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Symbolic Artificial Intelligence
In expert system, symbolic expert system (also called classical artificial intelligence or logic-based expert system) [1] [2] is the term for the collection of all approaches in artificial intelligence research study that are based on high-level symbolic (human-readable) representations of problems, reasoning and search. [3] Symbolic AI used tools such as logic programming, production guidelines, semantic webs 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 caused influential ideas in search, symbolic programs languages, representatives, multi-agent systems, the semantic web, and the strengths and constraints of formal understanding and reasoning systems.
Symbolic AI was the dominant paradigm of AI research from the mid-1950s until the mid-1990s. [4] Researchers in the 1960s and the 1970s were persuaded that symbolic approaches would ultimately succeed in creating a maker with artificial general intelligence and considered this the ultimate goal of their field. [citation needed] An early boom, with early successes such as the Logic Theorist and Samuel’s Checkers Playing Program, led to impractical expectations and guarantees and was followed by the first AI Winter as moneying dried up. [5] [6] A second boom (1969-1986) accompanied the rise of expert systems, their guarantee of catching corporate competence, and an enthusiastic business embrace. [7] [8] That boom, and some early successes, e.g., with XCON at DEC, was followed once again by later dissatisfaction. [8] Problems with difficulties in knowledge acquisition, maintaining big understanding bases, and brittleness in dealing with out-of-domain problems emerged. Another, second, AI Winter (1988-2011) followed. [9] Subsequently, AI scientists concentrated on dealing with underlying issues in managing unpredictability and in understanding acquisition. [10] Uncertainty was addressed with formal methods such as concealed Markov models, Bayesian reasoning, and analytical relational knowing. [11] [12] Symbolic machine discovering attended to the understanding acquisition issue with contributions consisting of Version Space, Valiant’s PAC knowing, Quinlan’s ID3 decision-tree learning, case-based knowing, and inductive logic shows to learn relations. [13]
Neural networks, a subsymbolic approach, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt’s perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, [14] and work in convolutional neural networks by LeCun et al. in 1989. [15] However, neural networks were not considered as successful till about 2012: “Until Big Data became prevalent, the general agreement in the Al neighborhood was that the so-called neural-network approach was hopeless. Systems simply didn’t work that well, compared to other methods. … A revolution came in 2012, when a variety of people, including a team of scientists dealing with Hinton, worked out a way to utilize the power of GPUs to tremendously increase the power of neural networks.” [16] Over the next numerous years, deep knowing had incredible success in handling vision, speech acknowledgment, speech synthesis, image generation, and machine translation. However, given that 2020, as fundamental difficulties with predisposition, description, coherence, and effectiveness ended up being more obvious with deep knowing methods; an increasing number of AI researchers have actually called for combining the finest of both the symbolic and neural network techniques [17] [18] and attending to locations that both methods have difficulty with, such as sensible thinking. [16]
A brief 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 differing a little for increased clearness.
The very first AI summer: unreasonable exuberance, 1948-1966
Success at early efforts in AI took place in three primary locations: synthetic neural networks, understanding representation, and heuristic search, contributing to high expectations. This section sums up Kautz’s reprise of early AI history.
Approaches influenced by human or animal cognition or behavior
Cybernetic methods attempted to reproduce the feedback loops between animals and their environments. A robotic turtle, with sensing units, motors for driving and steering, and 7 vacuum tubes for control, based on a preprogrammed neural web, was built as early as 1948. This work can be seen as an early precursor to later operate in neural networks, support knowing, and situated 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 show 38 primary theorems from Whitehead and Russell’s Principia Mathematica. Newell, Simon, and Shaw later generalized this work to develop a domain-independent issue solver, GPS (General Problem Solver). problems represented with official operators by means of state-space search using means-ends analysis. [21]
During the 1960s, symbolic approaches attained excellent success at replicating intelligent behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research study was concentrated in four organizations in the 1960s: Carnegie Mellon University, Stanford, MIT and (later on) University of Edinburgh. Each one established its own design of research study. Earlier methods based on 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 synthetic intelligence, as well as cognitive science, operations research and management science. Their research study group utilized the outcomes of mental experiments to establish programs that simulated the strategies that individuals utilized to solve issues. [22] [23] This custom, 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 on utilized in professional systems, early symbolic AI researchers discovered another more general application of knowledge. These were called heuristics, rules of thumb that assist a search in appealing directions: “How can non-enumerative search be useful when the underlying issue is exponentially hard? The technique advocated by Simon and Newell is to employ heuristics: quick algorithms that may stop working on some inputs or output suboptimal services.” [26] Another essential advance was to discover a method to apply these heuristics that ensures a solution will be discovered, if there is one, not enduring the occasional fallibility of heuristics: “The A * algorithm offered a general frame for total and optimum heuristically guided search. A * is used as a subroutine within virtually every AI algorithm today but is still no magic bullet; its warranty of completeness is purchased at the cost of worst-case exponential time. [26]
Early deal with understanding representation and thinking
Early work covered both applications of formal thinking stressing first-order reasoning, together with attempts to manage sensible thinking in a less formal manner.
Modeling official reasoning with reasoning: the “neats”
Unlike Simon and Newell, John McCarthy felt that machines did not need to replicate the precise systems of human idea, however might instead search for the essence of abstract thinking and problem-solving with reasoning, [27] despite whether people utilized the same algorithms. [a] His laboratory at Stanford (SAIL) concentrated on utilizing formal reasoning to solve a variety of issues, including understanding representation, preparation and learning. [31] Logic was likewise the focus of the work at the University of Edinburgh and somewhere else in Europe which caused the development of the shows language Prolog and the science of reasoning programming. [32] [33]
Modeling implicit sensible knowledge with frames and scripts: the “scruffies”
Researchers at MIT (such as Marvin Minsky and Seymour Papert) [34] [35] [6] discovered that solving hard issues in vision and natural language processing needed ad hoc solutions-they argued that no basic and general principle (like logic) would capture all the aspects of intelligent behavior. Roger Schank explained their “anti-logic” techniques as “scruffy” (as opposed to the “cool” paradigms at CMU and Stanford). [36] [37] Commonsense knowledge bases (such as Doug Lenat’s Cyc) are an example of “scruffy” AI, since they should be constructed by hand, one complex concept at a time. [38] [39] [40]
The first AI winter: crushed dreams, 1967-1977
The very first AI winter was a shock:
During the first AI summertime, many individuals thought that maker intelligence could be attained in just a couple of years. The Defense Advance Research Projects Agency (DARPA) introduced programs to support AI research study to utilize AI to fix problems of national security; in particular, to automate the translation of Russian to English for intelligence operations and to create self-governing tanks for the battlefield. Researchers had started to realize that achieving AI was going to be much more difficult than was expected a years earlier, however a combination of hubris and disingenuousness led numerous university and think-tank researchers to accept financing with pledges of deliverables that they should have understood they could not meet. By the mid-1960s neither useful natural language translation systems nor self-governing tanks had been created, and a significant backlash embeded in. New DARPA leadership 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 saw AI researchers as charlatans and a drain on research financing. A professor of applied mathematics, Sir James Lighthill, was commissioned by Parliament to evaluate the state of AI research in the nation. The report mentioned that all of the issues being worked on in AI would be much better handled by researchers from other disciplines-such as applied mathematics. The report likewise declared that AI successes on toy issues could never scale to real-world applications due to combinatorial explosion. [41]
The second AI summertime: knowledge is power, 1978-1987
Knowledge-based systems
As limitations with weak, domain-independent methods ended up being a growing number of obvious, [42] researchers from all three traditions began to develop understanding into AI applications. [43] [7] The knowledge transformation 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 describe that high efficiency in a particular domain needs both basic and extremely domain-specific understanding. Ed Feigenbaum and Doug Lenat called this The Knowledge Principle:
( 1) The Knowledge Principle: if a program is to carry out a complicated job well, it must understand an excellent offer about the world in which it runs.
( 2) A possible extension of that concept, called the Breadth Hypothesis: there are two additional capabilities essential for smart habits in unforeseen scenarios: falling back on significantly basic understanding, and analogizing to particular however far-flung understanding. [45]
Success with expert systems
This “understanding transformation” resulted in the advancement and release of specialist systems (presented by Edward Feigenbaum), the first commercially effective kind of AI software application. [46] [47] [48]
Key specialist systems were:
DENDRAL, which discovered the structure of natural molecules from their chemical formula and mass spectrometer readings.
MYCIN, which identified bacteremia – and suggested further laboratory tests, when necessary – by interpreting lab outcomes, patient history, and medical professional observations. “With about 450 rules, MYCIN was able to carry out in addition to some experts, and substantially better than junior doctors.” [49] INTERNIST and CADUCEUS which dealt with internal medication diagnosis. Internist tried to record the expertise of the chairman of internal medication at the University of Pittsburgh School of Medicine while CADUCEUS could eventually detect as much as 1000 different diseases.
– GUIDON, which demonstrated how an understanding base developed for professional issue resolving could be repurposed for mentor. [50] XCON, to set up VAX computer systems, a then tiresome process that could take up to 90 days. XCON lowered the time to about 90 minutes. [9]
DENDRAL is thought about the first professional system that count on knowledge-intensive analytical. It is described below, by Ed Feigenbaum, from a Communications of the ACM interview, Interview with Ed Feigenbaum:
Among the people at Stanford thinking about computer-based designs of mind was Joshua Lederberg, the 1958 Nobel Prize winner in genes. When I told him I wanted an induction “sandbox”, he said, “I have simply the one for you.” His lab was doing mass spectrometry of amino acids. The concern 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 approaches, and he had an algorithm that was proficient at creating the chemical problem 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 tablet, and also one of the world’s most respected mass spectrometrists. Carl and his postdocs were world-class experts in mass spectrometry. We began to contribute to their understanding, inventing 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 became. We had really great outcomes.
The generalization was: in the knowledge lies the power. That was the huge idea. In my profession that is the substantial, “Ah ha!,” and it wasn’t the method AI was being done formerly. Sounds simple, however it’s most likely AI’s most effective generalization. [51]
The other specialist systems pointed out above came after DENDRAL. MYCIN exhibits the timeless expert system architecture of a knowledge-base of guidelines combined to a symbolic thinking mechanism, consisting of using certainty aspects to handle unpredictability. GUIDON reveals how an explicit understanding base can be repurposed for a second application, tutoring, and is an example of a smart tutoring system, a particular sort of knowledge-based application. Clancey revealed that it was not adequate just to use MYCIN’s guidelines for guideline, however that he likewise needed to include guidelines for discussion management and student modeling. [50] XCON is significant due to the fact that of the millions of dollars it conserved DEC, which set off the professional system boom where most all significant corporations in the US had expert systems groups, to capture corporate know-how, preserve it, and automate it:
By 1988, DEC’s AI group had 40 expert systems deployed, with more on the way. 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 specialist knowledge was encoded in Deep Blue. In 1996, this permitted IBM’s Deep Blue, with the help of symbolic AI, to win in a video game of chess versus the world champ at that time, Garry Kasparov. [52]
Architecture of knowledge-based and skilled systems
A key part of the system architecture for all specialist systems is the understanding base, which stores truths and rules for problem-solving. [53] The most basic technique for a skilled system understanding base is just a collection or network of production rules. Production rules link symbols in a relationship similar to an If-Then statement. The specialist system processes the guidelines to make reductions and to determine what additional details it requires, i.e. what questions to ask, using human-readable symbols. For instance, 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 goals to required data and requirements – manner. More innovative knowledge-based systems, such as Soar can also carry out meta-level thinking, that is thinking about their own reasoning in terms of choosing how to resolve issues and keeping an eye on the success of problem-solving strategies.
Blackboard systems are a 2nd sort of knowledge-based or professional system architecture. They design a community of specialists incrementally contributing, where they can, to fix a problem. The problem is represented in several levels of abstraction or alternate views. The professionals (understanding sources) offer their services whenever they recognize they can contribute. Potential problem-solving actions are represented on an agenda that is updated as the issue scenario modifications. A controller decides how beneficial each contribution is, and who need to make the next analytical action. One example, the BB1 chalkboard architecture [54] was originally inspired by studies of how humans plan to carry out multiple tasks in a trip. [55] A development of BB1 was to use the exact same blackboard design to solving its control problem, i.e., its controller performed meta-level thinking with knowledge sources that kept an eye on how well a strategy or the problem-solving was proceeding and could switch from one strategy to another as conditions – such as goals or times – changed. BB1 has actually been used in multiple domains: construction website preparation, smart tutoring systems, and real-time client tracking.
The 2nd AI winter season, 1988-1993
At the height of the AI boom, business such as Symbolics, LMI, and Texas Instruments were selling LISP devices specifically targeted to accelerate the advancement of AI applications and research. In addition, a number of synthetic intelligence business, such as Teknowledge and Inference Corporation, were selling expert system shells, training, and consulting to corporations.
Unfortunately, the AI boom did not last and Kautz best describes the second AI winter season that followed:
Many reasons can be provided for the arrival of the 2nd AI winter season. The hardware business failed when much more cost-efficient general Unix workstations from Sun together with good compilers for LISP and Prolog came onto the marketplace. Many commercial releases of professional systems were ceased when they proved too pricey to maintain. Medical professional systems never ever caught on for numerous reasons: the problem in keeping them approximately date; the challenge for medical specialists to find out how to use a bewildering range of various professional systems for various medical conditions; and perhaps most crucially, the hesitation of physicians to rely on a computer-made medical diagnosis over their gut instinct, even for particular domains where the expert systems might exceed a typical medical professional. Equity capital cash deserted AI practically overnight. The world AI conference IJCAI hosted a huge and lavish trade show and thousands of 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]
Including more rigorous structures, 1993-2011
Uncertain reasoning
Both analytical methods and extensions to logic were tried.
One analytical method, concealed Markov designs, had currently been promoted in the 1980s for speech recognition work. [11] Subsequently, in 1988, Judea Pearl popularized the use of Bayesian Networks as a sound however efficient way of managing unsure thinking 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, in the 1990s, statistical relational learning, a technique that integrates possibility with logical solutions, allowed likelihood to be integrated with first-order reasoning, e.g., with either Markov Logic Networks or Probabilistic Soft Logic.
Other, non-probabilistic extensions to first-order logic to assistance were also attempted. For instance, non-monotonic thinking could be used with reality maintenance systems. A fact maintenance system tracked presumptions and reasons for all inferences. It allowed inferences to be withdrawn when assumptions were found out to be incorrect or a contradiction was obtained. Explanations might be attended to a reasoning by describing which rules were applied to develop it and after that continuing through underlying inferences and guidelines all the method back to root presumptions. [58] Lofti Zadeh had introduced a various kind of extension to handle the representation of ambiguity. For instance, in deciding how “heavy” or “tall” a guy is, there is regularly no clear “yes” or “no” response, and a predicate for heavy or high would instead return worths in between 0 and 1. Those worths represented to what degree the predicates held true. His fuzzy logic even more provided a method for propagating mixes of these values through sensible solutions. [59]
Artificial intelligence
Symbolic maker finding out approaches were investigated to attend to the knowledge acquisition bottleneck. One of the earliest is Meta-DENDRAL. Meta-DENDRAL used a generate-and-test method to generate possible guideline hypotheses to check versus spectra. Domain and task knowledge decreased the variety of candidates evaluated to a workable size. Feigenbaum explained Meta-DENDRAL as
… the culmination of my dream of the early to mid-1960s pertaining to 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 utilized layers of understanding to steer and prune the search. That understanding acted due to the fact that we spoke with individuals. But how did individuals get the knowledge? By taking a look at countless spectra. So we desired a program that would look at thousands of spectra and infer the understanding of mass spectrometry that DENDRAL might utilize to solve individual hypothesis development issues. We did it. We were even able to release new knowledge of mass spectrometry in the Journal of the American Chemical Society, giving credit only in a footnote that a program, Meta-DENDRAL, really did it. We had the ability to do something that had been a dream: to have a computer program created a brand-new and publishable piece of science. [51]
In contrast to the knowledge-intensive approach of Meta-DENDRAL, Ross Quinlan created a domain-independent technique to analytical category, decision tree knowing, beginning first with ID3 [60] and after that later extending its abilities to C4.5. [61] The decision trees created are glass box, interpretable classifiers, with human-interpretable category rules.
Advances were made in comprehending artificial intelligence theory, too. Tom Mitchell presented version area knowing which explains learning as an explore a space of hypotheses, with upper, more general, and lower, more particular, limits including all viable hypotheses constant with the examples seen so far. [62] More formally, Valiant presented Probably Approximately Correct Learning (PAC Learning), a structure for the mathematical analysis of maker knowing. [63]
Symbolic device finding out included more than discovering by example. E.g., John Anderson provided a cognitive model of human knowing where skill practice results in a compilation of guidelines from a declarative format to a procedural format with his ACT-R cognitive architecture. For instance, a student might discover to apply “Supplementary angles are two angles whose procedures sum 180 degrees” as numerous different procedural rules. E.g., one rule may state that if X and Y are extra and you understand X, then Y will be 180 – X. He called his technique “knowledge collection”. ACT-R has been used successfully to model elements of human cognition, such as learning and retention. ACT-R is likewise used in smart tutoring systems, called cognitive tutors, to successfully teach geometry, computer system programs, and algebra to school children. [64]
Inductive reasoning shows was another technique to discovering that enabled reasoning programs to be synthesized from input-output examples. E.g., Ehud Shapiro’s MIS (Model Inference System) could synthesize Prolog programs from examples. [65] John R. Koza used hereditary algorithms to program synthesis to produce hereditary programs, which he utilized to manufacture LISP programs. Finally, Zohar Manna and Richard Waldinger supplied a more basic technique to program synthesis that manufactures a functional program in the course of proving its specifications to be correct. [66]
As an option to reasoning, Roger Schank presented case-based reasoning (CBR). The CBR technique described in his book, Dynamic Memory, [67] focuses first on remembering key problem-solving cases for future use and generalizing them where suitable. When confronted with a new problem, CBR recovers the most similar previous case and adjusts it to the specifics of the present problem. [68] Another alternative to logic, hereditary algorithms and hereditary programming are based upon an evolutionary design of learning, where sets of guidelines are encoded into populations, the rules govern the habits of people, and selection of the fittest prunes out sets of unsuitable guidelines over many generations. [69]
Symbolic device learning was applied to learning concepts, guidelines, heuristics, and problem-solving. Approaches, other than those above, include:
1. Learning from direction or advice-i.e., taking human direction, impersonated advice, and determining how to operationalize it in particular situations. For instance, in a video game of Hearts, learning precisely how to play a hand to “avoid taking points.” [70] 2. Learning from exemplars-improving performance by accepting subject-matter professional (SME) feedback throughout training. When analytical stops working, querying the professional to either learn a new exemplar for problem-solving or to learn a new explanation as to precisely why one prototype is more pertinent than another. For example, the program Protos learned to identify ringing in the ears cases by connecting with an audiologist. [71] 3. Learning by analogy-constructing problem solutions based upon comparable problems seen in the past, and after that customizing their options to fit a brand-new situation or domain. [72] [73] 4. Apprentice learning systems-learning novel services to problems by observing human problem-solving. Domain knowledge discusses why novel solutions are proper and how the option can be generalized. LEAP found out how to create VLSI circuits by observing human designers. [74] 5. Learning by discovery-i.e., producing tasks to bring out experiments and then discovering from the outcomes. Doug Lenat’s Eurisko, for example, found out heuristics to beat human players at the Traveller role-playing game for 2 years in a row. [75] 6. Learning macro-operators-i.e., looking for helpful macro-operators to be gained from series of standard analytical actions. Good macro-operators streamline analytical by permitting issues to be fixed at a more abstract level. [76]
Deep knowing and neuro-symbolic AI 2011-now
With the rise of deep knowing, the symbolic AI method has actually been compared to deep knowing as complementary “… with parallels having actually been drawn often times by AI scientists in between Kahneman’s research on human thinking and decision making – reflected in his book Thinking, Fast and Slow – and the so-called “AI systems 1 and 2″, which would in principle be modelled by deep learning and symbolic thinking, respectively.” In this view, symbolic reasoning is more apt for deliberative reasoning, preparation, and explanation while deep learning is more apt for fast pattern recognition in perceptual applications with loud information. [17] [18]
Neuro-symbolic AI: integrating neural and symbolic techniques
Neuro-symbolic AI attempts to integrate neural and symbolic architectures in a way that addresses strengths and weaknesses of each, in a complementary fashion, in order to support robust AI capable of reasoning, discovering, and cognitive modeling. As argued by Valiant [77] and many others, [78] the effective construction of abundant computational cognitive designs demands the mix of sound symbolic thinking and effective (maker) learning models. Gary Marcus, likewise, argues that: “We can not construct rich cognitive designs in an adequate, automated way without the set of three of hybrid architecture, abundant prior knowledge, and sophisticated methods for thinking.”, [79] and in particular: “To develop a robust, knowledge-driven technique to AI we need to have the equipment of symbol-manipulation in our toolkit. Excessive of useful knowledge is abstract to make do without tools that represent and manipulate abstraction, and to date, the only machinery that we know of that can manipulate such abstract knowledge reliably is the device of symbol manipulation. ” [80]
Henry Kautz, [19] Francesca Rossi, [81] and Bart Selman [82] have likewise argued for a synthesis. Their arguments are based on a requirement to deal with the two type of believing discussed in Daniel Kahneman’s book, Thinking, Fast and Slow. Kahneman explains human thinking as having two elements, System 1 and System 2. System 1 is quick, automated, intuitive and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is the kind used for pattern acknowledgment while System 2 is far much better fit for preparation, deduction, and deliberative thinking. In this view, deep learning best designs the first sort of believing while symbolic thinking best models the second kind and both are required.
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 learning systems. [84] A series of workshops on neuro-symbolic thinking has actually been held every year given that 2005, see http://www.neural-symbolic.org/ for details.
In their 2015 paper, Neural-Symbolic Learning and Reasoning: Contributions and Challenges, Garcez et al. argue that:
The integration of the symbolic and connectionist paradigms of AI has been pursued by a fairly small research community over the last twenty years and has yielded numerous significant outcomes. Over the last decade, neural symbolic systems have actually been revealed capable of overcoming 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 shown capable of representing modal and temporal reasonings (d’Avila Garcez and Lamb, 2006) and pieces of first-order reasoning (Bader, Hitzler, Hölldobler, 2008; d’Avila Garcez, Lamb, Gabbay, 2009). Further, neural-symbolic systems have been applied to a variety of issues in the locations of bioinformatics, control engineering, software application verification and adjustment, visual intelligence, ontology knowing, and computer games. [78]
Approaches for combination are differed. Henry Kautz’s taxonomy of neuro-symbolic architectures, in addition to some examples, follows:
– Symbolic Neural symbolic-is the existing approach of numerous neural models in natural language processing, where words or subword tokens are both the ultimate input and output of big language designs. Examples consist of BERT, RoBERTa, and GPT-3.
– Symbolic [Neural] -is exemplified by AlphaGo, where symbolic methods are utilized to call neural strategies. In this case the symbolic technique is Monte Carlo tree search and the neural techniques discover how to assess game positions.
– Neural|Symbolic-uses a neural architecture to interpret affective information 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 subsequently found out by a deep learning model, e.g., to train a neural design for symbolic calculation by using a Macsyma-like symbolic mathematics system to produce or identify examples.
– Neural _ Symbolic -utilizes a neural internet that is created from symbolic guidelines. An example is the Neural Theorem Prover, [85] which constructs a neural network from an AND-OR evidence tree produced from understanding base rules and terms. Logic Tensor Networks [86] likewise fall into this classification.
– Neural [Symbolic] -allows a neural design to directly call a symbolic reasoning engine, e.g., to carry out an action or evaluate a state.
Many essential research study concerns stay, such as:
– What is the very best way to integrate neural and symbolic architectures? [87]- How should symbolic structures be represented within neural networks and extracted from them?
– How should sensible understanding be discovered and reasoned about?
– How can abstract knowledge that is hard to encode rationally be managed?
Techniques and contributions
This area provides an overview of techniques and contributions in an overall context resulting in 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 throughout the last symbolic AI boom period was LISP. LISP is the 2nd oldest programming language after FORTRAN and was produced in 1958 by John McCarthy. LISP offered the very first read-eval-print loop to support fast program advancement. Compiled functions could be freely blended with translated functions. Program tracing, stepping, and breakpoints were also supplied, together with the capability to alter values or functions and continue from breakpoints or errors. It had the very first self-hosting compiler, implying that the compiler itself was originally written in LISP and then ran interpretively to assemble the compiler code.
Other key developments originated by LISP that have infected other shows languages consist of:
Garbage collection
Dynamic typing
Higher-order functions
Recursion
Conditionals
Programs were themselves information structures that other programs might run on, permitting the simple meaning of higher-level languages.
In contrast to the US, in Europe the key AI shows language throughout that same period was Prolog. Prolog offered a built-in store of truths and stipulations that might be queried by a read-eval-print loop. The store could function as a knowledge base and the stipulations might act as rules or a restricted kind of reasoning. As a subset of first-order reasoning Prolog was based on Horn stipulations with a closed-world assumption-any facts not understood were thought about false-and a special name assumption for primitive terms-e.g., the identifier barack_obama was thought about to describe exactly one things. Backtracking and marriage are integrated to Prolog.
Alain Colmerauer and Philippe Roussel are credited as the innovators of Prolog. Prolog is a kind of reasoning programming, which was invented by Robert Kowalski. Its history was likewise influenced by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of methods. For more information see the area on the origins of Prolog in the PLANNER article.
Prolog is also a type of declarative programs. The reasoning clauses that describe programs are straight interpreted to run the programs specified. No specific series of actions is required, as is the case with imperative programs languages.
Japan promoted Prolog for its Fifth Generation Project, planning to construct special hardware for high efficiency. Similarly, LISP devices were developed to run LISP, however as the second AI boom turned to bust these business could not compete with new workstations that might now run LISP or Prolog natively at similar speeds. See the history section for more information.
Smalltalk was another influential AI programming language. For instance, it presented metaclasses and, along with Flavors and CommonLoops, influenced the Common Lisp Object System, or (CLOS), that is now part of Common Lisp, the existing basic Lisp dialect. CLOS is a Lisp-based object-oriented system that enables multiple inheritance, in addition to incremental extensions to both classes and metaclasses, hence supplying a run-time meta-object procedure. [88]
For other AI programs languages see this list of programs languages for expert system. Currently, Python, a multi-paradigm programs language, is the most popular shows language, partly due to its comprehensive package library that supports data 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 shows that consists of metaclasses.
Search
Search arises in numerous type of problem solving, consisting of preparation, restriction fulfillment, and playing video 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 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 techniques to represent understanding and then factor with those representations have actually been examined. Below is a quick introduction of methods to knowledge representation and automated thinking.
Knowledge representation
Semantic networks, conceptual charts, frames, and logic are all techniques to modeling knowledge such as domain knowledge, problem-solving knowledge, and the semantic meaning of language. Ontologies model essential concepts 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 also be considered as an ontology. YAGO includes WordNet as part of its ontology, to align realities 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 category of ontologies and for finding irregular classification data. OWL is a language used to represent ontologies with description reasoning. Protégé is an ontology editor that can read in OWL ontologies and then examine consistency with deductive classifiers such as such as HermiT. [89]
First-order reasoning is more general than description reasoning. The automated theorem provers discussed below can prove theorems in first-order logic. Horn provision logic is more restricted than first-order reasoning and is utilized in reasoning programming languages such as Prolog. Extensions to first-order reasoning include temporal logic, to manage time; epistemic logic, to reason about representative understanding; modal reasoning, to deal with possibility and need; and probabilistic logics to handle reasoning and possibility together.
Automatic theorem proving
Examples of automated theorem provers for first-order logic are:
Prover9.
ACL2.
Vampire.
Prover9 can be utilized in combination with the Mace4 model checker. ACL2 is a theorem prover that can deal with proofs by induction and is a descendant of the Boyer-Moore Theorem Prover, likewise understood as Nqthm.
Reasoning in knowledge-based systems
Knowledge-based systems have a specific knowledge base, generally of rules, to enhance reusability across domains by separating procedural code and domain knowledge. A separate inference engine procedures guidelines and adds, deletes, or modifies a knowledge shop.
Forward chaining reasoning engines are the most common, and are seen in CLIPS and OPS5. Backward chaining happens in Prolog, where a more limited logical representation is used, Horn Clauses. Pattern-matching, specifically marriage, is utilized in Prolog.
A more flexible sort of problem-solving happens when reasoning about what to do next takes place, rather than just picking one of the readily available actions. This type of meta-level reasoning is utilized in Soar and in the BB1 chalkboard architecture.
Cognitive architectures such as ACT-R may have additional abilities, such as the capability to put together often utilized knowledge into higher-level pieces.
Commonsense reasoning
Marvin Minsky first proposed frames as a way of translating common visual scenarios, such as an office, and Roger Schank extended this concept to scripts for common regimens, such as dining out. Cyc has attempted to capture beneficial common-sense understanding and has “micro-theories” to handle particular type of domain-specific reasoning.
Qualitative simulation, such as Benjamin Kuipers’s QSIM, [90] estimates human thinking about naive physics, such as what takes place when we warm a liquid in a pot on the range. We expect it to heat and potentially boil over, although we may not understand its temperature level, its boiling point, or other details, such as climatic 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 resolved with constraint solvers.
Constraints and constraint-based reasoning
Constraint solvers carry out a more minimal type of inference than first-order reasoning. They can simplify sets of spatiotemporal restrictions, such as those for RCC or Temporal Algebra, along with resolving other type of puzzle problems, such as Wordle, Sudoku, cryptarithmetic issues, and so on. Constraint reasoning programs can be used to resolve scheduling problems, for example with constraint managing guidelines (CHR).
Automated planning
The General Problem Solver (GPS) cast preparation as problem-solving used means-ends analysis to create strategies. STRIPS took a various technique, viewing preparation as theorem proving. Graphplan takes a least-commitment approach to preparation, instead of sequentially selecting actions from an initial state, working forwards, or a goal state if working in reverse. Satplan is a method to preparing where a preparation problem is minimized to a Boolean satisfiability issue.
Natural language processing
Natural language processing focuses on treating language as data to perform tasks such as determining subjects without always comprehending the designated significance. Natural language understanding, on the other hand, constructs a significance representation and utilizes that for additional processing, such as responding to concerns.
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, however given that improved by deep learning methods. In symbolic AI, discourse representation theory and first-order logic have been used to represent sentence significances. Latent semantic analysis (LSA) and explicit semantic analysis likewise supplied vector representations of documents. In the latter case, vector parts are interpretable as principles named by Wikipedia articles.
New deep knowing methods based on Transformer models have now eclipsed these earlier symbolic AI approaches and obtained modern efficiency in natural language processing. However, Transformer designs are nontransparent and do not yet produce human-interpretable semantic representations for sentences and files. Instead, they produce task-specific vectors where the meaning of the vector elements is opaque.
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 book on artificial intelligence is organized to show agent architectures of increasing sophistication. [91] The sophistication of representatives differs from easy reactive representatives, to those with a model of the world and automated planning capabilities, potentially a BDI agent, i.e., one with beliefs, desires, and intents – or alternatively a support finding out design found out with time to pick actions – as much as a combination of alternative architectures, such as a neuro-symbolic architecture [87] that consists of deep learning for perception. [92]
In contrast, a multi-agent system includes multiple representatives that interact amongst themselves with some inter-agent interaction language such as Knowledge Query and Manipulation Language (KQML). The agents require not all have the very same internal architecture. Advantages of multi-agent systems consist of the capability to divide work amongst the agents and to increase fault tolerance when agents are lost. Research issues consist of how representatives reach agreement, distributed problem resolving, multi-agent learning, multi-agent planning, and dispersed restraint optimization.
Controversies occurred 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 turned down symbolic approaches-primarily connectionists-and those outside the field. Critiques from exterior of the field were primarily from philosophers, on intellectual grounds, but likewise from financing companies, particularly throughout the two AI winter seasons.
The Frame Problem: understanding representation difficulties for first-order reasoning
Limitations were discovered in using easy first-order logic to factor about dynamic domains. Problems were found both with concerns to mentioning the preconditions for an action to prosper and in offering 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 “proving that a person individual could enter discussion with another”, as an axiom asserting “if an individual has a telephone he still has it after searching for a number in the telephone directory” would be needed for the reduction to be successful. Similar axioms would be required for other domain actions to specify what did not alter.
A comparable problem, called the Qualification Problem, takes place in trying to specify the preconditions for an action to succeed. A limitless number of pathological conditions can be envisioned, e.g., a banana in a tailpipe might avoid a car from running properly.
McCarthy’s technique to repair the frame issue was circumscription, a kind of non-monotonic reasoning where deductions could be made from actions that require just specify what would change while not having to explicitly specify everything that would not alter. Other non-monotonic reasonings provided reality maintenance systems that revised beliefs causing contradictions.
Other ways of handling more open-ended domains included probabilistic thinking systems and machine knowing to discover brand-new ideas and rules. McCarthy’s Advice Taker can be considered as an inspiration here, as it might include new understanding supplied by a human in the kind of assertions or guidelines. For example, speculative symbolic maker finding out systems explored the ability to take high-level natural language advice and to translate it into domain-specific actionable guidelines.
Similar to the problems in managing vibrant domains, sensible thinking is likewise tough to capture in formal thinking. Examples of sensible reasoning include implicit thinking about how individuals believe or basic understanding of daily events, objects, and living creatures. This sort of knowledge is considered given and not considered as noteworthy. Common-sense reasoning is an open area of research and challenging both for symbolic systems (e.g., Cyc has attempted to record crucial parts of this understanding 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 bicycle).
McCarthy saw his Advice Taker as having common-sense, however his meaning of sensible was various than the one above. [94] He specified a program as having typical sense “if it immediately deduces for itself an adequately large class of immediate repercussions of anything it is informed and what it already knows. “
Connectionist AI: philosophical obstacles and sociological disputes
Connectionist approaches consist of earlier deal with neural networks, [95] such as perceptrons; operate in the mid to late 80s, such as Danny Hillis’s Connection Machine and Yann LeCun’s advances in convolutional neural networks; to today’s more innovative techniques, such as Transformers, GANs, and other operate in deep knowing.
Three philosophical positions [96] have been laid out amongst connectionists:
1. Implementationism-where connectionist architectures execute the capabilities for symbolic processing,
2. Radical connectionism-where symbolic processing is rejected completely, and connectionist architectures underlie intelligence and are fully adequate to describe it,
3. Moderate connectionism-where symbolic processing and connectionist architectures are seen as complementary and both are needed for intelligence
Olazaran, in his sociological history of the debates within the neural network community, described the moderate connectionism view as basically compatible with present research study 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 eclectic view of the present debate between connectionism and symbolic AI. One of the researchers who has actually 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, partially connectionist) systems. He declared that (a minimum of) two type of theories are required in order to study and model cognition. On the one hand, for some information-processing jobs (such as pattern recognition) connectionism has benefits over symbolic designs. But on the other hand, for other cognitive procedures (such as serial, deductive thinking, and generative sign manipulation procedures) the symbolic paradigm provides adequate models, and not only “approximations” (contrary to what extreme connectionists would claim). [97]
Gary Marcus has actually declared that the animus in the deep learning community versus symbolic approaches now may be more sociological than philosophical:
To think that we can just desert symbol-manipulation is to suspend disbelief.
And yet, for the many part, that’s how most present AI profits. Hinton and numerous others have striven to eliminate signs entirely. The deep learning hope-seemingly grounded not a lot in science, however in a sort of historical grudge-is that intelligent behavior will emerge purely from the confluence of huge information and deep learning. Where classical computer systems and software application fix tasks by defining sets of symbol-manipulating rules dedicated to specific tasks, such as modifying a line in a word processor or carrying out an estimation in a spreadsheet, neural networks usually try to solve jobs by analytical approximation and finding out from examples.
According to Marcus, Geoffrey Hinton and his coworkers have actually been vehemently “anti-symbolic”:
When deep learning reemerged in 2012, it was with a sort of take-no-prisoners mindset that has defined most of the last decade. By 2015, his hostility towards all things symbols had actually completely taken shape. He offered a talk at an AI workshop at Stanford comparing symbols to aether, among science’s biggest mistakes.
…
Since then, his anti-symbolic project has just increased in strength. In 2016, Yann LeCun, Bengio, and Hinton composed a manifesto for deep knowing in one of science’s most crucial journals, Nature. It closed with a direct attack on symbol adjustment, calling not for reconciliation but for outright replacement. Later, Hinton informed a gathering of European Union leaders that investing any further money in symbol-manipulating techniques was “a big error,” comparing it to buying internal combustion engines in the era of electric automobiles. [98]
Part of these disagreements might be because of unclear terminology:
Turing award winner Judea Pearl uses a review of machine learning which, regrettably, conflates the terms maker learning and deep knowing. Similarly, when Geoffrey Hinton refers to symbolic AI, the undertone of the term tends to be that of specialist systems dispossessed of any ability to find out. Using the terminology needs clarification. Artificial intelligence is not restricted to association rule mining, c.f. the body of work on symbolic ML and relational learning (the differences to deep knowing being the choice of representation, localist rational rather than dispersed, and the non-use of gradient-based learning algorithms). Equally, symbolic AI is not practically production guidelines written by hand. A correct meaning of AI issues understanding representation and reasoning, autonomous multi-agent systems, preparation and argumentation, in addition to learning. [99]
Situated robotics: the world as a design
Another critique of symbolic AI is the embodied cognition method:
The embodied cognition approach claims that it makes no sense to think about the brain independently: cognition takes location within a body, which is embedded in an environment. We need to study the system as a whole; the brain’s operating exploits consistencies in its environment, including the rest of its body. Under the embodied cognition method, robotics, vision, and other sensors become main, not peripheral. [100]
Rodney Brooks invented 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 dispersed, as not just unnecessary, but as damaging. Instead, he created the subsumption architecture, a layered architecture for embodied agents. Each layer attains a different purpose and must operate in the real world. For instance, the first robotic he explains in Intelligence Without Representation, has 3 layers. The bottom layer interprets finder sensors to prevent things. The middle layer triggers the robotic to roam around when there are no challenges. The top layer causes the robot to go to more far-off locations for further exploration. Each layer can momentarily hinder or reduce a lower-level layer. He criticized AI scientists for specifying AI issues for their systems, when: “There is no tidy division in between understanding (abstraction) and reasoning in the real world.” [101] He called his robotics “Creatures” and each layer was “made up of a fixed-topology network of easy finite state makers.” [102] In the Nouvelle AI method, “First, it is extremely important to evaluate the Creatures we integrate in the real life; i.e., in the exact same world that we human beings inhabit. It is devastating to fall under the temptation of testing them in a streamlined world first, even with the best intents of later transferring activity to an unsimplified world.” [103] His focus on real-world testing was in contrast to “Early work in AI focused on games, geometrical problems, symbolic algebra, theorem proving, and other official systems” [104] and using the blocks world in symbolic AI systems such as SHRDLU.
Current views
Each approach-symbolic, connectionist, and behavior-based-has benefits, however has actually been criticized by the other methods. Symbolic AI has actually been criticized as disembodied, responsible to the credentials problem, and bad in handling the affective problems where deep discovering excels. In turn, connectionist AI has actually been slammed as improperly fit for deliberative step-by-step problem fixing, integrating knowledge, and handling planning. Finally, Nouvelle AI masters reactive and real-world robotics domains but has actually been criticized for troubles in incorporating learning and knowledge.
Hybrid AIs integrating one or more of these techniques are currently considered 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 therefore impossible; we now see a lot of these same areas undergoing ongoing research and advancement resulting in increased ability, not impossibility. [100]
Expert system.
Automated preparation and scheduling
Automated theorem proving
Belief modification
Case-based reasoning
Cognitive architecture
Cognitive science
Connectionism
Constraint programs
Deep knowing
First-order logic
GOFAI
History of expert system
Inductive reasoning programs
Knowledge-based systems
Knowledge representation and thinking
Logic programming
Machine learning
Model checking
Model-based reasoning
Multi-agent system
Natural language processing
Neuro-symbolic AI
Ontology
Philosophy of expert system
Physical sign systems hypothesis
Semantic Web
Sequential pattern mining
Statistical relational knowing
Symbolic mathematics
YAGO ontology
WordNet
Notes
^ McCarthy once said: “This is AI, so we don’t care if it’s emotionally genuine”. [4] McCarthy reiterated his position in 2006 at the AI@50 conference where he stated “Expert system is not, by meaning, simulation of human intelligence”. [28] Pamela McCorduck composes that there are “2 major branches of expert system: one focused on producing smart behavior no matter how it was accomplished, and the other targeted at modeling intelligent procedures found in nature, particularly human ones.”, [29] Stuart Russell and Peter Norvig composed “Aeronautical engineering texts do not specify the goal of their field as making ‘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 expert system: representing items and relations”. Current Opinion in Behavioral Sciences. 29: 17-23. doi:10.1016/ j.cobeha.2018.12.010. hdl:10044/ 1/67796.
^ Thomason, Richmond (February 27, 2024). “Logic-Based Artificial Intelligence”. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
^ Garnelo, Marta; Shanahan, Murray (2019-10-01). “Reconciling deep knowing with 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 limits of knowledge”. Proceedings of the International Workshop on Expert System 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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^ Marcus 2020, p. 17.
^ a b Rossi 2022.
^ a b Selman 2022.
^ Garcez & Lamb 2020, p. 2.
^ Garcez et al. 2002.
^ Rocktäschel, Tim; Riedel, Sebastian (2016 ). “Learning Knowledge Base Inference with Neural Theorem Provers”. Proceedings of the 5th Workshop on Automated Knowledge Base Construction. San Diego, CA: Association for Computational Linguistics. pp. 45-50. doi:10.18653/ v1/W16 -1309. Retrieved 2022-08-06.
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