Symbolic Artificial Intelligence

In synthetic intelligence, symbolic synthetic intelligence (likewise called classical synthetic intelligence or logic-based expert system) [1] [2] is the term for the collection of all methods in artificial intelligence research study that are based on top-level symbolic (human-readable) representations of issues, reasoning and search. [3] Symbolic AI used tools such as logic shows, production rules, semantic internet and frames, and it developed 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 critical ideas in search, symbolic shows languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of formal understanding and reasoning systems.

Symbolic AI was the dominant paradigm of AI research study from the mid-1950s till the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic approaches would ultimately be successful in creating a machine with artificial general intelligence and considered this the supreme objective of their field. [citation required] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, resulted in unrealistic expectations and guarantees and was followed by the first AI Winter as funding dried up. [5] [6] A second boom (1969-1986) took place with the rise of specialist systems, their guarantee of capturing business expertise, and a passionate business embrace. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed again by later disappointment. [8] Problems with troubles in understanding acquisition, maintaining big knowledge bases, and brittleness in dealing with out-of-domain problems arose. Another, 2nd, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists focused on resolving hidden issues in managing uncertainty and in understanding acquisition. [10] Uncertainty was attended to with official techniques such as hidden Markov designs, Bayesian reasoning, and statistical relational learning. [11] [12] Symbolic machine discovering dealt with the knowledge acquisition problem with contributions consisting of Version Space, Valiant’s PAC learning, Quinlan’s ID3 decision-tree knowing, case-based learning, and inductive reasoning programs to learn 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 work in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not deemed successful until about 2012: “Until Big Data became prevalent, the basic agreement in the Al community was that the so-called neural-network technique was hopeless. Systems simply didn’t work that well, compared to other methods. … A transformation was available in 2012, when a variety of people, consisting of a group of scientists dealing with Hinton, worked out a method to utilize the power of GPUs to enormously increase the power of neural networks.” [16] Over the next a number of years, deep learning had magnificent success in managing vision, speech recognition, speech synthesis, image generation, and device translation. However, considering that 2020, as intrinsic troubles with predisposition, explanation, comprehensibility, and effectiveness became more apparent with deep knowing methods; an increasing number of AI scientists have actually called for integrating the very best of both the symbolic and neural network techniques [17] [18] and resolving areas that both techniques have trouble with, such as common-sense reasoning. [16]

A short history of symbolic AI to the present day follows below. Time periods and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture [19] and the longer Wikipedia article on the History of AI, with dates and titles varying a little for increased clarity.

The very first AI summer: illogical vitality, 1948-1966

Success at early attempts in AI took place in three primary locations: synthetic neural networks, knowledge representation, and heuristic search, adding to high expectations. This section summarizes Kautz’s reprise of early AI history.

Approaches by human or animal cognition or habits

Cybernetic approaches attempted to duplicate the feedback loops in between animals and their environments. A robotic turtle, with sensing units, motors for driving and guiding, and seven vacuum tubes for control, based on a preprogrammed neural net, was constructed as early as 1948. This work can be seen as an early precursor to later operate in neural networks, reinforcement 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 was able to prove 38 elementary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later generalized this work to create a domain-independent problem solver, GPS (General Problem Solver). GPS solved issues represented with official operators via state-space search utilizing means-ends analysis. [21]

During the 1960s, symbolic approaches attained excellent success at simulating smart habits in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was concentrated in 4 organizations in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Each one developed its own design of research. Earlier approaches based upon cybernetics or artificial neural networks were deserted or pressed into the background.

Herbert Simon and Allen Newell studied human analytical abilities and tried to formalize them, and their work laid the foundations of the field of artificial intelligence, as well as cognitive science, operations research study and management science. Their research group used the results of mental experiments to develop programs that simulated the techniques that people used to resolve issues. [22] [23] This custom, focused at Carnegie Mellon University would eventually culminate in the development of the Soar architecture in the center 1980s. [24] [25]

Heuristic search

In addition to the extremely specialized domain-specific sort of knowledge that we will see later used in professional systems, early symbolic AI researchers discovered another more basic application of knowledge. These were called heuristics, rules of thumb that guide a search in appealing directions: “How can non-enumerative search be practical when the underlying issue is significantly difficult? The approach advocated by Simon and Newell is to utilize heuristics: fast algorithms that may fail on some inputs or output suboptimal options.” [26] Another crucial advance was to find a method to use these heuristics that ensures a solution will be found, if there is one, not enduring the periodic fallibility of heuristics: “The A * algorithm offered a basic frame for complete and ideal heuristically assisted search. A * is utilized as a subroutine within practically every AI algorithm today but is still no magic bullet; its assurance of efficiency is purchased the cost of worst-case rapid time. [26]

Early deal with understanding representation and reasoning

Early work covered both applications of official reasoning highlighting first-order logic, in addition to attempts to deal with sensible reasoning in a less formal manner.

Modeling formal thinking with logic: the “neats”

Unlike Simon and Newell, John McCarthy felt that machines did not require to imitate the exact systems of human idea, however could rather search for the essence of abstract thinking and problem-solving with logic, [27] regardless of whether individuals used the exact same algorithms. [a] His laboratory at Stanford (SAIL) concentrated on using official logic to solve a wide range of problems, including knowledge representation, preparation and knowing. [31] Logic was also the focus of the work at the University of Edinburgh and somewhere else in Europe which resulted in the development of the shows language Prolog and the science of logic shows. [32] [33]

Modeling implicit common-sense understanding with frames and scripts: the “scruffies”

Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] found that solving challenging issues in vision and natural language processing needed advertisement hoc solutions-they argued that no simple and general principle (like reasoning) would record all the elements of smart habits. Roger Schank described their “anti-logic” techniques 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 should be constructed by hand, one complicated concept at a time. [38] [39] [40]

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

The first AI winter was a shock:

During the very first AI summer season, lots of people believed that machine intelligence could be attained in just a couple of years. The Defense Advance Research Projects Agency (DARPA) released programs to support AI research study to use AI to fix issues of nationwide security; in particular, to automate the translation of Russian to English for intelligence operations and to develop self-governing tanks for the battlefield. Researchers had begun to understand that achieving AI was going to be much more difficult than was expected a decade previously, but a combination of hubris and disingenuousness led many university and think-tank scientists to accept financing with promises of deliverables that they need to have known they might not fulfill. By the mid-1960s neither beneficial natural language translation systems nor self-governing tanks had actually been produced, and a remarkable reaction embeded in. New DARPA leadership canceled existing AI funding programs.

Outside of the United States, the most fertile ground for AI research was the United Kingdom. The AI winter in the UK was spurred on not so much by disappointed military leaders as by competing academics who viewed AI scientists as charlatans and a drain on research study funding. A professor 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 problems being dealt with in AI would be much better handled by scientists from other disciplines-such as applied mathematics. The report likewise claimed that AI successes on toy problems could never ever scale to real-world applications due to combinatorial surge. [41]

The second AI summer: understanding is power, 1978-1987

Knowledge-based systems

As constraints with weak, domain-independent techniques became more and more evident, [42] scientists from all three customs started to construct understanding into AI applications. [43] [7] The knowledge revolution was driven by the awareness that knowledge underlies high-performance, domain-specific AI applications.

Edward Feigenbaum stated:

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

( 1) The Knowledge Principle: if a program is to carry out a complex job well, it needs to know a good deal about the world in which it operates.
( 2) A plausible extension of that concept, called the Breadth Hypothesis: there are two additional abilities necessary for intelligent habits in unforeseen circumstances: drawing on increasingly general understanding, and analogizing to particular however remote knowledge. [45]

Success with professional systems

This “understanding revolution” resulted in the development and deployment of specialist systems (introduced by Edward Feigenbaum), the first commercially successful form of AI software application. [46] [47] [48]

Key specialist systems were:

DENDRAL, which discovered the structure of natural particles from their chemical formula and mass spectrometer readings.
MYCIN, which diagnosed bacteremia – and suggested more laboratory tests, when needed – by translating laboratory outcomes, client history, and medical professional observations. “With about 450 rules, MYCIN had the ability to perform as well as some experts, and substantially much better than junior physicians.” [49] INTERNIST and CADUCEUS which took on internal medication medical diagnosis. Internist tried to capture the know-how of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS could eventually diagnose as much as 1000 various illness.
– GUIDON, which demonstrated how an understanding base built for professional issue resolving could be repurposed for teaching. [50] XCON, to set up VAX computer systems, a then laborious procedure that might use up to 90 days. XCON lowered the time to about 90 minutes. [9]
DENDRAL is thought about the very first specialist system that depend on knowledge-intensive analytical. It is explained below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:

Among the individuals at Stanford thinking about computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genetics. When I informed him I desired an induction “sandbox”, he said, “I have simply the one for you.” His lab was doing mass spectrometry of amino acids. The question was: how do you go from taking a look at the spectrum of an amino acid to the chemical structure of the amino acid? That’s how we started the DENDRAL Project: I was great at heuristic search methods, and he had an algorithm that was excellent at producing the chemical problem area.

We did not have a grandiose vision. We worked bottom up. Our chemist was Carl Djerassi, innovator of the chemical behind the birth control tablet, and also one of the world’s most appreciated mass spectrometrists. Carl and his postdocs were first-rate experts in mass spectrometry. We started to contribute to their understanding, creating understanding of engineering as we went along. These experiments totaled up to titrating DENDRAL a growing number of understanding. The more you did that, the smarter the program ended up being. We had very great results.

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 way AI was being done previously. Sounds basic, but it’s probably AI’s most powerful generalization. [51]

The other professional systems pointed out above followed DENDRAL. MYCIN exhibits the timeless specialist system architecture of a knowledge-base of guidelines coupled to a symbolic reasoning mechanism, consisting of making use of certainty aspects to handle unpredictability. GUIDON demonstrates how an explicit understanding base can be repurposed for a 2nd application, tutoring, and is an example of an intelligent tutoring system, a particular type of knowledge-based application. Clancey revealed that it was not adequate merely to utilize MYCIN’s guidelines for guideline, but that he also required to include guidelines for discussion management and trainee modeling. [50] XCON is considerable due to the fact that of the millions of dollars it saved DEC, which triggered the expert system boom where most all significant corporations in the US had skilled systems groups, to catch business proficiency, preserve it, and automate it:

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

Chess expert 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 against the world champ at that time, Garry Kasparov. [52]

Architecture of knowledge-based and expert systems

A key part of the system architecture for all specialist systems is the knowledge base, which shops realities and rules for problem-solving. [53] The most basic method for an expert system knowledge base is just a collection or network of production rules. Production rules connect signs in a relationship comparable to an If-Then declaration. The specialist system processes the guidelines to make reductions and to determine what extra information it needs, i.e. what questions to ask, using human-readable symbols. For example, OPS5, CLIPS and their followers Jess and Drools run in this style.

Expert systems can operate in either a forward chaining – from proof to conclusions – or backward chaining – from objectives to required information and requirements – way. Advanced knowledge-based systems, such as Soar can also carry out meta-level reasoning, that is thinking about their own reasoning in regards to deciding how to solve issues and keeping track of the success of analytical strategies.

Blackboard systems are a second kind of knowledge-based or skilled system architecture. They design a community of professionals incrementally contributing, where they can, to fix a problem. The problem is represented in numerous levels of abstraction or alternate views. The professionals (understanding sources) volunteer their services whenever they acknowledge they can contribute. Potential problem-solving actions are represented on an agenda that is 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 influenced by research studies of how humans plan to perform numerous jobs in a trip. [55] An innovation of BB1 was to use the very same blackboard design to fixing its control problem, i.e., its controller performed meta-level reasoning with knowledge sources that kept an eye on how well a strategy or the problem-solving was proceeding and could switch from one technique to another as conditions – such as objectives or times – altered. BB1 has actually been applied in multiple domains: construction site planning, smart 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 offering LISP devices particularly targeted to speed up the development of AI applications and research study. In addition, several synthetic intelligence companies, such as Teknowledge and Inference Corporation, were offering skilled system shells, training, and seeking advice from to corporations.

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

Many factors can be provided for the arrival of the second AI winter. The hardware business stopped working when a lot more cost-efficient general Unix workstations from Sun together with great compilers for LISP and Prolog came onto the marketplace. Many industrial deployments of expert systems were terminated when they proved too expensive to keep. Medical specialist systems never ever caught on for a number of reasons: the trouble in keeping them approximately date; the obstacle for medical professionals to find out how to use an overwelming range of various expert systems for various medical conditions; and maybe most crucially, the hesitation of medical professionals to rely on a computer-made diagnosis over their gut instinct, even for particular domains where the expert systems could outshine a typical physician. Venture capital money deserted AI virtually over night. The world AI conference IJCAI hosted a massive and extravagant trade convention and countless nonacademic participants 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]

Adding in more rigorous foundations, 1993-2011

Uncertain reasoning

Both statistical methods and extensions to logic were tried.

One analytical method, hidden Markov models, had already been promoted in the 1980s for speech acknowledgment work. [11] Subsequently, in 1988, Judea Pearl popularized using Bayesian Networks as a sound but effective method of handling uncertain reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. [56] and Bayesian methods were applied effectively in specialist systems. [57] Even later on, in the 1990s, analytical relational learning, a technique that integrates likelihood with sensible solutions, allowed probability 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 instance, non-monotonic reasoning might be used with fact maintenance systems. A truth upkeep system tracked presumptions and justifications for all reasonings. It permitted inferences to be withdrawn when presumptions were learnt to be inaccurate or a contradiction was derived. Explanations might be offered a reasoning by explaining which guidelines were used to develop it and then continuing through underlying reasonings and guidelines all the way back to root presumptions. [58] Lofti Zadeh had actually presented a different type of extension to handle the representation of vagueness. For example, in choosing how “heavy” or “tall” a guy is, there is frequently no clear “yes” or “no” answer, and a predicate for heavy or tall would rather return worths between 0 and 1. Those values represented to what degree the predicates were true. His fuzzy reasoning further offered a method for propagating mixes of these values through rational formulas. [59]

Machine knowing

Symbolic machine learning methods were investigated to resolve the knowledge acquisition bottleneck. One of the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test method to produce possible rule hypotheses to check against spectra. Domain and task understanding lowered the variety of candidates checked to a manageable size. Feigenbaum explained Meta-DENDRAL as

… the culmination of my dream of the early to mid-1960s relating to theory development. The conception was that you had an issue solver like DENDRAL that took some inputs and produced an output. In doing so, it used layers of knowledge to guide and prune the search. That understanding got in there due to the fact that we talked to individuals. But how did individuals get the understanding? By taking a look at thousands of spectra. So we desired a program that would look at countless spectra and presume the understanding of mass spectrometry that DENDRAL could utilize to solve private hypothesis formation problems. We did it. We were even able to publish new knowledge of mass spectrometry in the Journal of the American Chemical Society, providing credit just in a footnote that a program, Meta-DENDRAL, in fact did it. We had the ability to do something that had been a dream: to have a computer program developed a brand-new and publishable piece of science. [51]

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

Advances were made in understanding maker knowing theory, too. Tom Mitchell introduced version area knowing which explains knowing as a search through a space of hypotheses, with upper, more general, and lower, more specific, limits incorporating all practical hypotheses consistent with the examples seen so far. [62] More officially, Valiant presented Probably Approximately Correct Learning (PAC Learning), a framework for the mathematical analysis of artificial intelligence. [63]

Symbolic machine finding out included more than learning by example. E.g., John Anderson provided a cognitive model of human learning where ability practice leads to a collection of rules from a declarative format to a procedural format with his ACT-R cognitive architecture. For example, a trainee may learn to use “Supplementary angles are two angles whose steps sum 180 degrees” as several different procedural guidelines. E.g., one guideline may say that if X and Y are extra and you know X, then Y will be 180 – X. He called his approach “understanding compilation”. ACT-R has actually been utilized successfully to model elements of human cognition, such as discovering and retention. ACT-R is likewise utilized in intelligent tutoring systems, called cognitive tutors, to effectively teach geometry, computer system programming, and algebra to school kids. [64]

Inductive reasoning shows 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 hereditary algorithms to program synthesis to produce hereditary programming, which he used to synthesize LISP programs. Finally, Zohar Manna and Richard Waldinger provided a more basic method to program synthesis that manufactures a practical program in the course of showing its requirements to be right. [66]

As an option to logic, Roger Schank introduced case-based reasoning (CBR). The CBR technique laid out in his book, Dynamic Memory, [67] focuses first on remembering essential problem-solving cases for future use and generalizing them where suitable. When confronted with a new problem, CBR obtains the most similar previous case and adjusts it to the specifics of the present problem. [68] Another alternative to reasoning, hereditary algorithms and genetic shows are based upon an evolutionary model of learning, where sets of rules are encoded into populations, the guidelines govern the habits of people, and choice of the fittest prunes out sets of inappropriate rules over numerous generations. [69]

Symbolic maker knowing was used to finding out concepts, guidelines, heuristics, and problem-solving. Approaches, other than those above, include:

1. Learning from direction or advice-i.e., taking human direction, impersonated recommendations, and determining how to operationalize it in particular scenarios. 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 efficiency by accepting subject-matter specialist (SME) feedback throughout training. When problem-solving stops working, querying the specialist to either find out a brand-new prototype for analytical or to discover a brand-new explanation regarding exactly why one prototype is more pertinent than another. For example, the program Protos learned to diagnose tinnitus cases by connecting with an audiologist. [71] 3. Learning by analogy-constructing issue services based upon similar problems seen in the past, and after that modifying their options to fit a brand-new circumstance or domain. [72] [73] 4. Apprentice knowing systems-learning novel solutions to problems by observing human analytical. Domain understanding describes why unique solutions are appropriate and how the solution 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 bring out experiments and after that learning from the outcomes. Doug Lenat’s Eurisko, for instance, found out 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 fundamental analytical actions. Good macro-operators simplify problem-solving by allowing problems to be fixed at a more abstract level. [76]
Deep knowing and neuro-symbolic AI 2011-now

With the rise of deep learning, the symbolic AI technique has actually been compared to deep learning as complementary “… with parallels having been drawn often times by AI researchers in between Kahneman’s research study on human reasoning and choice making – shown in his book Thinking, Fast and Slow – and the so-called “AI systems 1 and 2″, which would in principle be designed by deep knowing and symbolic reasoning, respectively.” In this view, symbolic reasoning is more apt for deliberative thinking, preparation, and explanation while deep learning is more apt for fast pattern recognition in affective applications with noisy data. [17] [18]

Neuro-symbolic AI: integrating neural and symbolic methods

Neuro-symbolic AI efforts to incorporate neural and symbolic architectures in a manner that addresses strengths and weak points of each, in a complementary fashion, in order to support robust AI efficient in reasoning, discovering, and cognitive modeling. As argued by Valiant [77] and numerous others, [78] the effective building of rich computational cognitive designs demands the combination of sound symbolic reasoning and efficient (machine) knowing designs. Gary Marcus, similarly, argues that: “We can not construct rich cognitive models in an appropriate, automatic method without the triumvirate of hybrid architecture, rich prior understanding, and sophisticated strategies for thinking.”, [79] and in specific: “To construct a robust, knowledge-driven method to AI we need to have the equipment of symbol-manipulation in our toolkit. Too much of useful knowledge 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 knowledge reliably is the apparatus of sign adjustment. ” [80]

Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have likewise argued for a synthesis. Their arguments are based upon a need to address the two sort of believing discussed in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman describes human thinking as having two parts, System 1 and System 2. System 1 is quickly, automated, user-friendly 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 fit for planning, deduction, and deliberative thinking. In this view, deep learning finest models the very first sort of thinking while symbolic thinking finest models the second kind and both are needed.

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

In their 2015 paper, Neural-Symbolic Learning and Reasoning: Contributions and Challenges, Garcez et al. argue that:

The integration of the symbolic and connectionist paradigms of AI has been pursued by a fairly little research study community over the last 20 years and has actually yielded a number of substantial results. Over the last years, neural symbolic systems have actually been shown capable of overcoming the so-called propositional fixation of neural networks, as McCarthy (1988) put it in reaction to Smolensky (1988 ); see also (Hinton, 1990). Neural networks were revealed capable of representing modal and temporal reasonings (d’Avila Garcez and Lamb, 2006) and pieces of first-order logic (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have been used to a variety of issues in the locations of bioinformatics, control engineering, software confirmation and adaptation, visual intelligence, ontology learning, and computer games. [78]

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

– Symbolic Neural symbolic-is the existing technique of lots of neural models in natural language processing, where words or subword tokens are both the ultimate input and output of large language models. Examples consist of BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified 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 methods learn how to examine game positions.
– Neural|Symbolic-uses a neural architecture to interpret affective information as symbols and relationships that are then reasoned about symbolically.
– Neural: Symbolic → Neural-relies on symbolic reasoning to produce or identify training information that is subsequently discovered by a deep knowing model, e.g., to train a neural model for symbolic calculation by using a Macsyma-like symbolic mathematics system to create or label examples.
– Neural _ Symbolic -uses 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 knowledge base rules and terms. Logic Tensor Networks [86] likewise fall into this classification.
– Neural [Symbolic] -allows a neural model to straight call a symbolic thinking engine, e.g., to carry out an action or assess a state.

Many essential research study questions 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 extracted from them?
– How should common-sense understanding be found out and reasoned about?
– How can abstract understanding that is difficult to encode logically be dealt with?

Techniques and contributions

This area supplies a summary of techniques and contributions in a total context resulting in lots of other, more in-depth short articles in Wikipedia. Sections on Machine Learning and Uncertain Reasoning are covered earlier in the history area.

AI shows languages

The essential AI shows language in the US throughout the last symbolic AI boom duration was LISP. LISP is the second oldest programming language after FORTRAN and was created in 1958 by John McCarthy. LISP supplied the first read-eval-print loop to support rapid program advancement. Compiled functions could be freely blended with analyzed functions. Program tracing, stepping, and breakpoints were also offered, along with the ability to alter values or functions and continue from breakpoints or mistakes. It had the very first self-hosting compiler, suggesting that the compiler itself was initially composed in LISP and then ran interpretively to compile the compiler code.

Other crucial innovations pioneered by LISP that have actually spread to other programs languages consist of:

Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals

Programs were themselves information structures that other programs might operate on, enabling the simple definition of higher-level languages.

In contrast to the US, in Europe the key AI shows language during that exact same duration was Prolog. Prolog offered a built-in shop of truths and provisions that might be queried by a read-eval-print loop. The shop could act as a knowledge base and the provisions could serve as guidelines or a restricted form of reasoning. As a subset of first-order logic Prolog was based upon Horn clauses with a closed-world assumption-any realities not understood were thought about false-and an unique name assumption for primitive terms-e.g., the identifier barack_obama was considered to refer to precisely one item. Backtracking and marriage are built-in to Prolog.

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

Prolog is also a type of declarative shows. The logic stipulations that describe programs are straight translated to run the programs specified. No specific series of actions is required, as holds true with necessary programming languages.

Japan championed Prolog for its Fifth Generation Project, intending to develop special hardware for high efficiency. Similarly, LISP machines were developed to run LISP, but as the second AI boom turned to bust these business might not take on new workstations that could now run LISP or Prolog natively at similar speeds. See the history section for more information.

Smalltalk was another influential AI shows language. For instance, it presented metaclasses and, together with Flavors and CommonLoops, influenced the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the 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 programming languages see this list of programming languages for artificial intelligence. Currently, Python, a multi-paradigm shows language, is the most popular programming language, partially due to its extensive package library that supports information science, natural language processing, and deep knowing. Python consists of a read-eval-print loop, functional components such as higher-order functions, and object-oriented shows that includes metaclasses.

Search

Search emerges in many kinds of issue resolving, including preparation, constraint complete satisfaction, and playing video games such as checkers, chess, and go. The very best understood AI-search tree search algorithms are breadth-first search, depth-first search, A *, and Monte Carlo Search. Key search algorithms for Boolean satisfiability are WalkSAT, conflict-driven provision knowing, and the DPLL algorithm. For adversarial search when playing games, alpha-beta pruning, branch and bound, and minimax were early contributions.

Knowledge representation and thinking

Multiple various approaches to represent knowledge and then factor with those representations have actually been investigated. Below is a quick summary of approaches to knowledge representation and automated thinking.

Knowledge representation

Semantic networks, conceptual charts, frames, and reasoning are all techniques to modeling understanding such as domain knowledge, analytical knowledge, and the semantic significance of language. Ontologies model essential principles and their relationships in a domain. Example ontologies are YAGO, WordNet, and DOLCE. DOLCE is an example of an upper ontology that can be used for any domain while WordNet is a lexical resource that can likewise be deemed an ontology. YAGO integrates WordNet as part of its ontology, to line up truths extracted from Wikipedia with WordNet synsets. The Disease Ontology is an example of a medical ontology currently being used.

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

First-order logic is more general than description logic. The automated theorem provers talked about listed 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 reasoning include temporal reasoning, to manage time; epistemic logic, to factor about agent understanding; modal logic, to handle possibility and need; and probabilistic reasonings to manage reasoning and possibility together.

Automatic theorem proving

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

Prover9.
ACL2.
Vampire.

Prover9 can be utilized in conjunction with the Mace4 model checker. ACL2 is a theorem prover that can manage 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 a specific understanding base, usually of guidelines, to enhance reusability across domains by separating procedural code and domain knowledge. A separate reasoning engine procedures rules and includes, deletes, or customizes a knowledge store.

Forward chaining reasoning engines are the most common, and are seen in CLIPS and OPS5. Backward chaining happens in Prolog, where a more minimal sensible representation is utilized, Horn Clauses. Pattern-matching, specifically marriage, is utilized in Prolog.

A more flexible sort of analytical occurs when reasoning about what to do next occurs, instead of simply selecting among the available actions. This kind of meta-level thinking is utilized in Soar and in the BB1 chalkboard architecture.

Cognitive architectures such as ACT-R may have additional capabilities, such as the capability to compile frequently used understanding into higher-level portions.

Commonsense reasoning

Marvin Minsky first proposed frames as a method of translating typical visual situations, such as a workplace, and Roger Schank extended this idea to scripts for common routines, such as dining out. Cyc has attempted to record beneficial common-sense knowledge and has “micro-theories” to deal with particular type of domain-specific reasoning.

Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] approximates human thinking about naive physics, such as what occurs when we warm a liquid in a pot on the stove. We anticipate it to heat and possibly boil over, despite the fact that we may not know its temperature level, its boiling point, or other information, 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 reasoning about spatial relationships. Both can be solved with constraint solvers.

Constraints and constraint-based reasoning

Constraint solvers carry out a more restricted type of reasoning than first-order logic. They can simplify sets of spatiotemporal restraints, such as those for RCC or Temporal Algebra, along with resolving other kinds of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic programming can be utilized to fix scheduling problems, for example with constraint dealing with rules (CHR).

Automated planning

The General Problem Solver (GPS) cast planning as problem-solving utilized means-ends analysis to create strategies. STRIPS took a different technique, seeing planning as theorem proving. Graphplan takes a least-commitment approach to preparation, rather than sequentially selecting actions from an initial state, working forwards, or an objective state if working backwards. Satplan is a method to planning where a planning issue is lowered to a Boolean satisfiability problem.

Natural language processing

Natural language processing focuses on dealing with language as information to perform tasks such as recognizing topics without always understanding the desired significance. Natural language understanding, in contrast, constructs a significance representation and uses that for further 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 handled by symbolic AI, however considering that enhanced by deep knowing approaches. In symbolic AI, discourse representation theory and first-order logic have been utilized to represent sentence meanings. Latent semantic analysis (LSA) and specific semantic analysis likewise provided vector representations of documents. In the latter case, vector elements are interpretable as principles called by Wikipedia posts.

New deep learning methods based on Transformer designs have actually now eclipsed these earlier symbolic AI techniques and achieved modern efficiency 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 significance of the vector parts is nontransparent.

Agents and multi-agent systems

Agents are self-governing systems embedded in an environment they perceive and act on in some sense. Russell and Norvig’s standard book on artificial intelligence is arranged to reflect agent architectures of increasing sophistication. [91] The sophistication of representatives varies from easy reactive agents, to those with a design of the world and automated preparation capabilities, perhaps a BDI agent, i.e., one with beliefs, desires, and objectives – or additionally a support discovering model learned with time to choose actions – as much as a mix of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep knowing for perception. [92]

In contrast, a multi-agent system consists of several agents that interact among themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML). The agents require not all have the exact same internal architecture. Advantages of multi-agent systems include the capability to divide work amongst the agents and to increase fault tolerance when agents are lost. Research issues include how agents reach consensus, distributed issue solving, multi-agent learning, multi-agent planning, and distributed restraint optimization.

Controversies occurred from early 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 accepted AI but rejected symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were mostly from thinkers, on intellectual premises, however likewise from funding agencies, especially during the two AI winters.

The Frame Problem: knowledge representation challenges for first-order logic

Limitations were discovered in using simple first-order reasoning to reason about vibrant domains. Problems were found both with regards to specifying the preconditions for an action to succeed and in providing axioms for what did not change after an action was carried out.

McCarthy and Hayes introduced the Frame Problem in 1969 in the paper, “Some Philosophical Problems from the Standpoint of Expert System.” [93] A basic example occurs in “showing that a person person could get into conversation with another”, as an axiom asserting “if an individual has a telephone he still has it after looking up a number in the telephone book” would be needed for the deduction to prosper. Similar axioms would be needed for other domain actions to specify what did not change.

A comparable issue, called the Qualification Problem, occurs in attempting to identify the preconditions for an action to succeed. A limitless variety of pathological conditions can be thought of, e.g., a banana in a tailpipe might prevent a cars and truck from operating properly.

McCarthy’s technique to repair the frame problem was circumscription, a type of non-monotonic reasoning where deductions could be made from actions that require only define what would change while not having to explicitly define whatever that would not change. Other non-monotonic reasonings offered fact upkeep systems that modified beliefs resulting in contradictions.

Other ways of handling more open-ended domains consisted of probabilistic reasoning systems and maker learning to discover new principles and rules. McCarthy’s Advice Taker can be deemed an inspiration here, as it might incorporate new understanding provided by a human in the kind of assertions or guidelines. For example, speculative symbolic device discovering systems explored the ability to take high-level natural language suggestions and to interpret it into domain-specific actionable rules.

Similar to the problems in handling vibrant domains, common-sense thinking is likewise tough to catch in official reasoning. Examples of sensible reasoning consist of implicit reasoning about how people believe or basic understanding of daily occasions, things, and living animals. This type of understanding is taken for given and not deemed noteworthy. Common-sense thinking is an open location of research and challenging both for symbolic systems (e.g., Cyc has actually tried to catch essential parts of this knowledge over more than a decade) and neural systems (e.g., self-driving cars that do not understand not to drive into cones or not to hit pedestrians strolling a bike).

McCarthy saw his Advice Taker as having sensible, but his meaning of common-sense was different than the one above. [94] He defined a program as having common sense “if it immediately deduces for itself a sufficiently broad class of instant effects of anything it is informed and what it already knows. “

Connectionist AI: philosophical difficulties and sociological conflicts

Connectionist techniques include 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 innovative approaches, such as Transformers, GANs, and other operate in deep knowing.

Three philosophical positions [96] have actually been laid out among connectionists:

1. Implementationism-where connectionist architectures carry out the abilities for symbolic processing,
2. Radical connectionism-where symbolic processing is declined completely, and connectionist architectures underlie intelligence and are totally sufficient to explain it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are considered 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 deem essentially compatible with current research study in neuro-symbolic hybrids:

The 3rd and last position I would like to analyze here is what I call the moderate connectionist view, a more diverse view of the existing argument in between connectionism and symbolic AI. Among the scientists who has elaborated this position most explicitly is Andy Clark, a philosopher from the School of Cognitive and Computing Sciences of the University of Sussex (Brighton, England). Clark protected hybrid (partially symbolic, partly connectionist) systems. He claimed that (at least) two kinds of theories are needed in order to study and design cognition. On the one hand, for some information-processing tasks (such as pattern recognition) connectionism has advantages over symbolic designs. But on the other hand, for other cognitive processes (such as serial, deductive reasoning, and generative symbol manipulation processes) the symbolic paradigm provides sufficient models, and not only “approximations” (contrary to what radical connectionists would claim). [97]

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

To believe that we can simply desert symbol-manipulation is to suspend shock.

And yet, for the most part, that’s how most present AI proceeds. Hinton and numerous others have striven to get rid of symbols entirely. The deep learning hope-seemingly grounded not a lot in science, however in a sort of historic grudge-is that intelligent behavior will emerge simply from the confluence of massive data and deep learning. Where classical computer systems and software application fix jobs by defining sets of symbol-manipulating rules dedicated to particular jobs, such as modifying a line in a word processor or carrying out an estimation in a spreadsheet, neural networks normally attempt to fix jobs by statistical approximation and finding out from examples.

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

When deep knowing reemerged in 2012, it was with a sort of take-no-prisoners attitude that has characterized most of the last years. By 2015, his hostility toward all things symbols had totally taken shape. He provided a talk at an AI workshop at Stanford comparing symbols to aether, one of science’s biggest mistakes.

…

Since then, his anti-symbolic campaign has actually just increased in strength. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep learning in one of science’s essential journals, Nature. It closed with a direct attack on sign manipulation, calling not for reconciliation but for outright replacement. Later, Hinton informed a gathering of European Union leaders that investing any additional money in symbol-manipulating methods was “a big error,” comparing it to purchasing internal combustion engines in the era of electrical automobiles. [98]

Part of these conflicts might be because of uncertain terms:

Turing award winner Judea Pearl offers a critique of artificial intelligence which, sadly, conflates the terms artificial intelligence and deep knowing. 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 discover. Using the terminology needs 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 sensible rather than dispersed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not just about production rules written by hand. An appropriate definition of AI concerns understanding representation and thinking, autonomous multi-agent systems, planning and argumentation, in addition to knowing. [99]

Situated robotics: the world as a design

Another critique of symbolic AI is the embodied cognition technique:

The embodied cognition technique declares that it makes no sense to consider the brain independently: cognition takes place within a body, which is embedded in an environment. We require to study the system as a whole; the brain’s operating exploits regularities 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 viewed as an alternative to both symbolic AI and connectionist AI. His method rejected representations, either symbolic or distributed, as not just unnecessary, however as destructive. Instead, he created the subsumption architecture, a layered architecture for embodied representatives. Each layer achieves a various function and must operate in the real life. For example, the very first robotic 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 obstacles. The leading layer triggers the robot to go to more distant places for further expedition. Each layer can temporarily inhibit or suppress a lower-level layer. He criticized AI researchers for defining AI problems for their systems, when: “There is no tidy division in between understanding (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 easy limited state devices.” [102] In the Nouvelle AI method, “First, it is vitally important to evaluate the Creatures we develop in the real life; i.e., in the exact same world that we human beings live in. It is devastating to fall into the temptation of checking them in a streamlined world first, even with the best intentions of later transferring activity to an unsimplified world.” [103] His emphasis on real-world screening remained in contrast to “Early operate in AI focused on video games, geometrical problems, 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 benefits, but has actually been criticized by the other methods. Symbolic AI has actually been criticized as disembodied, liable to the credentials problem, and poor in dealing with the affective problems where deep finding out excels. In turn, connectionist AI has actually been criticized as badly suited for deliberative step-by-step problem solving, incorporating knowledge, and handling preparation. Finally, Nouvelle AI masters reactive and real-world robotics domains but has actually been criticized for troubles in including knowing and knowledge.

Hybrid AIs including several of these methods are presently viewed as the path forward. [19] [81] [82] Russell and Norvig conclude that:

Overall, Dreyfus saw locations where AI did not have complete responses and stated that Al is for that reason difficult; we now see a number of these exact same locations undergoing continued research and advancement causing increased ability, not impossibility. [100]

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

Notes

^ McCarthy when stated: “This is AI, so we don’t care if it’s emotionally real”. [4] McCarthy reiterated his position in 2006 at the AI@50 conference where he said “Artificial intelligence is not, by definition, simulation of human intelligence”. [28] Pamela McCorduck composes that there are “2 significant branches of expert system: one intended at producing smart behavior despite how it was accomplished, and the other targeted at modeling intelligent procedures found in nature, particularly human ones.”, [29] Stuart Russell and Peter Norvig wrote “Aeronautical engineering texts do not define the goal of their field as making ‘machines that fly so precisely like pigeons that they can fool even other pigeons.'” [30] Citations

^ Garnelo, Marta; Shanahan, Murray (October 2019). “Reconciling deep learning with symbolic artificial intelligence: representing objects and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). “Logic-Based Artificial Intelligence”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep learning with symbolic expert system: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796. S2CID 72336067.
^ a b Kolata 1982.
^ Kautz 2022, pp. 107-109.
^ a b Russell & Norvig 2021, p. 19.
^ a b Russell & Norvig 2021, pp. 22-23.
^ a b Kautz 2022, pp. 109-110.
^ a b c Kautz 2022, p. 110.
^ Kautz 2022, pp. 110-111.
^ a b Russell & Norvig 2021, p. 25.
^ Kautz 2022, p. 111.
^ Kautz 2020, pp. 110-111.
^ Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. (1986 ). “Learning representations by back-propagating errors”. Nature. 323 (6088 ): 533-536. Bibcode:1986 Natur.323..533 R. doi:10.1038/ 323533a0. ISSN 1476-4687. S2CID 205001834.
^ LeCun, Y.; Boser, B.; Denker, I.; Henderson, D.; Howard, R.; Hubbard, W.; Tackel, L. (1989 ). “Backpropagation Applied to Handwritten Postal Code Recognition”. Neural Computation. 1 (4 ): 541-551. doi:10.1162/ neco.1989.1.4.541. S2CID 41312633.
^ a b Marcus & Davis 2019.
^ a b Rossi, Francesca. “Thinking Fast and Slow in AI”. AAAI. Retrieved 5 July 2022.
^ a b Selman, Bart. “AAAI Presidential Address: The State of AI“. AAAI. Retrieved 5 July 2022.
^ a b c Kautz 2020.
^ Kautz 2022, p. 106.
^ Newell & Simon 1972.
^ & McCorduck 2004, pp. 139-179, 245-250, 322-323 (EPAM).
^ Crevier 1993, pp. 145-149.
^ McCorduck 2004, pp. 450-451.
^ Crevier 1993, pp. 258-263.
^ a b Kautz 2022, p. 108.
^ Russell & Norvig 2021, p. 9 (logicist AI), p. 19 (McCarthy’s work).
^ Maker 2006.
^ McCorduck 2004, pp. 100-101.
^ Russell & Norvig 2021, p. 2.
^ McCorduck 2004, pp. 251-259.
^ Crevier 1993, pp. 193-196.
^ Howe 1994.
^ McCorduck 2004, pp. 259-305.
^ Crevier 1993, pp. 83-102, 163-176.
^ McCorduck 2004, pp. 421-424, 486-489.
^ Crevier 1993, p. 168.
^ McCorduck 2004, p. 489.
^ Crevier 1993, pp. 239-243.
^ Russell & Norvig 2021, p. 316, 340.
^ Kautz 2022, p. 109.
^ Russell & Norvig 2021, p. 22.
^ McCorduck 2004, pp. 266-276, 298-300, 314, 421.
^ Shustek, Len (June 2010). “An interview with Ed Feigenbaum”. Communications of the ACM. 53 (6 ): 41-45. doi:10.1145/ 1743546.1743564. ISSN 0001-0782. S2CID 10239007. Retrieved 2022-07-14.
^ Lenat, Douglas B; Feigenbaum, Edward A (1988 ). “On the thresholds 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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^ 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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^ Garcez & Lamb 2020, p. 2.
^ Garcez et al. 2002.
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