.
Three philosophical positions [96] have been described amongst connectionists:
1. Implementationism-where connectionist architectures execute the abilities for symbolic processing,
2. Radical connectionism-where symbolic processing is declined absolutely, and connectionist architectures underlie intelligence and are totally adequate to describe 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 debates within the neural network community, explained the moderate connectionism view as essentially suitable with existing research in neuro-symbolic hybrids:
The third and last position I would like to take a look at here is what I call the moderate connectionist view, a more diverse view of the current argument between connectionism and symbolic AI. Among the researchers who has elaborated this position most clearly is Andy Clark, a philosopher from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark defended hybrid (partly symbolic, partly connectionist) systems. He declared that (a minimum of) 2 kinds of theories are required in order to study and model cognition. On the one hand, for some information-processing tasks (such as pattern acknowledgment) connectionism has advantages over symbolic models. But on the other hand, for other cognitive processes (such as serial, deductive reasoning, and generative symbol manipulation procedures) the symbolic paradigm offers appropriate models, and not only “approximations” (contrary to what radical connectionists would claim). [97]
Gary Marcus has actually declared that the animus in the deep knowing neighborhood versus symbolic methods now may be more sociological than philosophical:
To believe that we can simply desert symbol-manipulation is to suspend shock.
And yet, for the many part, that’s how most existing AI profits. Hinton and many others have attempted hard to eliminate symbols entirely. The deep knowing hope-seemingly grounded not so much in science, but in a sort of historic grudge-is that smart habits will emerge simply from the confluence of enormous information and deep learning. Where classical computers and software application fix jobs by specifying sets of symbol-manipulating guidelines dedicated to particular tasks, such as modifying a line in a word processor or performing a calculation in a spreadsheet, neural networks typically try to fix jobs by analytical approximation and discovering from examples.
According to Marcus, Geoffrey Hinton and his colleagues have actually been emphatically “anti-symbolic”:
When deep knowing reemerged in 2012, it was with a kind of take-no-prisoners attitude that has identified the majority of the last years. By 2015, his hostility towards all things symbols had completely crystallized. He gave a talk at an AI workshop at Stanford comparing symbols to aether, among science’s greatest errors.
…
Since then, his anti-symbolic campaign has only increased in strength. In 2016, Yann LeCun, Bengio, and Hinton wrote a manifesto for deep knowing in one of science’s essential journals, Nature. It closed with a direct attack on sign adjustment, calling not for reconciliation however for straight-out replacement. Later, Hinton informed a gathering of European Union leaders that investing any further cash in symbol-manipulating techniques was “a huge error,” comparing it to purchasing internal combustion engines in the age of electric cars. [98]
Part of these disputes might be due to uncertain terms:
Turing award winner Judea Pearl offers a review of artificial intelligence which, regrettably, conflates the terms device learning and deep learning. Similarly, when Geoffrey Hinton refers to symbolic AI, the connotation of the term tends to be that of expert systems dispossessed of any capability to learn. Using the terminology requires information. Artificial intelligence is not confined to association guideline mining, c.f. the body of work on symbolic ML and relational knowing (the distinctions to deep knowing being the option of representation, localist sensible rather than dispersed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not practically production guidelines composed by hand. A proper definition of AI issues understanding representation and reasoning, self-governing multi-agent systems, preparation and argumentation, in addition to knowing. [99]
Situated robotics: the world as a model
Another critique of symbolic AI is the embodied cognition method:
The embodied cognition method claims that it makes no sense to think about the brain individually: cognition occurs within a body, which is embedded in an environment. We need to study the system as a whole; the brain’s functioning exploits regularities in its environment, consisting of the rest of its body. Under the embodied cognition method, robotics, vision, and other sensing units end up being main, not peripheral. [100]
Rodney Brooks created behavior-based robotics, one approach to embodied cognition. Nouvelle AI, another name for this technique, is considered as an alternative to both symbolic AI and connectionist AI. His technique turned down representations, either symbolic or distributed, as not just unnecessary, but as detrimental. Instead, he created the subsumption architecture, a layered architecture for embodied representatives. Each layer achieves a different purpose and needs to function in the genuine world. For example, the very first robot he describes in Intelligence Without Representation, has 3 layers. The bottom layer interprets finder sensing units to prevent things. The middle layer causes the robotic to roam around when there are no barriers. The leading layer causes the robotic to go to more far-off locations for further exploration. Each layer can temporarily prevent or suppress a lower-level layer. He criticized AI scientists for specifying AI issues for their systems, when: “There is no clean department in between perception (abstraction) and thinking in the real life.” [101] He called his robotics “Creatures” and each layer was “made up of a fixed-topology network of simple finite state makers.” [102] In the Nouvelle AI technique, “First, it is essential to test the Creatures we develop in the real life; i.e., in the same world that we humans inhabit. It is dreadful to fall into the temptation of testing them in a simplified world initially, even with the very best objectives of later transferring activity to an unsimplified world.” [103] His focus on real-world screening was in contrast to “Early work in AI concentrated on games, geometrical issues, symbolic algebra, theorem proving, and other official systems” [104] and making use of the blocks world in symbolic AI systems such as SHRDLU.
Current views
Each approach-symbolic, connectionist, and behavior-based-has advantages, however has actually been slammed by the other techniques. Symbolic AI has actually been slammed as disembodied, liable to the credentials problem, and poor in managing the perceptual problems where deep discovering excels. In turn, connectionist AI has been criticized as badly fit for deliberative step-by-step problem fixing, incorporating understanding, and managing preparation. Finally, Nouvelle AI masters reactive and real-world robotics domains but has actually been criticized for problems in integrating knowing and knowledge.
Hybrid AIs including one or more of these approaches are presently viewed as the course forward. [19] [81] [82] Russell and Norvig conclude that:
Overall, Dreyfus saw locations where AI did not have total responses and stated that Al is for that reason difficult; we now see much of these same locations undergoing ongoing research study and development leading to increased ability, not impossibility. [100]
Artificial intelligence.
Automated planning and scheduling
Automated theorem proving
Belief modification
Case-based reasoning
Cognitive architecture
Cognitive science
Connectionism
Constraint programming
Deep knowing
First-order logic
GOFAI
History of expert system
Inductive logic programming
Knowledge-based systems
Knowledge representation and thinking
Logic programs
Artificial intelligence
Model monitoring
Model-based reasoning
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of expert system
Physical sign systems hypothesis
Semantic Web
Sequential pattern mining
Statistical relational learning
Symbolic mathematics
YAGO ontology
WordNet
Notes
^ McCarthy as soon as said: “This is AI, so we don’t care if it’s psychologically real”. [4] McCarthy repeated his position in 2006 at the AI@50 conference where he stated “Artificial intelligence is not, by definition, of human intelligence”. [28] Pamela McCorduck composes that there are “2 major branches of synthetic intelligence: one focused on producing smart behavior regardless of how it was accomplished, and the other intended at modeling smart processes found in nature, especially human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not specify the goal of their field as making ‘makers that fly so exactly like pigeons that they can trick even other pigeons.'” [30] Citations
^ Garnelo, Marta; Shanahan, Murray (October 2019). “Reconciling deep knowing with symbolic artificial 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 Expert System”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep learning with symbolic artificial 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.
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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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^ Shapiro, Ehud Y (1981 ). “The Model Inference System”. Proceedings of the 7th international joint conference on Expert system. IJCAI. Vol. 2. p. 1064.
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^ 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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